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authorKarl Berry <karl@freefriends.org>2009-07-22 23:04:33 +0000
committerKarl Berry <karl@freefriends.org>2009-07-22 23:04:33 +0000
commit11352d180cd2e149fbd69c6389f24bd32d175622 (patch)
treefef737d3ea5274146f21af634b605077626188a2 /Master/texmf-dist/doc
parent3828776db346b09b65a2b6a5b5e86a6168878fb3 (diff)
rm lnotes, renamed to latex-notes-zh-cn
git-svn-id: svn://tug.org/texlive/trunk@14381 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc')
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/README71
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/history.txt33
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/license.txt71
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/lnotes.pdfbin799369 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/basics.tex490
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/dscf4684.jpgbin51402 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/arrow.mps39
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/color.mps21
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/colors.mps46
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/curve.mps73
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/dashed.mps24
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/dot.mps33
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/fill.mps31
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/label.mps45
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/line.mps21
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/loop.mps35
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/path.mps21
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/predefined.mps50
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_arc.eps1654
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_arrow.eps1657
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_axis.eps1828
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_bezier.eps1644
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_circle.eps1645
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_color.eps1653
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_curve.eps1667
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_dot.eps1647
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_fill.eps1661
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_frame.eps1644
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_grid.eps1649
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_label.eps1752
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_line.eps1646
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_linestyle.eps1653
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_origin.eps1644
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_parabola.eps1644
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_polygon.eps1646
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_rput.eps1649
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/pst_uput.eps1752
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/subfig.mps34
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/subfig_left.mps18
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/subfig_right.mps18
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/transform.mps25
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/examples/uline.mps15
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/fonts.tex183
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/graphics.tex1256
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/i18n.tex73
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/introduction.tex111
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/lnotes.tex296
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/math.tex350
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/misc.tex322
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/postcript.tex9
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/preface.tex31
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/reading.bib914
-rw-r--r--Master/texmf-dist/doc/generic/lnotes/src/tables.tex345
53 files changed, 0 insertions, 36839 deletions
diff --git a/Master/texmf-dist/doc/generic/lnotes/README b/Master/texmf-dist/doc/generic/lnotes/README
deleted file mode 100644
index 39f3a08c626..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/README
+++ /dev/null
@@ -1,71 +0,0 @@
-LaTeX Notes
-
-This Chinese document is an introduction to TeX/LaTeX. It covers basic text
-typesetting, math, graphics, table, Chinese language & fonts, and some
-miscellaneous features (hyperlink, long document, bibliography, index, page
-layout).
-
-This package contains five major files: readme.txt, history.txt, license.txt,
-lnotes.dvi, lnotes.pdf, and the following source files,
-
-src
-│ basics.tex
-│ dscf4684.jpg
-│ fonts.tex
-│ graphics.tex
-│ i18n.tex
-│ introduction.tex
-│ lnotes.tex
-│ math.tex
-│ misc.tex
-│ postcript.tex
-│ preface.tex
-│ reading.bib
-│ tables.tex
-│
-└─examples
- arrow.mps
- color.mps
- colors.mps
- curve.mps
- dashed.mps
- dot.mps
- fill.mps
- label.mps
- line.mps
- loop.mps
- path.mps
- predefined.mps
- pst_arc.eps
- pst_arrow.eps
- pst_axis.eps
- pst_bezier.eps
- pst_circle.eps
- pst_color.eps
- pst_curve.eps
- pst_dot.eps
- pst_fill.eps
- pst_frame.eps
- pst_grid.eps
- pst_label.eps
- pst_line.eps
- pst_linestyle.eps
- pst_origin.eps
- pst_parabola.eps
- pst_polygon.eps
- pst_rput.eps
- pst_uput.eps
- subfig.mps
- subfig_left.mps
- subfig_right.mps
- transform.mps
- uline.mps
-
-The source files are encoded in UTF-8.
-
-This readme is in English because CTAN websites support only ASCII readmes.
-
-Any comments are welcome. I could be accessed at TeX board of smth.org or by email.
-
-Alpha Huang
-huang.xingang@gmail.com \ No newline at end of file
diff --git a/Master/texmf-dist/doc/generic/lnotes/history.txt b/Master/texmf-dist/doc/generic/lnotes/history.txt
deleted file mode 100644
index 7a93ea4acbe..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/history.txt
+++ /dev/null
@@ -1,33 +0,0 @@
-原文链接:
-http://www.dralpha.com/chs/tech/lnotes.pdf
-http://www.dralpha.com/chs/tech/lnotes_src.zip
-
-感谢各位同学的帮助和支持,群众的眼睛是贼亮的:)
-
-无以为报,只好为每位同学的意见增加一个版本号。
-
-v1.20 2008/07/26
-- 更正了29、30页两处multline的拼写错误。感谢贾朋。
-- 20页表2.5中ex更正为“当前字体中字母x的高度”。感谢张晓南。
-- 92页的得隆望蜀更正为得陇望蜀。感谢Kov Chai。
-- 序中DreamWeaver更正为Dreamweaver,第4页RedHat更正为Red Hat,Unbuntu更正为Ubuntu;第2页和跋中的象字更正为像;33页Shakespear更正为Shakespeare;80页的编字更正为遍。感谢hkkhhk。
-- 第二章中对齐方式术语统一改为居左、居中、居右、居顶、居底;90页表8.1中的Times Roman更正为Times;跋中挥手改为挥衣袖,家里有本徐志摩诗集,基本没看过。感谢yakun@smth.org。
-- 跋加到了目录中,以前漏掉了一个\backmatter。
-- 43页MetaPost版本号更新为1.005。感谢Xubuntu@smth.org。
-- 去掉了58页多余的一个句号。感谢tex@smth.org。
-- 去掉了27页表3.3中重复的\ddot;28页两处分割改为分隔;补上了29页漏掉的对齐两字;42页gnulot更正为gnuplot。再次感谢IMB@smth.org。
-- 关于披阅和批阅,当代多用批阅,但是我手头的《红楼梦》庚辰本和程乙本用的都是披阅,故不更改。感谢yyzz11@smth.org。
-- 插图和字体两章中Bezier的翻译更正为贝塞尔。感谢careworn@smth.org。
-- 第二章和第六章中cross-reference的翻译改为交叉引用;20页小节标题和23页脚注中英文单词之间加入空格;43页MetaPost版本号更新为1.004;更正了80页图6.2的标题;跋中采用了XeTeX和LuaTeX的logo。感谢LittleLeo@smth.org。
-- 86页脚注中张林波的单位更正为计算数学所。感谢yli@smth.org。
-- 更正了78页图6.1的标题。感谢meteorrain@smth.org。
-- 去掉了94页多余的\verb。感谢snoopyzhao@smth.org。
-- 24页两个\sigma中后一个更正为\varsigma;87页一脚注加了句号。感谢primenumber@smth.org。
-- 更正了9页脚注中Fuchs的名字;11页去掉一个重复的“用”字。感谢IMB@smth.org。
-- 去掉了35页\latex的反斜杠。感谢PiscesGold@smth.org。
-- 去掉了c70usong.fd中utf8hei的\CJKbold,黑体原本不该再加粗。感谢PaladinHL@smth.org。
-
-v1.0 2008/05/15
-- 大约花了两个半月。
-- 感谢jjgod@smth.org的“kpsewhich cid-x.map”。
-- 感谢Langpku@smth.org的“initexmf --edit-config-file=dvipdfmx”。 \ No newline at end of file
diff --git a/Master/texmf-dist/doc/generic/lnotes/license.txt b/Master/texmf-dist/doc/generic/lnotes/license.txt
deleted file mode 100644
index 896bdc07953..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/license.txt
+++ /dev/null
@@ -1,71 +0,0 @@
-%% LaTeX Notes
-%% Copyright 2008 Alpha Huang
-%
-% This work may be distributed and/or modified under the
-% conditions of the LaTeX Project Public License, either version 1.3
-% of this license or (at your option) any later version.
-% The latest version of this license is in
-% http://www.latex-project.org/lppl.txt
-% and version 1.3 or later is part of all distributions of LaTeX
-% version 2005/12/01 or later.
-%
-% This work has the LPPL maintenance status `maintained'.
-%
-% The Current Maintainer of this work is Alpha Huang.
-%
-% This work contains five major files: readme.txt, history.txt, license.txt,
-% lnotes.dvi, lnotes.pdf, and the following source files,
-%
-% src
-% │ basics.tex
-% │ dscf4684.jpg
-% │ fonts.tex
-% │ graphics.tex
-% │ i18n.tex
-% │ introduction.tex
-% │ lnotes.tex
-% │ math.tex
-% │ misc.tex
-% │ postcript.tex
-% │ preface.tex
-% │ reading.bib
-% │ tables.tex
-% │
-% └─examples
-% arrow.mps
-% color.mps
-% colors.mps
-% curve.mps
-% dashed.mps
-% dot.mps
-% fill.mps
-% label.mps
-% line.mps
-% loop.mps
-% path.mps
-% predefined.mps
-% pst_arc.eps
-% pst_arrow.eps
-% pst_axis.eps
-% pst_bezier.eps
-% pst_circle.eps
-% pst_color.eps
-% pst_curve.eps
-% pst_dot.eps
-% pst_fill.eps
-% pst_frame.eps
-% pst_grid.eps
-% pst_label.eps
-% pst_line.eps
-% pst_linestyle.eps
-% pst_origin.eps
-% pst_parabola.eps
-% pst_polygon.eps
-% pst_rput.eps
-% pst_uput.eps
-% subfig.mps
-% subfig_left.mps
-% subfig_right.mps
-% transform.mps
-% uline.mps
-% \ No newline at end of file
diff --git a/Master/texmf-dist/doc/generic/lnotes/lnotes.pdf b/Master/texmf-dist/doc/generic/lnotes/lnotes.pdf
deleted file mode 100644
index bbbf24edc94..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/lnotes.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/basics.tex b/Master/texmf-dist/doc/generic/lnotes/src/basics.tex
deleted file mode 100644
index 29367ddcbca..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/basics.tex
+++ /dev/null
@@ -1,490 +0,0 @@
-\chapter{入门}
-
-\section{Hello, World!}
-\label{sec:hello_world}
-把下面例子用编辑器保存为~\verb|hello_world.tex|,这就是一个最简单的~\LaTeX~源文件。
-
-\begin{code}
-%hello_world.tex
-\documentclass{article}
-\begin{document}
- Hello, World!
-\end{document}
-\end{code}
-
-有了源文件,我们可以在命令行把它编译成~DVI~文件(DVI~格式见\ref{sec:dvi}小节)。此命令知道输入的是~\LaTeX~源文件,所以这里的~\verb|.tex|~后缀可以省略。以后的示例中可以省略的后缀都用~\verb|()|~标出,不再特别声明。
-\begin{code}
-latex hello_world(.tex)
-\end{code}
-
-如果系统显示类似下面的错误信息,请检查源文件是否有拼写错误。\verb|.log|~文件里有更详细的编译信息。
-\begin{code}
-! LaTeX Error:
-...
-! Emergency stop.
-...
-No pages of output.
-Transcript written on hello_world.log.
-\end{code}
-
-如果编译成功,系统会报出类似下面的信息:
-\begin{code}
-Output written on hello_world.dvi (1 page, 232 bytes).
-Transcript written on hello_world.log.
-\end{code}
-
-每种~\LaTeX~发行包附带不同的~DVI~浏览器,比如~MiKTeX~的是~yap。
-\begin{code}
-yap hello_world(.dvi)
-\end{code}
-
-\section{格式及其转换}
-\subsection{页面描述语言}
-\label{sec:pdl}
-页面描述语言(Page Description Language,PDL)是一种在较高层次上描述实际输出结果的语言。本文只讨论其中三种与~\LaTeX~紧密相关的格式:DVI、PostScript、PDF。
-
-\subsubsection{PostScript}
-最早的打印机只用于打印字符,它使用的硬字符与打字机类似。后来出现的点阵(dot matrix)打字机用一系列的点来“画”出字符,当然它也可以画出图形。当时矢量图的打印只能由绘图仪(plotter)来完成。
-
-1976~年,施乐(Xerox)推出了首台激光打印机,它结合了点阵打印机和绘图仪的优点,可以同时打印高质量的图形和文字。
-
-同一时期,John Warnock~也在酝酿一种类似于~Forth~的图形设计语言,也就是后来的~PostScript(PS),当时他正在旧金山一家电脑图形公司~Evans \& Sutherland~工作。1978~年老板想让~Warnock~搬到位于犹他州的总部,他不想搬家就跳槽到了施乐。
-
-Warnock~和~Martin Newell~开发了新的图形系统~JaM(John and Martin),它后来被合并到施乐的打印机驱动程序~InterPress~中去。这两位还开发过另一个系统~MaJ。
-
-1982~年,Warnock~和施乐研究中心图形实验室主任~Chuck Geschke~一起离开施乐,成立了~Adobe~公司。Newell~后来也加入了~Adobe。
-
-1984~年~Adobe~发布~PS~后不久,Steve Jobs~跑来参观,并建议用它来驱动激光打印机。次年,武装着~PS~驱动的~Apple LaserWriter~横空出世,打响了~80~年代中期桌面出版革命的第一枪。
-
-90~年代中后期,廉价喷墨打印机的流行使得~PS~逐渐式微,因为~PS~驱动对它们毕竟是一个成本负担。
-
-\subsubsection{PDF}
-1993~年,Adobe~推出了一种开放的格式:Portable Document Format(PDF),它于~2007~年成为~ISO 32000~标准。除了开放,PDF~比起~PS~还有一些其它优势:
-\begin{itemize}
- \item PDF~基本上是~PS~的一个子集,因此更轻便。
- \item PDF~可以嵌入更先进的字体,具体见\ref{sec:font}节。
- \item PDF~支持嵌入乱七八糟的东东,比如动画。
- \item PDF~支持透明图形。
-\end{itemize}
-
-PDF~虽然拥有上述优势,起初它的推广却并不顺利,因为其读写工具~Acrobat~太贵。Adobe~很快推出了免费的~Acrobat Reader(后更名为~Adobe Reader),并不断改进~PDF,终于使它超越了曾经的事实标准~PS,成为网络时代电子文档的新标准。
-
-\subsubsection{DVI}
-\label{sec:dvi}
-Knuth~最初设计的~\TeX~只能用于~XGP~打印机,这台打印机本身还需要一台~PDP-6~主机为它服务。1979~年,David Fuchs\footnote{Fuchs~本科毕业于普林斯顿,1978~年进入斯坦福攻读博士学位。他不是~Knuth~的学生,但是完成过一些~\TeX~的开发任务。他在~Adobe~工作过一段时间,现在混入了娱乐圈,担任过电影《Red Diaper Baby》和《Haiku Tunnel》的制片人。}提出把~\TeX~的输出改为设备无关的格式,也就是~Device Independent format(DVI)。
-
-DVI~只是一种中间格式,用户还需要另外的处理程序(driver)把它转换为其它格式,比如~PS~或~PDF~,甚至~PNG、SVG~等。DVI~不能嵌入字体和图形,PS~和~PDF~可以选择是否嵌入字体。
-
-\subsubsection{Ghostscript}
-\label{sec:ghostscript}
-PS~输出时需要一个解释器(Raster Image Processor,RIP)来把它转换为点阵图形。RIP~可以是软件,也可以是固件(firmware)或硬件\footnote{固件~RIP~在打印机内置处理器上运行,硬件~RIP~常见于高端打印设备。}。
-
-Ghostscript~是一个基于~RIP~的软件包,除了~RIP~它还有一些其它功能,比如处理~EPS,把~PS~转换为~PDF~等。Ghostscript~已经被移植到~Windows、Unix/Linux、Mac OS~等多种操作系统,和它匹配的前端图形用户界面(GUI)有\href{http://pages.cs.wisc.edu/~ghost/}{GSview、Ghostview、gv}等。
-
-\subsection{格式转换}
-\label{sec:convert_format}
-DVI、PS、PDF~等格式的的转换关系如\Fref{fig:convert_format}所示。
-
-\begin{figure}[htbp]
-\centering
-\begin{tikzpicture}
- \node[box] (tex) {.tex};
- \node[box] (dvi) [right=5 of tex] {.dvi};
- \node[box] (pdf) [right=6 of dvi] {.pdf};
- \node[box] (ps) [above=3 of pdf] {.ps};
- \path (tex) edge [arrow] node[auto] {latex} (dvi)
- (dvi) edge [arrow] node[auto] {dvipdfm} (pdf)
- (dvi.north) [arrow,draw] to node[above,sloped] {dvips} (ps.west)
- (ps) edge [arrow] node[right] {ps2pdf} (pdf)
- (tex) edge [arrow,bloop] (pdf);
- \node [below=.7 of dvi] {pdflatex};
-\end{tikzpicture}
-\caption{格式转换}
-\label{fig:convert_format}
-\end{figure}
-
-最早的~driver~是~\verb|dvips|,它把~DVI~转换为~PS。\verb|dvipdf|~把~DVI~转为~PDF,它后来被~\verb|dvipdfm|~所取代;\verb|dvipdfm|~主要用于处理单字节字符,1999~年之后停止开发;在~\verb|dvipdfm|~基础上发展来的~\verb|dvipdfmx|~可以处理多字节编码(字符编码详见\ref{sec:encoding}节)。
-
-pdf\TeX~是一种特殊的driver,它跳过~DVI,直接用~\TeX~源文件生成~PDF。基于~pdf\TeX~的~pdf\LaTeX~则把\LaTeX~源文件转为~PDF。
-
-包老师倾向于~\verb|dvipdfmx|,因为它对图形格式的兼容性较好,而且擅长处理中文。
-
-得到~DVI~后,我们可以在控制台用以下命令把它转为~PDF。
-\begin{code}
-dvipdfm hello_world(.dvi)
-\end{code}
-
-我们也可以把它转为~PS,接着用~Ghostscript~的一个命令行程序把它转换为~PDF,注意第二个命令需要~\verb|.ps|~后缀。一般情况下不推荐这种方法,因为它多了个步骤。
-\begin{code}
-dvips hello_world(.dvi)
-ps2pdf hello_world.ps
-\end{code}
-
-pdf\LaTeX~用法如下。
-\begin{code}
-pdflatex hello_world(.tex)
-\end{code}
-
-\section{\LaTeX~语句}
-\LaTeX~源文件的每一行称作一条语句(statement),语句可以分三种:命令(command)、数据(data)和注释(comment)。
-
-命令分为两种:普通命令和环境(environment)。普通命令以\verb|\|~起始,大多只有一行;而环境包含一对起始声明和结尾声明,用于多行的场合。命令和环境可以互相嵌套。
-
-数据就是普通内容。注释语句以~\verb|%|~起始,它在编译过程中被忽略。
-
-例如在\ref{sec:hello_world}节例1中,第一行是注释,第二行是普通命令;第三、五行是环境的起始和结尾声明;第四行是数据。
-
-\section{文档结构}
-\subsection{文档类、序言、正文}
-\LaTeX~源文件的结构分三大部分,依次为:文档类声明、序言(可选)、正文。
-
-文档类声明用来指定文档的类型;序言(preamble)用来完成一些特殊任务,比如引入宏包,定义命令,设置环境等;文档的实际内容则放在正文部分。这里的正文指得是\verb|\begin{document}|和\verb|\end|~\verb|{document}|之间的部分,和通常人们心目中的“正文”概念有所出入。
-
-这三部分的基本语法如下:
-\begin{code}
-\documentclass[options]{class} %文档类声明
-\usepackage[options]{package} %引入宏包
-...
-\begin{document} %正文
-...
-\end{document}
-\end{code}
-
-常用的文档类(documentclass)有三种:\verb|article、report、book|,它们的常用选项见\fref{tab:class_options}。
-
-\begin{table}[htbp]
-\centering
-\caption{文档类常用选项}
-\label{tab:class_options}
-\begin{tabularx}{350pt}{lX}
- \toprule
- 10pt, 11pt, 12pt & 正文字号,缺省10pt。\LaTeX~会根据正文字号选择标题、上下标等的字号。\\
- letterpaper, a4paper & 纸张尺寸,缺省是~letter。\\
- notitlepage, titlepage & 标题后是否另起新页。article~缺省~notitlepage,report~和~book~缺省有~titlepage。\\
- onecolumn, twocolumn & 栏数,缺省单栏。\\
- oneside, twoside & 单面双面。article~和~report~缺省单面,book~缺省双面。\\
- landscape & 打印方向横向,缺省纵向。\\
- openany, openright & 此选项只用于~report~和~book。report~缺省~openany~,book~缺省~openright。\\
- draft & 草稿模式。有时某些行排得过满,draft~模式可以在它们右边标上粗黑线提醒用户。\\
- \bottomrule
-\end{tabularx}
-\end{table}
-
-\LaTeX~的核心只提供基本的功能,系统以宏包(package)的形式提供附加功能或增强原有功能。其它一些编程语言也有类似的模块化机制,比如~C/C++~的~\verb|#include|,Java~的~\verb|import|。
-
-\subsection{标题、摘要、章节}
-
-
-一份文档正文部分的开头通常有标题、作者、摘要等信息,之后是章节等层次结构,内容则散布于层次结构之间。
-
-标题、作者、日期等命令如下,注意\verb|\maketitle|~命令要放在最后。
-\begin{code}
-\title{标题}
-\author{作者}
-\today
-\maketitle
-\end{code}
-
-摘要环境用法如下:
-\begin{code}
-\begin{abstract}
-...
-\end{abstract}
-\end{code}
-
-常用的层次结构命令如下,
-\begin{code}
-\chapter{...}
-\section{...}
-\subsection{...}
-\subsubsection{...}
-\end{code}
-
-每个高级层次可以包含若干低级层次。\verb|article|~中没有~\verb|chapter|,而~\verb|report|~和~\verb|book|~则支持上面所有层次。
-
-\subsection{目录}
-
-我们可以用~\verb|\tableofcontents|~命令来生成整个文档的目录,\LaTeX~会自动设定目录包含的章节层次,也可以用~\verb|\setcounter|~命令来指定目录层次深度。
-\begin{code}
-\tableofcontents
-\setcounter{tocdepth}{2}
-\end{code}
-
-如果不想让某个章节标题出现在目录中,可以使用以下带~\verb|*|~的命令来声明章节。
-\begin{code}
-\chapter*{...}
-\section*{...}
-\subsection*{...}
-\end{code}
-
-类似地,我们也可以用以下命令生成插图和表格的目录,插图和表格功能将在后面章节中介绍。
-
-\begin{code}
-\listoffigures
-\listoftables
-\end{code}
-
-当章节或图表等结构发生变化时,我们需要执行两遍编译命令以获得正确结果。\LaTeX~之所以设计成这样可能是因为当时的电脑内存容量有限。
-
-\section{文字排版}
-\subsection{字符输入}
-文档中可以输入的内容大致可以分为:普通字符、控制符、特殊符号、注音符号、预定义字符串等。而这些内容有两种输入模式:文本模式(缺省)和数学模式,普通的行间(inline)数学模式用\verb|\$...\$|来表示。
-
-\LaTeX~中有些字符(例如~\verb|# $ % ^ & _ { } ~ \|~等)被用作特殊的控制符,所以不能直接输入,多数需要在前面加个~\verb|\|。而~\verb|\|~本身则要用~\verb|\textbackslash|~命令来输入,因为~\verb|\\|~被用作了换行指令。很奇怪为什么不用~C~语言的~\verb|\n|,也许是因为~\TeX~的编程语言是~Pascal。
-
-\begin{code}
-\# \$ \% \^{} \& \_ \{ \} \~{} \textbackslash
-\end{code}
-
-\Fref{tab:symbol}~提供了一些符号的输入方法示例,完整的符号列表见~Scott Pakin的《The Comprehensive \LaTeX~ Symbol List》\citep{Pakin_2008}。
-
-\begin{table}[htbp]
-\centering
-\caption{一些符号和预定义字符串}
-\label{tab:symbol}
-\begin{tabular}{llllll}
- \toprule
- \multicolumn{2}{c}{特殊符号} & \multicolumn{2}{c}{注音符号} &
- \multicolumn{2}{c}{预定义字符串} \\
- \cmidrule(lr){1-2} \cmidrule(lr){3-4} \cmidrule(lr){5-6}
- \textcopyright & \verb|\textcopyright| & \aa & \verb|\aa| &
- \today & \verb|\today| \\
- \textregistered & \verb|\textregistered| & \AA & \verb|\AA| &
- \TeX & \verb|\TeX| \\
- $^\circ$C & \verb|$^\circ$C| & \ae & \verb|\ae| &
- \LaTeX & \verb|\LaTeX| \\
- \textyen & \verb|\textyen| & \o & \verb|\o| &
- \LaTeXe & \verb|\LaTeXe| \\
- \pounds & \verb|\pounds| & \"o & \verb|\"o| &
- \MF & \verb|\MF| \\
- \texteuro & \verb|\texteuro| & \^o & \verb|\^o| &
- \MP & \verb|\MP| \\
- \dots & \verb|\dots| & \~o & \verb|\~o| & \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\subsection{换行、换页、断字}
-通常~\LaTeX~会自动换行、换页。用户也可以用~\verb|\\|~或~\verb|\newline|~来强制换行;用~\verb|\newpage|~来强制换页。
-
-一般情况下~\LaTeX~会尽量均匀地断字(Hyphenate),使得每一行的字间距分布整齐。但有时我们也需要显式指明断字位置,比如下例就指明~BASIC~这个词不能断开,而~blar-blar-blar~可以在-处断开。
-\begin{code}
-\hyphenation{BASIC blar-blar-blar}
-\end{code}
-
-\subsection{字样、字号}
-
-\LaTeX~会自动调整正文、标题、章节、上下标、脚注等的字样\footnote{关于字样详见\ref{sec:typeface}节}、字号。我们也可以用\fref{tab:typeface_command}中的命令来设置字样;用\fref{tab:fontsize_command}中的命令来设置相对字号,比如正文字号是~10pt、11pt、12pt~时,tiny的字号就分别是~5pt、6pt、6pt。
-
-\LaTeX~有一个特别的字样强调命令:\verb|\emph|,它在不同字样和装饰环境下有不同效果。比如周围文字是正体,它就是斜体;反之它就是正体。
-
-\begin{table}[hbtp]
-\centering
-\caption{字样命令}
-\label{tab:typeface_command}
-\begin{tabular}{llll}
- \toprule
- \verb|\textrm{...}| & \textrm{roman} &
- \verb|\textbf{...}| & \textbf{bold face} \\
- \verb|\textsf{...}| & \textsf{sans serif} &
- \verb|\textit{...}| & \textit{italic} \\
- \verb|\texttt{...}| & \texttt{typewriter} &
- \verb|\textsl{...}| & \textsl{slanted} \\
- \\
- \verb|\emph{...}| & \emph{emphasized} &
- \verb|\underline{...}| & \underline{underline} \\
- \verb|\textsc{...}| & \textsc{Small Caps} & & \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\begin{table}[htbp]
-\centering
-\caption{字号命令}
-\label{tab:fontsize_command}
-\begin{tabular}{llll}
- \toprule
- & \multicolumn{3}{c}{正文字号} \\
- \cmidrule(lr){2-4}
- 命令 & 10pt & 11pt & 12pt \\
- \midrule
- \verb|\tiny| & 5pt & 6pt & 6pt \\
- \verb|\scriptsize| & 7pt & 8pt & 8pt \\
- \verb|\footnotesize| & 8pt & 9pt & 10pt \\
- \verb|\small| & 9pt & 10pt & 11pt \\
- \verb|\normalsize| & 10pt & 11pt & 12pt \\
- \verb|\large| & 12pt & 12pt & 14pt \\
- \verb|\Large| & 14pt & 14pt & 17pt \\
- \verb|\LARGE| & 17pt & 17pt & 20pt \\
- \verb|\huge| & 20pt & 20pt & 25pt \\
- \verb|\Huge| & 25pt & 25pt & 25pt \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{常用命令环境}
-\subsection{列表}
-
-\LaTeX~中有三种列表环境:\verb|itemize、enumerate、description|,它们的一般用法如下:
-
-\begin{demo}
-\begin{itemize}
- \item C++
- \item Java
- \item HTML
-\end{itemize}
-\end{demo}
-
-\begin{demo}
-\begin{enumerate}
- \item C++
- \item Java
- \item HTML
-\end{enumerate}
-\end{demo}
-
-\begin{demo}
-\begin{description}
- \item{C++} 一种编程语言
- \item{Java} 另一种编程语言
- \item{HTML} 一种标记语言
-\end{description}
-\end{demo}
-
-\subsection{对齐}
-\LaTeX~中的段落缺省两端对齐(fully justified),我们也可以让段落居左、居右或居中对齐。
-
-\begin{demo}
-\begin{flushleft}
-本段落\\
-居左
-\end{flushleft}
-\end{demo}
-
-\begin{demo}
-\begin{flushright}
-本段落\\
-居右
-\end{flushright}
-\end{demo}
-
-\begin{demo}
-\begin{center}
-本段落\\
-居中
-\end{center}
-\end{demo}
-
-\subsection{摘录}
-\LaTeX~中有三种摘录环境:\verb|quote、quotation、verse|。\verb|quote|~两端都缩进,\verb|quotation|~在~\verb|quote|~的基础上增加了首行缩进,\verb|verse|~比~\verb|quote|~多了第二行起的缩进。
-
-\begin{demo}
-正文
-\begin{quote}
-引文两端都缩进。
-\end{quote}
-正文
-\end{demo}
-
-\begin{demo}
-正文
-\begin{quotation}
-引文两端缩进,首行缩进。
-\end{quotation}
-正文
-\end{demo}
-
-\begin{demo}
-正文
-\begin{verse}
-引文两端缩进,第二行起缩进。
-\end{verse}
-正文
-\end{demo}
-
-\subsection{原文照排}
-一般文档中,命令和源代码通常使用等宽字样来表示,也就是原文照排。对此~\LaTeX~提供了~\verb|\verb|~命令(一般用于在正文中插入较短的命令)和~\verb|verbatim|~环境。后者有带~\verb|*|~的版本用来标明空格。
-
-\begin{demo}
-正文中插入\verb|command|
-\begin{verbatim}
-printf("Hello, world!");
-\end{verbatim}
-\begin{verbatim*}
-printf("Hello, world!");
-\end{verbatim*}
-\end{demo}
-
-\subsection{交叉引用}
-我们常常需要引用文档中~\verb|section、subsection、figure、table|~等对象的编号,这种功能叫作交叉引用(cross referencing)。
-
-\LaTeX~中可以用~\verb|\label{marker}|~命令来定义一个标记,标记名可以是任意字符串,但是在全文中须保持唯一。之后可以用~\verb|\ref{marker}|~命令来引用标记处章节或图表的编号,用~\verb|\pageref{marker}|~来引用标记处的页码。
-
-\begin{demo}
-被引用处\label{sec}\\
-...\\
-第\pageref{sec}页\ref{sec}节
-\end{demo}
-
-文档中新增交叉引用后,第一次执行~\verb|latex|~或~\verb|pdflatex|~编译命令时会得到类似下面的警告信息。因为第一次编译只会扫描出有交叉引用的地方,第二次编译才能得到正确结果。
-
-\begin{code}
-LaTeX Warning: There were undefined references.
-...
-LaTeX Warning: Label(s) may have changed. Rerun to get cross-
-references right.
-\end{code}
-
-\subsection{脚注}
-脚注(footnote)的一般用法如下:
-\begin{demo}
-这里是一段正文。\footnote{这里是一段脚注。}
-\end{demo}
-
-\section{长度单位}
-\LaTeX~中的常用长度单位如\Fref{tab:unit}~所示。point~是个传统印刷业采用的单位,而~big point~是~Adobe~推出~PS~时新定义的单位。em~是个相对单位,比如当前字体是~11pt~时,1em~就是~11pt。
-\begin{table}[htbp]
-\caption{常用长度单位}
-\label{tab:unit}
-\centering
-\begin{tabular}{llllll}
- \toprule
- in & 英寸 & pt & point, 1/72.27 in & em & 当前字体中字母M的宽度 \\
- cm & 厘米 & bp & big point, 1/72 in & ex & 当前字体中字母x的高度 \\
- mm & 毫米 & pc & pica, 12 pt & mu & math unit,1/18 em \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{盒子}
-\LaTeX~在排版时把每个对象(小到一个字母,大到一个段落)都视为一个矩形盒子(box),我们在~HTML~和~CSS~中也可以见到类似的模型。
-
-\subsection{mbox~和~fbox}
-
-\LaTeX~中最简单的盒子是~\verb|\mbox|~和~\verb|\fbox|。前者把一组对象组合起来,后者在此基础上加了个边框。
-\begin{demo}
-\mbox{010 6278 5001}
-\fbox{010 6278 5001}
-\end{demo}
-
-\subsection{makebox~和~framebox}
-稍复杂的~\verb|\makebox|~和~\verb|\framebox|~提供了宽度和对齐方式控制选项。这里用~l、r、s~分别代表居左、居右和分散对齐。
-\begin{demo}
-%语法:[宽度][对齐方式]{内容}
-\makebox[100pt][l]{居左}
-\framebox[100pt][r]{居右}
-\end{demo}
-
-\subsection{parbox~和~minipage}
-大一些的对象比如整个段落可以用~\verb|\parbox|~命令和~\verb|\minipage|~环境,两者语法类似,也提供了对齐方式和宽度的选项。但是这里的对齐方式是指与周围内容的纵向关系,用~t、c、b~分别代表居顶、居中和居底对齐。
-
-\begin{demo}
-%语法:[对齐方式]{宽度}{内容}
-\parbox[c]{90pt}{锦瑟无端五十弦,\\一弦一柱思华年。}李商隐
-\end{demo}
-
-细心的读者会发现~\verb|\parbox|~和~\verb|\minipage|~的选项排列顺序和~\verb|\makebox|~和~\verb~\framebox|~的不一致,可能出自不同的作者。
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/dscf4684.jpg b/Master/texmf-dist/doc/generic/lnotes/src/dscf4684.jpg
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index 7aa8b8630ea..00000000000
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diff --git a/Master/texmf-dist/doc/generic/lnotes/src/examples/color.mps b/Master/texmf-dist/doc/generic/lnotes/src/examples/color.mps
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-%!PS
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-%!PS
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-grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
-imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
-exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
-fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
-delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
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-rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
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-%%BeginProcSet: pstricks.pro 0 0
-% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $
-%
-% PostScript prologue for pstricks.tex.
-% Version 1.03, 2008/01/01
-% For distribution and copyright, see pstricks.tex.
-%
-%
-systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
-systemdict /.setblendmode known not {/.setblendmode { pop } def } if
-systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
-%
-/tx@Dict 200 dict def tx@Dict begin
-/ADict 25 dict def
-/CM { matrix currentmatrix } bind def
-/SLW /setlinewidth load def
-/CLW /currentlinewidth load def
-/CP /currentpoint load def
-/ED { exch def } bind def
-/L /lineto load def
-/T /translate load def
-/TMatrix { } def
-/RAngle { 0 } def
-/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments
-/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
-/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
-/Div { dup 0 eq { pop } { div } ifelse } def % control the division
-/tan { dup cos abs 1.e-10 lt
- { pop 1.e10 } % return 1.e10 as infinit
- { dup sin exch cos div } ifelse % default sin/cos
-} def
-/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
-/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
- pop pop 0 }{ sqrt exch atan} ifelse } def
-/NET { neg exch neg exch T } def % change coordinate system to the negative one
-/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
-/Pyth2 { % Pythagoras, xA yA xB yB
- 3 -1 roll % xA xB yB yA
- sub % xA xB yB-yA
- 3 1 roll % yB-yA xA xB
- sub % yB-yA xA-xB
- Pyth } def
-/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
-%----------------- hv added 20050516 ---------------
-/PiDiv2 1.57079632680 def
-/Pi 3.14159265359 def
-/TwoPi 6.28318530718 def
-/Euler 2.71828182846 def
-%/e Euler bind def
-/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
-/DegtoRad { Pi mul 180 div } bind def % viceversa
-%----------------- hv end---------------------------
-/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
-/PathLength { flattenpath /z 0 def
- { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
- }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
- /pathforall load stopped { pop pop pop pop } if z } def
-/STP { .996264 dup scale } def
-/STV { SDict begin normalscale end STP } def
-%
-%%-------------- DG begin patch 15 ---------------%%
-%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
-%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
-%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
-%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
-%0 } ifelse setdash stroke } def
-/DashLine {
- dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
- /b ED /x1 ED /y1 ED /x ED /y ED
- /z y x add y1 add x1 add def
- /Coef b a .5 sub 2 mul y mul sub z Div round
- z mul a .5 sub 2 mul y mul add b exch Div def
- /y y Coef mul def
- /x x Coef mul def
- /y1 y1 Coef mul def
- /x1 x1 Coef mul def
- x1 0 gt y1 0 gt or x 0 gt or y 0 gt and
- { [ y x y1 x1 ] 1 a sub y mul }
- { [ 1 0 ] 0 } ifelse
- setdash stroke
-} def
-%%-------------- DG end patch 15 ---------------%%
-/DotLine {
- /b PathLength def
- /a ED /z ED /y CLW def
- /z y z add def
- a 0 gt {
- /b b a div def
- }{
- a 0 eq {
- /b b y sub def
- }{ a -3 eq {
- /b b y add def } if
- } ifelse
- } ifelse
- [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
- a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
- setdash 1 setlinecap stroke
-} def
-%
-/LineFill { % hv ------------ patch 7 -------------
- gsave
- abs /hatchWidthInc ED
- abs /hatchSepInc ED
- abs CLW add /a ED
- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
- idtransform pop /a ED
- .25 .25 itransform pathbbox
- /y2 ED
- a Div ceiling cvi /x2 ED /y1 ED
- a Div cvi /x1 ED /y2 y2 y1 sub def
- clip
- newpath
- 2 setlinecap
- systemdict
- /setstrokeadjust known { true setstrokeadjust } if
- x2 x1 sub 1 add {
- x1 a mul y1 moveto 0 y2 rlineto stroke
- /x1 x1 1 add
- hatchWidthInc 0 gt { CLW add } if
- def
- hatchSepInc 0 gt hatchWidthInc 0 gt or {
- /a a hatchSepInc add def
- CLW hatchWidthInc add SLW
- } if
- } repeat
- grestore
- pop pop } def
-%
-%gsave abs CLW add /a ED a 0 dtransform round exch round exch
-%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
-%% DG/SR modification begin - Dec. 12, 1997 - Patch 2
-%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%% DG/SR modification end
-%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
-%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
-%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-%% def
-%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-%pop pop } def
-%% DG/SR modification end
-%
-/BeginArrow { ADict begin
- /@mtrx CM def
- gsave
- 2 copy T
- 2 index sub neg exch
- 3 index sub exch Atan
- rotate newpath
-} def
-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
-} def
-%
-/Bracket {
- CLW mul add dup CLW sub 2 div
- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
- x neg CLW 2 div L x CLW 2 div L x y L stroke
- 0 CLW moveto
-} def
-%
-/RoundBracket {
- CLW mul add dup 2 div
- /x ED mul /y ED /mtrx CM def
- 0 CLW 2 div T x y mul 0 ne { x y scale } if
- 1 1 moveto
- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
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-%% PostScript prologue for pstricks.tex.
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-%% For distribution, see pstricks.tex.
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-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
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- { gsave c i a cvs dup stringwidth pop
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- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
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- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
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-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
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- 8 index StrConcat AddClPar
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- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
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- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
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- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
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- PreCommonFunc
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- PreCommonFunc
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
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- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
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-%% Add open parenthesis in string at the given index
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-%% Add open parenthesis in string at the given index
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
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-% DG modification begin - Jan. 15, 1997
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-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
-/ch { dup Ex exch neg Ex add 2 div } def
-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
-/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
-end
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-dots.pro 0 0
-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
-%% to add /Diamond, /SolidDiamond and /BoldDiamond
-%
-10 dict dup begin
- /FontType 3 def
- /FontMatrix [.001 0 0 .001 0 0] def
- /FontBBox [-571.5 -742.5 571.5 742.5] def
-% /FontBBox [-1000 -1000 1000 1000] def
-% See end of file in /BuildGlyph
- /Encoding 256 array def
- 0 1 255 {Encoding exch/.notdef put} for
- Encoding
- dup (b) 0 get /Bullet put
- dup (c) 0 get /Circle put
- dup (C) 0 get /BoldCircle put
- dup (u) 0 get /SolidTriangle put
- dup (t) 0 get /Triangle put
- dup (T) 0 get /BoldTriangle put
- dup (r) 0 get /SolidSquare put
- dup (s) 0 get /Square put
- dup (S) 0 get /BoldSquare put
- dup (q) 0 get /SolidPentagon put
- dup (p) 0 get /Pentagon put
- dup (P) 0 get /BoldPentagon put
-%%%
- dup (k) 0 get /Asterisk put
- dup (K) 0 get /BoldAsterisk put
- dup (J) 0 get /SolidAsterisk put
- dup (h) 0 get /Hexagon put
- dup (H) 0 get /BoldHexagon put
- dup (G) 0 get /SolidHexagon put
- dup (a) 0 get /Add put
- dup (A) 0 get /BoldAdd put
- dup (x) 0 get /Mul put
- dup (X) 0 get /BoldMul put
- dup (m) 0 get /Oplus put
- dup (M) 0 get /BOplus put
- dup (e) 0 get /SolidOplus put
- dup (n) 0 get /Otimes put
- dup (N) 0 get /BOtimes put
- dup (E) 0 get /SolidOtimes put
- dup (i) 0 get /Bar put
- dup (I) 0 get /BoldBar put
- dup (l) 0 get /SolidDiamond put
- dup (d) 0 get /Diamond put
- (D) 0 get /BoldDiamond put
-%%%
-/CharProcs 47 dict def
- CharProcs begin
- /CirclePath {0 0 500 0 360 arc closepath} def
- /Bullet {CirclePath fill} def
- /Circle {CirclePath .9 .9 scale CirclePath eofill} def
- /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
- /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto
- closepath} def
- /SolidTriangle {TrianglePath fill} def
- /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
- /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
- /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto
- closepath} def
- /SolidSquare {SquarePath fill} def
- /Square {SquarePath .89 .89 scale SquarePath eofill} def
- /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
- /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
- 0 574.7 lineto -546.6 177.6 lineto closepath} def
- /SolidPentagon {PentagonPath fill} def
- /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
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-%-------------- hv begin 2004/07/25 from: er 2003/03/24
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deleted file mode 100644
index 0d27094bf3d..00000000000
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- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
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- { StrConcat }
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- { StrConcat }
- { StrConcat
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- 5 index dup dup (2) eq exch (2.0) eq or
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- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
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- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
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-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
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-/EvalFunc_Derive {%
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
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- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
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- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
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- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
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- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
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-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
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-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
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-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
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-%-------------- hv begin 2004/07/25 from: er 2003/03/24
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- .775 .775 scale BoldCrossPath fill} def
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- closepath} def
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- /SolidDiamond {DiamondPath fill} def
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- /h d a sin Div h add def
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- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
-/ch { dup Ex exch neg Ex add 2 div } def
-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
-/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
-end
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-dots.pro 0 0
-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
-%% to add /Diamond, /SolidDiamond and /BoldDiamond
-%
-10 dict dup begin
- /FontType 3 def
- /FontMatrix [.001 0 0 .001 0 0] def
- /FontBBox [-571.5 -742.5 571.5 742.5] def
-% /FontBBox [-1000 -1000 1000 1000] def
-% See end of file in /BuildGlyph
- /Encoding 256 array def
- 0 1 255 {Encoding exch/.notdef put} for
- Encoding
- dup (b) 0 get /Bullet put
- dup (c) 0 get /Circle put
- dup (C) 0 get /BoldCircle put
- dup (u) 0 get /SolidTriangle put
- dup (t) 0 get /Triangle put
- dup (T) 0 get /BoldTriangle put
- dup (r) 0 get /SolidSquare put
- dup (s) 0 get /Square put
- dup (S) 0 get /BoldSquare put
- dup (q) 0 get /SolidPentagon put
- dup (p) 0 get /Pentagon put
- dup (P) 0 get /BoldPentagon put
-%%%
- dup (k) 0 get /Asterisk put
- dup (K) 0 get /BoldAsterisk put
- dup (J) 0 get /SolidAsterisk put
- dup (h) 0 get /Hexagon put
- dup (H) 0 get /BoldHexagon put
- dup (G) 0 get /SolidHexagon put
- dup (a) 0 get /Add put
- dup (A) 0 get /BoldAdd put
- dup (x) 0 get /Mul put
- dup (X) 0 get /BoldMul put
- dup (m) 0 get /Oplus put
- dup (M) 0 get /BOplus put
- dup (e) 0 get /SolidOplus put
- dup (n) 0 get /Otimes put
- dup (N) 0 get /BOtimes put
- dup (E) 0 get /SolidOtimes put
- dup (i) 0 get /Bar put
- dup (I) 0 get /BoldBar put
- dup (l) 0 get /SolidDiamond put
- dup (d) 0 get /Diamond put
- (D) 0 get /BoldDiamond put
-%%%
-/CharProcs 47 dict def
- CharProcs begin
- /CirclePath {0 0 500 0 360 arc closepath} def
- /Bullet {CirclePath fill} def
- /Circle {CirclePath .9 .9 scale CirclePath eofill} def
- /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
- /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto
- closepath} def
- /SolidTriangle {TrianglePath fill} def
- /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
- /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
- /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto
- closepath} def
- /SolidSquare {SquarePath fill} def
- /Square {SquarePath .89 .89 scale SquarePath eofill} def
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- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
- idtransform pop /a ED
- .25 .25 itransform pathbbox
- /y2 ED
- a Div ceiling cvi /x2 ED /y1 ED
- a Div cvi /x1 ED /y2 y2 y1 sub def
- clip
- newpath
- 2 setlinecap
- systemdict
- /setstrokeadjust known { true setstrokeadjust } if
- x2 x1 sub 1 add {
- x1 a mul y1 moveto 0 y2 rlineto stroke
- /x1 x1 1 add
- hatchWidthInc 0 gt { CLW add } if
- def
- hatchSepInc 0 gt hatchWidthInc 0 gt or {
- /a a hatchSepInc add def
- CLW hatchWidthInc add SLW
- } if
- } repeat
- grestore
- pop pop } def
-%
-%gsave abs CLW add /a ED a 0 dtransform round exch round exch
-%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
-%% DG/SR modification begin - Dec. 12, 1997 - Patch 2
-%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%% DG/SR modification end
-%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
-%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
-%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-%% def
-%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-%pop pop } def
-%% DG/SR modification end
-%
-/BeginArrow { ADict begin
- /@mtrx CM def
- gsave
- 2 copy T
- 2 index sub neg exch
- 3 index sub exch Atan
- rotate newpath
-} def
-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
-} def
-%
-/Bracket {
- CLW mul add dup CLW sub 2 div
- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
- x neg CLW 2 div L x CLW 2 div L x y L stroke
- 0 CLW moveto
-} def
-%
-/RoundBracket {
- CLW mul add dup 2 div
- /x ED mul /y ED /mtrx CM def
- 0 CLW 2 div T x y mul 0 ne { x y scale } if
- 1 1 moveto
- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
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-% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $
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-% PostScript prologue for pstricks.tex.
-% Version 1.03, 2008/01/01
-% For distribution and copyright, see pstricks.tex.
-%
-%
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-/L /lineto load def
-/T /translate load def
-/TMatrix { } def
-/RAngle { 0 } def
-/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments
-/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
-/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
-/Div { dup 0 eq { pop } { div } ifelse } def % control the division
-/tan { dup cos abs 1.e-10 lt
- { pop 1.e10 } % return 1.e10 as infinit
- { dup sin exch cos div } ifelse % default sin/cos
-} def
-/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
-/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
- pop pop 0 }{ sqrt exch atan} ifelse } def
-/NET { neg exch neg exch T } def % change coordinate system to the negative one
-/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
-/Pyth2 { % Pythagoras, xA yA xB yB
- 3 -1 roll % xA xB yB yA
- sub % xA xB yB-yA
- 3 1 roll % yB-yA xA xB
- sub % yB-yA xA-xB
- Pyth } def
-/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
-%----------------- hv added 20050516 ---------------
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-/Pi 3.14159265359 def
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-/Euler 2.71828182846 def
-%/e Euler bind def
-/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
-/DegtoRad { Pi mul 180 div } bind def % viceversa
-%----------------- hv end---------------------------
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-/PathLength { flattenpath /z 0 def
- { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
- }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
- /pathforall load stopped { pop pop pop pop } if z } def
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-%
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- /y y Coef mul def
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- }{
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- }{ a -3 eq {
- /b b y add def } if
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- [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
- a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
- setdash 1 setlinecap stroke
-} def
-%
-/LineFill { % hv ------------ patch 7 -------------
- gsave
- abs /hatchWidthInc ED
- abs /hatchSepInc ED
- abs CLW add /a ED
- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
- idtransform pop /a ED
- .25 .25 itransform pathbbox
- /y2 ED
- a Div ceiling cvi /x2 ED /y1 ED
- a Div cvi /x1 ED /y2 y2 y1 sub def
- clip
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- def
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- /a a hatchSepInc add def
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-%
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-%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-%% def
-%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-%pop pop } def
-%% DG/SR modification end
-%
-/BeginArrow { ADict begin
- /@mtrx CM def
- gsave
- 2 copy T
- 2 index sub neg exch
- 3 index sub exch Atan
- rotate newpath
-} def
-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
-} def
-%
-/Bracket {
- CLW mul add dup CLW sub 2 div
- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
- x neg CLW 2 div L x CLW 2 div L x y L stroke
- 0 CLW moveto
-} def
-%
-/RoundBracket {
- CLW mul add dup 2 div
- /x ED mul /y ED /mtrx CM def
- 0 CLW 2 div T x y mul 0 ne { x y scale } if
- 1 1 moveto
- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
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-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
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-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
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-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
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-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
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-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
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- /i x1 def
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- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
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- dup t f moveto
- g t L stroke
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- } repeat
- grestore
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- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
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- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
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- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
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- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
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-%
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- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
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- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
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-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
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-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
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-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
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-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
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-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
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-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
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- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
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- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
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- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
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- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
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-/th { dup sh exch ch div } def
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-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
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-
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
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- /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
-%-------------- hv begin 2004/07/25 from: er 2003/03/24
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- 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
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- .775 .775 scale BoldCrossPath fill} def
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- 45 rotate .775 .775 scale BoldCrossPath fill } def
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- closepath} def
- /Bar {BarPath fill} def
- /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto
- closepath} def
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- /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
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- /SolidDiamond {DiamondPath fill} def
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index 042963eba2b..00000000000
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- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
-/ch { dup Ex exch neg Ex add 2 div } def
-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
-/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
-end
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-dots.pro 0 0
-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
-%% to add /Diamond, /SolidDiamond and /BoldDiamond
-%
-10 dict dup begin
- /FontType 3 def
- /FontMatrix [.001 0 0 .001 0 0] def
- /FontBBox [-571.5 -742.5 571.5 742.5] def
-% /FontBBox [-1000 -1000 1000 1000] def
-% See end of file in /BuildGlyph
- /Encoding 256 array def
- 0 1 255 {Encoding exch/.notdef put} for
- Encoding
- dup (b) 0 get /Bullet put
- dup (c) 0 get /Circle put
- dup (C) 0 get /BoldCircle put
- dup (u) 0 get /SolidTriangle put
- dup (t) 0 get /Triangle put
- dup (T) 0 get /BoldTriangle put
- dup (r) 0 get /SolidSquare put
- dup (s) 0 get /Square put
- dup (S) 0 get /BoldSquare put
- dup (q) 0 get /SolidPentagon put
- dup (p) 0 get /Pentagon put
- dup (P) 0 get /BoldPentagon put
-%%%
- dup (k) 0 get /Asterisk put
- dup (K) 0 get /BoldAsterisk put
- dup (J) 0 get /SolidAsterisk put
- dup (h) 0 get /Hexagon put
- dup (H) 0 get /BoldHexagon put
- dup (G) 0 get /SolidHexagon put
- dup (a) 0 get /Add put
- dup (A) 0 get /BoldAdd put
- dup (x) 0 get /Mul put
- dup (X) 0 get /BoldMul put
- dup (m) 0 get /Oplus put
- dup (M) 0 get /BOplus put
- dup (e) 0 get /SolidOplus put
- dup (n) 0 get /Otimes put
- dup (N) 0 get /BOtimes put
- dup (E) 0 get /SolidOtimes put
- dup (i) 0 get /Bar put
- dup (I) 0 get /BoldBar put
- dup (l) 0 get /SolidDiamond put
- dup (d) 0 get /Diamond put
- (D) 0 get /BoldDiamond put
-%%%
-/CharProcs 47 dict def
- CharProcs begin
- /CirclePath {0 0 500 0 360 arc closepath} def
- /Bullet {CirclePath fill} def
- /Circle {CirclePath .9 .9 scale CirclePath eofill} def
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-%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
-%0 } ifelse setdash stroke } def
-/DashLine {
- dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
- /b ED /x1 ED /y1 ED /x ED /y ED
- /z y x add y1 add x1 add def
- /Coef b a .5 sub 2 mul y mul sub z Div round
- z mul a .5 sub 2 mul y mul add b exch Div def
- /y y Coef mul def
- /x x Coef mul def
- /y1 y1 Coef mul def
- /x1 x1 Coef mul def
- x1 0 gt y1 0 gt or x 0 gt or y 0 gt and
- { [ y x y1 x1 ] 1 a sub y mul }
- { [ 1 0 ] 0 } ifelse
- setdash stroke
-} def
-%%-------------- DG end patch 15 ---------------%%
-/DotLine {
- /b PathLength def
- /a ED /z ED /y CLW def
- /z y z add def
- a 0 gt {
- /b b a div def
- }{
- a 0 eq {
- /b b y sub def
- }{ a -3 eq {
- /b b y add def } if
- } ifelse
- } ifelse
- [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
- a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
- setdash 1 setlinecap stroke
-} def
-%
-/LineFill { % hv ------------ patch 7 -------------
- gsave
- abs /hatchWidthInc ED
- abs /hatchSepInc ED
- abs CLW add /a ED
- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
- idtransform pop /a ED
- .25 .25 itransform pathbbox
- /y2 ED
- a Div ceiling cvi /x2 ED /y1 ED
- a Div cvi /x1 ED /y2 y2 y1 sub def
- clip
- newpath
- 2 setlinecap
- systemdict
- /setstrokeadjust known { true setstrokeadjust } if
- x2 x1 sub 1 add {
- x1 a mul y1 moveto 0 y2 rlineto stroke
- /x1 x1 1 add
- hatchWidthInc 0 gt { CLW add } if
- def
- hatchSepInc 0 gt hatchWidthInc 0 gt or {
- /a a hatchSepInc add def
- CLW hatchWidthInc add SLW
- } if
- } repeat
- grestore
- pop pop } def
-%
-%gsave abs CLW add /a ED a 0 dtransform round exch round exch
-%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
-%% DG/SR modification begin - Dec. 12, 1997 - Patch 2
-%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%% DG/SR modification end
-%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
-%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
-%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-%% def
-%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-%pop pop } def
-%% DG/SR modification end
-%
-/BeginArrow { ADict begin
- /@mtrx CM def
- gsave
- 2 copy T
- 2 index sub neg exch
- 3 index sub exch Atan
- rotate newpath
-} def
-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
-} def
-%
-/Bracket {
- CLW mul add dup CLW sub 2 div
- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
- x neg CLW 2 div L x CLW 2 div L x y L stroke
- 0 CLW moveto
-} def
-%
-/RoundBracket {
- CLW mul add dup 2 div
- /x ED mul /y ED /mtrx CM def
- 0 CLW 2 div T x y mul 0 ne { x y scale } if
- 1 1 moveto
- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
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-% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $
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-% For distribution and copyright, see pstricks.tex.
-%
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-/Div { dup 0 eq { pop } { div } ifelse } def % control the division
-/tan { dup cos abs 1.e-10 lt
- { pop 1.e10 } % return 1.e10 as infinit
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-/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
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- 3 1 roll % yB-yA xA xB
- sub % yB-yA xA-xB
- Pyth } def
-/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
-%----------------- hv added 20050516 ---------------
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-/DegtoRad { Pi mul 180 div } bind def % viceversa
-%----------------- hv end---------------------------
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- setdash 1 setlinecap stroke
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-%
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- gsave
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- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
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-%% def
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- gsave
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- rotate newpath
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-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
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-%
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- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
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- 0 CLW moveto
-} def
-%
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- CLW mul add dup 2 div
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- 0 CLW 2 div T x y mul 0 ne { x y scale } if
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- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
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- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
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- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
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-/Line {
- NArray n 0 eq not
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- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
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- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
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-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
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-def
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-/NC { CC x1 y1 x2 y2 x y curveto } def
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-/OpenCurve {
- NArray n 3 lt
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-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
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-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
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-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
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-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
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-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
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-%
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- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
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-% /Helvetica findfont b scalefont setfont
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- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
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- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
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-%
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- gsave
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- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
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-%
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-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
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- 4 2 roll 4 index (1) ne
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
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- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
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- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
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- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
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- } if
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-%% Add open parenthesis in string at the given index
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
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- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
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- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
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- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
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- %% read the increment value
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- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
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- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
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-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
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-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
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-%%%
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- /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
-%-------------- hv begin 2004/07/25 from: er 2003/03/24
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- -180 500 -10 250 -20 0 curveto closepath} def
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- 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
- fill} def
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- .775 .775 scale BoldCrossPath fill} def
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- 45 rotate .775 .775 scale CrossPath fill} def
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- 45 rotate .775 .775 scale BoldCrossPath fill } def
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- closepath} def
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-/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
-/Div { dup 0 eq { pop } { div } ifelse } def % control the division
-/tan { dup cos abs 1.e-10 lt
- { pop 1.e10 } % return 1.e10 as infinit
- { dup sin exch cos div } ifelse % default sin/cos
-} def
-/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
-/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
- pop pop 0 }{ sqrt exch atan} ifelse } def
-/NET { neg exch neg exch T } def % change coordinate system to the negative one
-/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
-/Pyth2 { % Pythagoras, xA yA xB yB
- 3 -1 roll % xA xB yB yA
- sub % xA xB yB-yA
- 3 1 roll % yB-yA xA xB
- sub % yB-yA xA-xB
- Pyth } def
-/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
-%----------------- hv added 20050516 ---------------
-/PiDiv2 1.57079632680 def
-/Pi 3.14159265359 def
-/TwoPi 6.28318530718 def
-/Euler 2.71828182846 def
-%/e Euler bind def
-/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
-/DegtoRad { Pi mul 180 div } bind def % viceversa
-%----------------- hv end---------------------------
-/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
-/PathLength { flattenpath /z 0 def
- { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
- }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
- /pathforall load stopped { pop pop pop pop } if z } def
-/STP { .996264 dup scale } def
-/STV { SDict begin normalscale end STP } def
-%
-%%-------------- DG begin patch 15 ---------------%%
-%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
-%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
-%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
-%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
-%0 } ifelse setdash stroke } def
-/DashLine {
- dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
- /b ED /x1 ED /y1 ED /x ED /y ED
- /z y x add y1 add x1 add def
- /Coef b a .5 sub 2 mul y mul sub z Div round
- z mul a .5 sub 2 mul y mul add b exch Div def
- /y y Coef mul def
- /x x Coef mul def
- /y1 y1 Coef mul def
- /x1 x1 Coef mul def
- x1 0 gt y1 0 gt or x 0 gt or y 0 gt and
- { [ y x y1 x1 ] 1 a sub y mul }
- { [ 1 0 ] 0 } ifelse
- setdash stroke
-} def
-%%-------------- DG end patch 15 ---------------%%
-/DotLine {
- /b PathLength def
- /a ED /z ED /y CLW def
- /z y z add def
- a 0 gt {
- /b b a div def
- }{
- a 0 eq {
- /b b y sub def
- }{ a -3 eq {
- /b b y add def } if
- } ifelse
- } ifelse
- [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
- a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
- setdash 1 setlinecap stroke
-} def
-%
-/LineFill { % hv ------------ patch 7 -------------
- gsave
- abs /hatchWidthInc ED
- abs /hatchSepInc ED
- abs CLW add /a ED
- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
- idtransform pop /a ED
- .25 .25 itransform pathbbox
- /y2 ED
- a Div ceiling cvi /x2 ED /y1 ED
- a Div cvi /x1 ED /y2 y2 y1 sub def
- clip
- newpath
- 2 setlinecap
- systemdict
- /setstrokeadjust known { true setstrokeadjust } if
- x2 x1 sub 1 add {
- x1 a mul y1 moveto 0 y2 rlineto stroke
- /x1 x1 1 add
- hatchWidthInc 0 gt { CLW add } if
- def
- hatchSepInc 0 gt hatchWidthInc 0 gt or {
- /a a hatchSepInc add def
- CLW hatchWidthInc add SLW
- } if
- } repeat
- grestore
- pop pop } def
-%
-%gsave abs CLW add /a ED a 0 dtransform round exch round exch
-%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
-%% DG/SR modification begin - Dec. 12, 1997 - Patch 2
-%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%% DG/SR modification end
-%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
-%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
-%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-%% def
-%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-%pop pop } def
-%% DG/SR modification end
-%
-/BeginArrow { ADict begin
- /@mtrx CM def
- gsave
- 2 copy T
- 2 index sub neg exch
- 3 index sub exch Atan
- rotate newpath
-} def
-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
-} def
-%
-/Bracket {
- CLW mul add dup CLW sub 2 div
- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
- x neg CLW 2 div L x CLW 2 div L x y L stroke
- 0 CLW moveto
-} def
-%
-/RoundBracket {
- CLW mul add dup 2 div
- /x ED mul /y ED /mtrx CM def
- 0 CLW 2 div T x y mul 0 ne { x y scale } if
- 1 1 moveto
- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
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diff --git a/Master/texmf-dist/doc/generic/lnotes/src/examples/pst_linestyle.eps b/Master/texmf-dist/doc/generic/lnotes/src/examples/pst_linestyle.eps
deleted file mode 100644
index 4d2597ccf33..00000000000
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+++ /dev/null
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
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- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
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- PreCommonFunc
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
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-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
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-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
-/ch { dup Ex exch neg Ex add 2 div } def
-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
-/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
-end
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-dots.pro 0 0
-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
-%% to add /Diamond, /SolidDiamond and /BoldDiamond
-%
-10 dict dup begin
- /FontType 3 def
- /FontMatrix [.001 0 0 .001 0 0] def
- /FontBBox [-571.5 -742.5 571.5 742.5] def
-% /FontBBox [-1000 -1000 1000 1000] def
-% See end of file in /BuildGlyph
- /Encoding 256 array def
- 0 1 255 {Encoding exch/.notdef put} for
- Encoding
- dup (b) 0 get /Bullet put
- dup (c) 0 get /Circle put
- dup (C) 0 get /BoldCircle put
- dup (u) 0 get /SolidTriangle put
- dup (t) 0 get /Triangle put
- dup (T) 0 get /BoldTriangle put
- dup (r) 0 get /SolidSquare put
- dup (s) 0 get /Square put
- dup (S) 0 get /BoldSquare put
- dup (q) 0 get /SolidPentagon put
- dup (p) 0 get /Pentagon put
- dup (P) 0 get /BoldPentagon put
-%%%
- dup (k) 0 get /Asterisk put
- dup (K) 0 get /BoldAsterisk put
- dup (J) 0 get /SolidAsterisk put
- dup (h) 0 get /Hexagon put
- dup (H) 0 get /BoldHexagon put
- dup (G) 0 get /SolidHexagon put
- dup (a) 0 get /Add put
- dup (A) 0 get /BoldAdd put
- dup (x) 0 get /Mul put
- dup (X) 0 get /BoldMul put
- dup (m) 0 get /Oplus put
- dup (M) 0 get /BOplus put
- dup (e) 0 get /SolidOplus put
- dup (n) 0 get /Otimes put
- dup (N) 0 get /BOtimes put
- dup (E) 0 get /SolidOtimes put
- dup (i) 0 get /Bar put
- dup (I) 0 get /BoldBar put
- dup (l) 0 get /SolidDiamond put
- dup (d) 0 get /Diamond put
- (D) 0 get /BoldDiamond put
-%%%
-/CharProcs 47 dict def
- CharProcs begin
- /CirclePath {0 0 500 0 360 arc closepath} def
- /Bullet {CirclePath fill} def
- /Circle {CirclePath .9 .9 scale CirclePath eofill} def
- /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
- /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto
- closepath} def
- /SolidTriangle {TrianglePath fill} def
- /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
- /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
- /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto
- closepath} def
- /SolidSquare {SquarePath fill} def
- /Square {SquarePath .89 .89 scale SquarePath eofill} def
- /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
- /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
- 0 574.7 lineto -546.6 177.6 lineto closepath} def
- /SolidPentagon {PentagonPath fill} def
- /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
- /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
-%-------------- hv begin 2004/07/25 from: er 2003/03/24
- /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto
- 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def
- /SolidHexagon {HexagonPath fill} def
- /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
- /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
- /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto
- -180 500 -10 250 -20 0 curveto closepath} def
- /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
- 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
- fill} def
- /Basterp {50 250 220 500 0 500 curveto
- -220 500 -50 250 -50 30 cos 100 mul curveto} def
- /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp
- 60 rotate Basterp 60 rotate Basterp
- 60 rotate Basterp 60 rotate Basterp
- 60 rotate Basterp closepath} def
- /BoldAsterisk {BoldAsteriskPath fill} def
- /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
- /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
- -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
- 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def
- /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
- -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
- 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def
- /Add {CrossPath fill} def
- /Mul {45 rotate CrossPath fill} def
- /BoldAdd {BoldCrossPath fill} def
- /BoldMul {45 rotate BoldCrossPath fill} def
- /Oplus {CirclePath .9 .9 scale CirclePath eofill
- .775 .775 scale CrossPath fill} def
- /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
- /BOplus {CirclePath .8 .8 scale CirclePath eofill
- .775 .775 scale BoldCrossPath fill} def
- /Otimes {CirclePath .9 .9 scale CirclePath eofill
- 45 rotate .775 .775 scale CrossPath fill} def
- /BOtimes {CirclePath .8 .8 scale CirclePath eofill
- 45 rotate .775 .775 scale BoldCrossPath fill } def
- /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
- /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto
- closepath} def
- /Bar {BarPath fill} def
- /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto
- closepath} def
- /BoldBar {BoldBarPath fill} def
- /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
- 428.5 0 lineto closepath} def
- /SolidDiamond {DiamondPath fill} def
- /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
- /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
-%%%
- /.notdef { } def
- end
- /BuildGlyph {
- exch
- begin
-% Metrics 1 index get exec 0
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-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
-/ch { dup Ex exch neg Ex add 2 div } def
-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
-/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
-end
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-dots.pro 0 0
-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
-%% to add /Diamond, /SolidDiamond and /BoldDiamond
-%
-10 dict dup begin
- /FontType 3 def
- /FontMatrix [.001 0 0 .001 0 0] def
- /FontBBox [-571.5 -742.5 571.5 742.5] def
-% /FontBBox [-1000 -1000 1000 1000] def
-% See end of file in /BuildGlyph
- /Encoding 256 array def
- 0 1 255 {Encoding exch/.notdef put} for
- Encoding
- dup (b) 0 get /Bullet put
- dup (c) 0 get /Circle put
- dup (C) 0 get /BoldCircle put
- dup (u) 0 get /SolidTriangle put
- dup (t) 0 get /Triangle put
- dup (T) 0 get /BoldTriangle put
- dup (r) 0 get /SolidSquare put
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- }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
- /pathforall load stopped { pop pop pop pop } if z } def
-/STP { .996264 dup scale } def
-/STV { SDict begin normalscale end STP } def
-%
-%%-------------- DG begin patch 15 ---------------%%
-%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
-%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
-%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
-%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
-%0 } ifelse setdash stroke } def
-/DashLine {
- dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
- /b ED /x1 ED /y1 ED /x ED /y ED
- /z y x add y1 add x1 add def
- /Coef b a .5 sub 2 mul y mul sub z Div round
- z mul a .5 sub 2 mul y mul add b exch Div def
- /y y Coef mul def
- /x x Coef mul def
- /y1 y1 Coef mul def
- /x1 x1 Coef mul def
- x1 0 gt y1 0 gt or x 0 gt or y 0 gt and
- { [ y x y1 x1 ] 1 a sub y mul }
- { [ 1 0 ] 0 } ifelse
- setdash stroke
-} def
-%%-------------- DG end patch 15 ---------------%%
-/DotLine {
- /b PathLength def
- /a ED /z ED /y CLW def
- /z y z add def
- a 0 gt {
- /b b a div def
- }{
- a 0 eq {
- /b b y sub def
- }{ a -3 eq {
- /b b y add def } if
- } ifelse
- } ifelse
- [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
- a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
- setdash 1 setlinecap stroke
-} def
-%
-/LineFill { % hv ------------ patch 7 -------------
- gsave
- abs /hatchWidthInc ED
- abs /hatchSepInc ED
- abs CLW add /a ED
- a 0 dtransform round exch round exch
- 2 copy idtransform
- exch Atan rotate
- idtransform pop /a ED
- .25 .25 itransform pathbbox
- /y2 ED
- a Div ceiling cvi /x2 ED /y1 ED
- a Div cvi /x1 ED /y2 y2 y1 sub def
- clip
- newpath
- 2 setlinecap
- systemdict
- /setstrokeadjust known { true setstrokeadjust } if
- x2 x1 sub 1 add {
- x1 a mul y1 moveto 0 y2 rlineto stroke
- /x1 x1 1 add
- hatchWidthInc 0 gt { CLW add } if
- def
- hatchSepInc 0 gt hatchWidthInc 0 gt or {
- /a a hatchSepInc add def
- CLW hatchWidthInc add SLW
- } if
- } repeat
- grestore
- pop pop } def
-%
-%gsave abs CLW add /a ED a 0 dtransform round exch round exch
-%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
-%% DG/SR modification begin - Dec. 12, 1997 - Patch 2
-%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-%% DG/SR modification end
-%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
-%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
-%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-%% def
-%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-%pop pop } def
-%% DG/SR modification end
-%
-/BeginArrow { ADict begin
- /@mtrx CM def
- gsave
- 2 copy T
- 2 index sub neg exch
- 3 index sub exch Atan
- rotate newpath
-} def
-%
-/EndArrow { @mtrx setmatrix CP grestore end } def
-%
-/Arrow {
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /a ED
- { 0 h T 1 -1 scale } if
- w neg h moveto
- 0 0 L w h L w neg a neg rlineto
- gsave fill grestore
-} def
-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
- 2 div /w ED
- mul dup /h ED
- mul /Inset ED
- { 0 h T 1 -1 scale } if % changes the direction
-% we use y=w/h^2 * x^2 as equation for the control points
-% for the coordinates the arrow is seen from top to bottom
-% the bottom (tip) is (0;0)
- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
- w 9 div neg h 3 div
- 0 0 curveto % tip of >
- w 9 div h 3 div
- w 9 div 4 mul h 3 div 2 mul
- w h curveto % upper left of >
- w neg Inset neg rlineto % move to x=0 and inset
- gsave fill grestore
-} def
-%
-/Tbar {
- CLW mul add /z ED
- z -2 div CLW 2 div moveto
- z 0 rlineto stroke
- 0 CLW moveto
-} def
-%
-/Bracket {
- CLW mul add dup CLW sub 2 div
- /x ED mul CLW add /y ED /z CLW 2 div def
- x neg y moveto
- x neg CLW 2 div L x CLW 2 div L x y L stroke
- 0 CLW moveto
-} def
-%
-/RoundBracket {
- CLW mul add dup 2 div
- /x ED mul /y ED /mtrx CM def
- 0 CLW 2 div T x y mul 0 ne { x y scale } if
- 1 1 moveto
- .85 .5 .35 0 0 0 curveto
- -.35 0 -.85 .5 -1 1 curveto
- mtrx setmatrix stroke 0 CLW moveto
-} def
-%
-/SD { 0 360 arc fill } def
-%
-/EndDot { % DS is the dot size
- { /z DS def } { /z 0 def } ifelse
- /b ED 0 z DS SD b { 0 z DS CLW sub SD } if
- 0 DS z add CLW 4 div sub moveto } def
-%
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
- /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
- load } if ] cvx newpath 3 1 roll T exec } def
-%
-%/NArray {
-% aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-% cvi def
-%} def
-%
-/NArray { % holds the coordinates and on top of stack the showpoints boolean
- /showpoints ED
- counttomark 2 div dup cvi /n ED
- n eq not { exch pop } if
- showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
-} def
-/Line {
- NArray n 0 eq not
- { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
- n { Lineto } repeat
- CP 4 2 roll ArrowB L pop pop
- } if
-} def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
- ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
- and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
- repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
- ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
- moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
- Lineto pop pop closepath } ifelse } def
-/Diamond {
- /mtrx CM def
- T rotate
- /h ED
- /w ED
- dup 0 eq { pop } { CLW mul neg
- /d ED
- /a w h Atan def
- /h d a sin Div h add def
- /w d a cos Div w add def } ifelse
- mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
- /ArrowA { moveto } def
- /ArrowB { } def
- false Line
- closepath mtrx setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve {
- NArray n 3 lt
- { n { pop pop } repeat }
- { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
-} def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
- 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_IfTE {%
- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
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- gsave fill grestore
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-%
-/ArrowD { % the sides are drawn as curves (hv 20071211)
- CLW mul add dup
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-% we use y=w/h^2 * x^2 as equation for the control points
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- w neg h moveto % lower left of >
- w 9 div 4 mul neg h 3 div 2 mul
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-%
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-% DG modification begin - Jan. 15, 1997
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-% setmatrix } def
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-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
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-ifelse } def
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-%
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-%
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-%
-/ArcAdjust { %%%% Vincent Guirardel
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-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
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- targetLength 57.2958 mul
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- add sqrt div
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-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
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-% if D almost equals targetLength, we stop
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-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
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- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
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-%% first last parpos Expr[first:parpos-1] ->
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
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- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
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- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
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- PreCommonFunc
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
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- PostCommonFunc } def
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- PreCommonFunc
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- PreCommonFunc
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
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-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
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-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-%
-/Grid {
- newpath
- /a 4 string def
- /b ED /c ED /n ED
- cvi dup 1 lt { pop 1 } if
- /s ED
- s div dup 0 eq { pop 1 } if
- /dy ED s div dup 0 eq { pop 1 } if
- /dx ED dy div round dy mul
- /y0 ED dx div round dx mul
- /x0 ED dy div round cvi
- /y2 ED dx div round cvi
- /x2 ED dy div round cvi
- /y1 ED dx div round cvi
- /x1 ED
- /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
- /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
- b 0 gt {
- /z1 b 4 div CLW 2 div add def
-% /Helvetica findfont b scalefont setfont
- /b b .95 mul CLW 2 div add def } if
- systemdict /setstrokeadjust known
- { true setstrokeadjust /t { } def }
- { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
- exch itransform } bind def } ifelse
- gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
- /i x1 def
- /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
- /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
- x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
- { i dx mul dup y0 moveto
- b 0 gt
- { gsave c i a cvs dup stringwidth pop
- /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
- h 0 gt {b neg}{z1} ifelse
- rmoveto show grestore } if
- dup t f moveto
- g t L stroke
- /i i w add def
- } repeat
- grestore
- gsave
- n 0 gt
- % DG/SR modification begin - Nov. 7, 1997 - Patch 1
- %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
- { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
- % DG/SR modification end
- { 2 setlinecap } ifelse
- /i y1 def
- /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
- /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
- y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
- { newpath i dy mul dup x0 exch moveto
- b 0 gt { gsave c i a cvs dup stringwidth pop
- /z2 ED
- w 0 gt {z1 z2 add neg} {z1} ifelse
- h 0 gt {z1} {b neg} ifelse
- rmoveto show grestore } if
- dup f exch t moveto
- g exch t L stroke
- /i i h add def
- } repeat
- grestore
-} def
-%
-/ArcArrow {
- /d ED /b ED /a ED
- gsave
- newpath 0 -1000 moveto clip
- newpath
- 0 1 0 0 b
- grestore
- c mul
- /e ED
- pop pop pop r a e d PtoC y add exch x add
- exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
- mul neg d
-} def
-%
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-%
-/ArcAdjust { %%%% Vincent Guirardel
-% given a target length (targetLength) and an initial angle (angle0) [in the stack],
-% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
-% This computes an angle t such that (x0,y0) is at distance
-% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
-% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
-% contrary to TvZ's code.
-% To achieve, this, one iterates the following process: start with some angle t,
-% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
-% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
-%
-% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
-% the value of d = add/sub is used to know on which side we have to move.
-% It is only used in the initialisation of the angle before the iteration.
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Input stack: 1: target length 2: initial angle
-% variables used : rx, ry, d (=add/sub)
-%
- /targetLength ED /angle0 ED
- /x0 rx angle0 cos mul def
- /y0 ry angle0 sin mul def
-% we are looking for an angle t such that (x0,y0) is at distance targetLength
-% from the point M(t)=(rx*cos(t),ry*sin(t)))
-%initialisation of angle (using 1st order approx = TvZ's code)
- targetLength 57.2958 mul
- angle0 sin rx mul dup mul
- angle0 cos ry mul dup mul
- add sqrt div
-% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
-% (if the ellipse is very curved at the point where we draw the arrow, %
-% the value can be much more than 360 degrees !)
-% this should avoid going on the wrong side (more than 180 degrees) or go near
-% a bad attractive point (at 180 degrees)
- dup 90 ge { pop 90 } if
- angle0 exch d % add or sub
-% maximum number of times to iterate the iterative procedure:
-% iterative procedure: takes an angle t on top of stack, computes a
-% better angle (and put it on top of stack)
- 30 { dup
-% compute distance D between (x0,y0) and M(t)
- dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
-% if D almost equals targetLength, we stop
- dup targetLength sub abs 1e-5 le { pop exit } if
-% stack now contains D t
-% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
-% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
- exch dup cos rx mul x0 sub exch sin ry mul y0 sub
-% stack contains: y(t)-y0, x(t)-x0, d
- 2 index Div targetLength mul y0 add ry Div exch
- 2 index Div targetLength mul x0 add rx Div
-% stack contains x(t')/rx , y(t')/ry , d
-% now compute t', and remove D from stack
- atan exch pop
- } repeat
-% we don't look at what happened... in particular, if targetLength is greater
-% than the diameter of the ellipse...
-% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
-% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
-% to give back the result as a an angle relative to angle0 we could add the following line:
-% angle0 sub 0 exch d
-%
-% begin bug fix 2006-01-11
-% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
-%(we don't want to make the ellipse turn more or less than it should)...
-dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
-% end bug fix
-} def
-%
-/EllipticArcArrow {
- /d ED % is add or sub
- /b ED % arrow procedure
- /a1 ED % angle
- gsave
- newpath
- 0 -1000 moveto
- clip % Set clippath far from arrow.
- newpath
- 0 1 0 0 b % Draw arrow to determine length.
- grestore
-% Length of arrow is on top of stack. Next 3 numbers are junk.
-%
- a1 exch ArcAdjust % Angular position of base of arrow.
- /a2 ED
- pop pop pop
- a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
- a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
- a1 cos rx mul xOrig add %
- a1 sin ry mul yOrig add %
-% Now arrow tip coor and base coor are on stack.
- b pop pop pop pop % Draw arrow, and discard coordinates.
- a2 CLW 8 div
-% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
- ArcAdjust
-% resets original value of d
- 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
-} def
-%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
-%
-/Rot { CP CP translate 3 -1 roll neg rotate NET } def
-%
-/RotBegin {
- tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
- /TMatrix [ TMatrix CM ] cvx def
- /a ED
- a Rot /RAngle [ RAngle dup a add ] cvx def
-} def
-%
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def
-%
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-%-----------------------------------------------------------------------------%
-
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-algparser.pro 0 0
-% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $
-%
-% PostScript prologue for PSTricks algorithm parser
-% Version 0.01, 2008/01/01
-% For distribution and copyright, see pstricks.tex. hv@pstricks.de
-%
-%-----------------------------------------------------------------------------%
-/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
-%
-/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
-%
-% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12
-% E->T|E+T
-% T->FS|T*FS
-% FS -> F | +FS | -FS
-% F->P|F^SF
-% P->(E)|literal
-% literal->number|var|var[E]|func(params)
-% params->E|E,param
-% number->TOBEFINISHED
-%
-%% E expression, T term, SF signed factor, F factor, P power
-%
-%% parser
-%
-%% str
-%
-%% C->E<condition_operators>E
-%% STR index -> STR index+lenExpr
-/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
-%
-%% analyze Expression List (separator , or | )
-%% STR index -> STR index+lenExpr
-%% /AnalyzeListOfE {
-%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
-%% NextNonBlankChar dup 0 eq { pop exit } if
-%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
-%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
-%% AnalyzeListOfEPostHook
-%% } def
-/AnalyzeListOfE {
- /NotFirst false def
- { NextNonBlankChar pop AnalyzeExpr
- NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
- dup Strlen eq { exit } if NextNonBlankChar
- dup 44 ne 1 index 124 ne and
- { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
- if pop 1 add } loop
- AnalyzeListOfEPostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% E->T|E+T
-%% STR index -> STR index+lenExpr
-/AnalyzeExpr {
- AnalyzePreHook AnalyzeTerm IsEndingExpr
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% T->FS|T*FS
-%% STR index
-/AnalyzeTerm {
- AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
- ifelse
- AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% FS -> F | +FS | -FS
-%% STR index
-/AnalyzeSignedFactor {
- AnalyzePreHook 2 copy get dup IsUnaryOp
- { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
- { pop AnalyzeFactor }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% F->P|F^P
-%% STR index
-/AnalyzeFactor {
- AnalyzePreHook AnalyzePower IsEndingFactor
- { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
- { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop }
- ifelse AnalyzePostHook
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% P->(E)|literal
-%% STR index
-/AnalyzePower {
- %% depending of first char either a number, or a literal
- 2 copy get dup 40 eq%%an open par
- { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
- { AnalyzeLiteral }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index STR[index] -> STR index
-%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
-/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% recognize + or -
-%% chr -> T/F
-/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadNumber {
- exch dup 3 -1 roll dup 3 1 roll
- %%read mantissa
- { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
- dup 101 eq exch 69 eq or
- %%% there is a "e" or "E" -> read exponant
- { 1 add 2 copy get dup IsUnaryOp
- { pop 1 add 2 copy get } if
- { IsNumber not { exit } if 1 add 2 copy get } loop }
- if
- dup 4 1 roll
- 3 -1 roll exch 1 index sub getinterval
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a number can contain only : 0123456789.
-%% chr -> T/F
-/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index number
-%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
-%% STR index -> STR index' number
-/ReadCondOp {
- NextNonBlankChar 1 index 4 1 roll
- { IsCondOp not { exit } if 1 add 2 copy get } loop
- 2 copy 5 -1 roll
- exch 1 index sub getinterval 3 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can contain only : 0123456789.
-%% chr -> T/F
-/IsLiteral {%
- dup 48 ge exch dup 57 le 3 -1 roll and exch
- dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
- dup 97 ge exch 122 le and or } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
-%% STR index -> literal STR index' nextchr
-/ReadLiteral {
- exch dup 3 -1 roll dup 3 1 roll
- %%read literal core
- { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
- 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a clpar
-%% STR index -> STR index STR[index] T/F
-/IsEndingExpr {%
- 2 copy dup Strlen eq
- %% if end of str is reached -> end !
- { pop pop 0 true }
- %% ending chr -> clpar, comma, |, <, >, =, !,
- {get dup dup 41 eq
- exch dup 124 eq
- exch dup 93 eq
- exch dup 44 eq
- exch dup 30 eq
- exch dup 60 ge exch 62 le and or or or or or}
- ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or a +-
-%% STR index -> STR index STR[index] T/F
-/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or */
-%% STR index -> STR index STR[index] T/F
-/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% expr is ended by end of str or ^
-%% STR index -> STR index STR[index] T/F
-/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% STR index -> STR index STR[index]
-/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
-/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%
-%% DEBUG
-/BRK {false} def
-/BRKtrue {/BRK true def} def
-/BRKStop {BRK {BRKtoto} if } def
-/BRKEvalStop {BRK exch if } def
-/BRKBRK2true {BRK {BRK2true} if } def
-/BRK2 {false} def
-/BRK2true {/BRK2 true def} def
-/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
-end
-%
-%-------------------------------------------------------------------------------%
-%
-/tx@AlgToPs 12 dict def tx@AlgToPs begin
-%
-%% algExpr -> PSVector
-/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
-/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
-/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
-/Strlen 0 def
-/EvalListOfExpr {} def%
-/EvalNumber {%
- ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
- exch 1 add array astore def NextNonBlankChar pop } def
-/EvalAddSub {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
-} def
-/EvalMulDiv {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
-} def
-/EvalPower {%
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
- pop /exp cvx exch 1 add array astore def
-} def
-/EvalLiteral {%
- ReadLiteral
- dup 40 eq%%% there is an open par -> function call
- { pop 2 index
- dup (Sum) eq { EvalSum }
- { dup (IfTE) eq { EvalCond }
- { dup (Derive) eq { pop EvalDerive }
- { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
- /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
- exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
- { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
- dup 91 eq%%% there is an open bracket -> vector element
- { pop 1 add NextNonBlankChar pop AnalyzeExpr
- /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
- { pop NextNonBlankChar pop }
- ifelse}
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% the derive function : Derive(n,f(x))
-%% firstparindex lastparindex ->
-/EvalDerive {
- %% manage the function descripiton
- 1 add ReadNumber 3 1 roll NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- 1 add NextNonBlankChar pop
- 3 -1 roll cvi
- dup 0 eq
- { pop AnalyzeExpr 3 -1 roll pop 1 add }
- { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
- { (x) tx@Derive begin Derive end } repeat
- ExpressionVector exch /ExpressionVector [] def
- AlgToPs aload length
- /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
- l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
- 1 index length /Strlen exch def } ifelse
-} def
-/EvalSum {%
- pop 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the increment value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
- 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
- /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
- 5 -1 roll 4 add array astore def
- %% keep ExpressionVector for later and create a new one for internal Sum computation
- ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
- 1 add NextNonBlankChar pop AnalyzeExpr
- %% add each term
- /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
- /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
- array astore def 3 -1 roll pop 1 add
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-/EvalCond {%
- pop 1 add AnalyzeCond NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- ExpressionVector 3 1 roll /ExpressionVector [] def
- 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
- NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add AnalyzeExpr
- NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
- ExpressionVector
- /ExpressionVector 6 -1 roll aload length dup
- 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
- 1 add 3 -1 roll pop
-} def
-%% CondOp STR index
-/EvalCondOp {%
- 3 -1 roll
- dup (=) eq { /eq } {%
- dup (<) eq { /lt } {%
- dup (>) eq { /gt } {%
- dup (>=) eq { /ge } {%
- dup (<=) eq { /ge } {%
- dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
- ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
- cvx exch pop
- /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
-/EvalUnaryOp {
- 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook {} bind def
-/PreEvalHook {} bind def
-/AnalyzeListOfEPostHook {} bind def
-/AnalyzePostHook {} def
-/RollOp { 3 1 roll } bind def
-end %tx@CoreAnalyzerDict
-%
-%--------------------------------------------------------------------%
-%
-/tx@Derive 41 dict def tx@Derive begin
-%%increase ^^ for each function added
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable -> PSVector
-/Derive {%
- 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
-} def
-/Strlen 0 def
-/InitParser { dup length /Strlen exch def 0 } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% algExpr variable index -> PSVector
-/DeriveIndexed {%
- 3 1 roll 10240 string 3 1 roll 0 3 1 roll
- /Variable exch def
- tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u,v)'=-(u',v')
-/EvalListOfExpr {%
- 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
- 2 copy 7 -1 roll dup length 4 1 roll putinterval add
- 6 -2 roll pop pop
- 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (-u)'=-(u')
-/EvalUnaryOp {
- 4 -2 roll 4 index (0) eq
- { (0) StrConcat 7 -1 roll pop }
- { 7 -1 roll 45 eq
- { AddSub AddOpPar true } { false } ifelse
- 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (number)'=0
-/EvalNumber { ReadNumber (0) 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u+v)'=u'+v'
-/EvalAddSub {%
- 7 index dup (0) eq
- { pop true }%% du=0 nothing added
- { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
- ifelse
- 5 index dup (0) eq
- { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
- { exch
- { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
- { 5 -2 roll 7 index 43 eq%%something yet added
- { AddAdd false } { AddSub AddOpPar true } ifelse }
- ifelse 11 1 roll
- 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
- 2 copy pop 0 6 2 roll GetIntervalNewStr }
- ifelse
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)' or (u/v)'
-/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u*v)'=u'*v+u*v'
-/EvalMul {%
- 4 -2 roll 7 index dup (0) eq
- { pop false }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
- true }%%du!=0
- ifelse
- 5 1 roll 5 index (0) eq
- { 5 -1 roll not { (0) StrConcat } if }%%dv=0
- { 5 -1 roll { AddAdd } if
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- }%%dv!=0
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u/v)'=(u'*v-u*v')/v^2
-/EvalDiv {%
- 4 -2 roll
- 4 index (0) eq%%dv=0 -> u'/v
- { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
- { 7 index dup (0) eq
- { pop }%%du=0
- { (1) eq%%du=1
- { false }
- { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
- 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
- ifelse
- AddSub
- 4 index (1) eq
- { 8 index StrConcat }
- { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
- ifelse
- %}%%dv!=0
- 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
- AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
- ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str1 index str2 -> str1 index
-/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
-/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
-/EvalPower {%
- 4 -2 roll 7 index (0) eq
- {%%if du=0 then (u^v)'=v'ln(u)u^v
- 4 index (0) eq
- { (0) StrConcat }%%if dv=0 then (u^v)'=0
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
- AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
- }
- {%%du!=0
- 4 index (0) eq
- {%%if dv=0 then (u^v)'=vu'u^(v-1)
- 5 index dup IsStrNumber
- { dup (0) eq
- { StrConcat }
- { dup dup (1) eq exch (1.0) eq or
- { StrConcat }
- { StrConcat
- 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
- { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
- (*\() StrConcat 8 index StrConcat (\)) StrConcat
- 5 index dup dup (2) eq exch (2.0) eq or
- { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
- { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)) StrConcat } ifelse
- }
- {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
- 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
- AddOpPar 5 index StrConcat (\)*\() StrConcat
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (-1\)+\() StrConcat
- 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
- 8 index StrConcat (\)^\() StrConcat
- 5 index StrConcat (\)*ln\() StrConcat
- 8 index StrConcat AddClPar
- } ifelse
- } ifelse
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% str -> true/false
-/IsStrNumber {%
- true exch
- { dup 48 lt exch dup 57 gt 3 -1 roll or
- exch dup 46 ne%%.
- exch dup 43 ne%%+
- exch 45 ne%%-
- and and and { pop false } if } forall
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalLiteral {%
- ReadLiteral dup 40 eq%%% there is an open par -> function call
- { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
- { dup 91 eq%%% there is an open bracket -> vector element
- { ERROR_vector_not_yet_implemented }
- { pop EvalVariable }
- ifelse }
- ifelse
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% first last parpos Expr[first:parpos-1] ->
-/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% (f(u))'=u'f'(u)
-/EvalFunc {
- 4 2 roll 4 index (1) ne
- { AddOpPar 4 index StrConcat (\)*) StrConcat } if
- (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Func derivative -> Eval<func>
-/EvalFunc_sin {%
- PreCommonFunc
- { (cos\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_cos {%
- PreCommonFunc
- { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_tan {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_asin {%
- PreCommonFunc
- { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_acos {%
- PreCommonFunc
- { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_atg {%
- PreCommonFunc
- { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_ln {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_exp {%
- PreCommonFunc
- { (exp\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_sqrt {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Fact {%
- PreCommonFunc { ERROR_no_variable_expression_in_Fact } if
- PostCommonFunc } def
-/EvalFunc_sh {%
- PreCommonFunc
- { (ch\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_ch {%
- PreCommonFunc
- { (sh\() StrConcat 5 index StrConcat AddClPar } if
- PostCommonFunc } def
-/EvalFunc_th {%
- PreCommonFunc
- { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argsh {%
- PreCommonFunc
- { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argch {%
- PreCommonFunc
- { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
- PostCommonFunc } def
-/EvalFunc_Argth {%
- PreCommonFunc
- { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
- PostCommonFunc } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-/PreCommonFunc {
- 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
- 4 2 roll 4 index (0) eq
- { (0) StrConcat false }
- { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
-} def
-/PostCommonFunc {
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-/EvalFunc_Derive {%
- 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
- 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
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- 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
- exch 6 2 roll } def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
-/EvalFunc_Sum {%
- 1 add NextNonBlankChar pop
- %% read the variable name
- ReadLiteral pop 3 -1 roll pop NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
- %% read the initial value
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- %% read the increment value
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- 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
- %% read the limit value
- 1 add NextNonBlankChar pop ReadNumber pop
- 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
- 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
- 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% literal switch -> func call, vector, variables
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- 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
- NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
- 1 add NextNonBlankChar pop dup 5 1 roll
- AnalyzeExpr NextNonBlankChar
- 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
- 1 add NextNonBlankChar pop
- AnalyzeExpr 1 add NextNonBlankChar pop
- 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
- 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
- 2 copy pop 0 6 2 roll GetIntervalNewStr
- mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% advance in str until a comma is found (no error detection!)
-%% str index -> str index'
-/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Convert to radians if trigo function call
-%% (name) ->
-/TrigoFunc {
- dup (cos) eq 1 index (sin) eq or exch (tan) eq or
- { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
- array astore def
- } if
-} def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% No derivative for condition....
-/EvalCondOp { 3 -1 roll pop } bind def
-/PutIntervalOneAdd {putinterval 1 add} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add close parenthesis in string at the given index
-%% str index -> str index+1
-/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add 0 in string at the given index
-%% str index -> str index+1
-/AddZero {2 copy (0) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddMul {2 copy (*) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add open parenthesis in string at the given index
-%% str index -> str index+1
-/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a plus sign in string at the given index
-%% str index -> str index+1
-/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a minus sign in string at the given index
-%% str index -> str index+1
-/AddSub {2 copy (-) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Add a pipe sign in string at the given index
-%% str index -> str index+1
-/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% H O O K S
-/AnalyzePreHook { dup 5 1 roll } bind def
-/PreEvalHook {} def
-/AnalyzePostHook { 7 -1 roll pop } bind def
-/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
-/RollOp { 5 1 roll } bind def
-end%%%tx@CoreAnalyzerDict
-/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% NEW FUNC
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
-%% x -> theta
-/asin {%
- dup abs 1 gt { EQDFasinrangeerror } if
- dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
-} def
-%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
-%% x -> theta
-/acos {%
- dup abs 1 gt { EQDFacosrangeerror } if
- dup dup mul 1 exch sub sqrt exch atan DegtoRad
-} def
-%% function arctangent in radians
-%% x -> theta
-/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
-%% HYPERBOLIC FUNCTIONS
-/sh { dup Ex exch neg Ex sub 2 div } def
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-/th { dup sh exch ch div } def
-/Argsh { dup dup mul 1 add sqrt add ln } def
-/Argch { dup dup mul 1 sub sqrt add ln } def
-/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
-%% modified exponential funtion for 0
-%% x n -> x^n
-/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
-%% modified exponential funtion for 0
-%% x -> e^x
-/Ex { Euler exch exp } bind def
-%%
-%% factorial function
-%% n -> n!
-/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
-/fact { Fact } bind def
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-
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-% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $
-%
-%% PostScript prologue for pstricks.tex.
-%% Version 2.00, 2006/12/19
-%% For distribution, see pstricks.tex.
-%%
-%% Timothy Van Zandt <tvz@Princeton.EDU>
-%%
-%% Modified by Etienne Riga - Dec. 16, 1999
-%% Modified by Herbert Voss (hv) - 2004/12/27
-%% Modified by Etienne Riga - 2005/01/01 (er)
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-%%%
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- /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
-%-------------- hv begin 2004/07/25 from: er 2003/03/24
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- -180 500 -10 250 -20 0 curveto closepath} def
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- 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
- fill} def
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- -220 500 -50 250 -50 30 cos 100 mul curveto} def
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- 60 rotate Basterp 60 rotate Basterp
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- .775 .775 scale CrossPath fill} def
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- .775 .775 scale BoldCrossPath fill} def
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- 45 rotate .775 .775 scale CrossPath fill} def
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- 45 rotate .775 .775 scale BoldCrossPath fill } def
- /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
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- closepath} def
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- /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
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- /SolidDiamond {DiamondPath fill} def
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diff --git a/Master/texmf-dist/doc/generic/lnotes/src/fonts.tex b/Master/texmf-dist/doc/generic/lnotes/src/fonts.tex
deleted file mode 100644
index c4f58644815..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/fonts.tex
+++ /dev/null
@@ -1,183 +0,0 @@
-\chapter{字体}
-
-关于字体有三个重要概念:glyph、typeface、font。glyph~通常被翻译为字形,也有翻译为字体的;typeface~是一个书法和印刷领域的概念,它通常被翻译为字体或书体;font~曾经和~typeface~混用,但现在一般用作电脑领域的概念,在中国大陆被翻译为字体,在台湾被翻译为字型。
-
-上述翻译的混乱令人十分无奈,包老师决定在本文中把它们分别翻译为字形、字样、字体,以正视听。
-
-字形是一个字符的具体图形表现形式,一个字符可以有多个字形,比如汉字中的“強/强”、“戶/户/戸”;字样是一组相同风格样式的字形的集合,比如中文字样有宋、仿、楷、黑、隶、篆等;一种字样可以对应电脑上的几种字体。
-
-\section{字样}
-\label{sec:typeface}
-拉丁字母的字样主要有三大类:Serif(Roman)、Sans Serif~和~Mono-space~(Typewriter)。Serif~的笔画边缘部分有些装饰,类似于中文的宋体、仿宋、楷体、魏书等。Sans Serif~的笔画则是平滑的,类似于中文的黑体。Sans~这个词来源于法语,就是“没有”的意思。Monospace~则是等宽字样。
-
-每一类字样都可以有加粗(bold)、斜体(italic)、倾斜(oblique)等修饰效果。Italic~通常对原字样进行过重新设计,它修饰精细,多用于~Serif;~Oblique~也称作~slanted,基本上是把正体倾斜,多用于~Sans Serif。通常~oblique~看起来比~italic~要宽一些。
-
-\Fref{tab:typeface}列出了几种常见的字样。
-
-\begin{table}[htbp]
-\caption{常见字样}
-\label{tab:typeface}
-\centering
-\begin{tabular}{llll}
- \toprule
- 操作系统 & Serif & Sans Serif & Monospace \\
- \midrule
- Mac OS & Times & Helvetica & Courier \\
- Windows & Times New Roman & Arial & Courier New \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{字体格式}
-\label{sec:font}
-
-\subsection{点阵字体和矢量字体}
-电脑上用的字体(font)按数据格式可以分为三大类:点阵字体(bitmap)、轮廓(outline)字体和笔画(stroke-based)字体。
-
-点阵字体通过点阵来描述字形。早期的电脑受到容量和绘图速度的限制,多采用点阵字体。点阵字体后来渐渐被轮廓字体所取代,但是很多小字号字体仍然使用它,因为这种情况下轮廓字体缩放太多会导致笔画不清晰。
-
-轮廓字体又称作矢量字体,它通过一组直线段和曲线来描述字形。轮廓字体易于通过数学函数进行缩放等变换,形成平滑的轮廓。轮廓字体的主要缺陷在于它所采用的贝塞尔曲线(Bézier curves)在光栅(raster)设备(比如显示器和打印机)上不能精确渲染,因而需要额外的补偿处理比如字体微调(font hinting)。但是随着电脑硬件的发展,人们一般不在意它比点阵字体多出的处理时间。
-
-笔画字体其实也是轮廓字体,不过它描述的不是完整的字形,而是笔画。它多用于东亚文字。
-
-\subsection{常见字体}
-
-常见的轮廓字体技术有:Type 1~和~Type 3、TrueType、OpenType、~\MF~等。
-
-Adobe~的~Type 1~和~Type 3~基于~PS,它们采用三次贝塞尔曲线。Type 1~支持微调,它使用一个简化的~PS~子集;Type 3~不支持微调,但它可以使用全部~PS~功能,因此既可以包含轮廓字体也可以包含点阵字体信息。
-
-1991~年,Apple~发布了~TrueType,它采用二次贝塞尔曲线。二次曲线处理起来比三次曲线快,但是需要更多的点来描述。所以从~TrueType~到~Type 1的转换是无损的,反之是有损的。1994~年,Apple~着手研究~TrueType~的下一代技术:TrueType GX,它后来演变为Apple Advanced Typography(AAT)。
-
-1996~年,微软和~Adobe~联合发布了~OpenType。它比起~AAT~的优势有:跨平台、开放和易于开发、支持更多的语言比如阿拉伯语。
-
-早在~1984~年~Knuth~就发布了~\MF,它与~TrueType~和~OpenType的区别是,不直接描述字形轮廓,而描述生成轮廓的笔的轨迹。笔的形状可以是椭圆形或多边形,尺寸缩放自如,字形边缘也柔和一些。两种字体可以用同一个~\MF~文件,当然还有不同的参数。\MF~技术如此先进,却没有流行开来。对此~Knuth~解释道,要求一位设计字体的艺术家掌握~60~个参数太变态了,那是用来折磨数学家的。
-
-Type 1~和~Type 3~把字体信息存储在两种文件里:metrics~和~glyph~文件。metrics~文件有~AFM(Adobe font metrics)和~PFM(printer font metrics),glyph~文件有~PFA(printer font ASCII)和~PFB(printer font binary)。~\LaTeX~使用的~metrics~格式是~TFM(TeX Font Metrics)。
-
-TrueType~的文件后缀是~.ttf,OpenType~的是~.ttf~和~.otf。\MF~虽然用矢量图形来定义字形,实际输出的却是一种点阵格式:PK~(packed raster)。
-
-上述字体按技术的先进性,从高到低的排序为:OpenType、~TrueType、Type 1、Type 3、PK,我们应优先选用~OpenType~和~TrueType。
-
-\subsection{合纵连横}
-Adobe~收取的~Type 1~专利许可费一度十分昂贵,穷人们只好用免费的~Type 3。为了打破这种垄断,Apple~开发了~TrueType。1991~年~TrueType~发布之后,Adobe随即公开了~Type 1~的规范,~Type 1~字体从贵族堕落为平民,因而流行开来。
-
-1980~年代中后期,Adobe~的大部分盈利来自于~PS~解释器的许可费。面对这种垄断局面,微软和~Apple~联合了起来。微软把买来的~PS~解释器~TrueImage~授权给~Apple,Apple~则把~TrueType~授权给微软。
-
-微软得陇望蜀,又企图获得~AAT~的许可证,未遂。为了打破~Apple~的垄断,微软联合~Adobe~在1996年发布了~OpenType。Adobe~在2002~年末将其字体库全面转向~OpenType。
-
-上面这几出精彩好戏充分展示了商场上的勾心斗角、尔虞我诈,没有永恒的伙伴,只有永恒的利益。但它同时也告诉我们,市场竞争中受益的还是广大的消费者。
-
-\section{字体应用}
-
-PS~支持~Type 1~和~Type 3,而~PDF~除了这两种还支持~TrueType~和~OpenType。\verb|latex|、DVI浏览器、各种~driver~分别采用不同的字体技术。
-
-\subsection{DVI}
-\verb|latex|~编译~\LaTeX~源文件生成~DVI~时只需要\verb|.tfm|~文件,因为~DVI~并不包含字形信息,而只包含对字体的引用。DVI~浏览器显示~DVI~时一般使用~PK,它在系统中查找相应的~\verb|.pk|~文件,若找不到就调用~\MF~在后台自动生成。
-
-\subsection{dvips}
-缺省情况下,\verb|dvips|~也会查找~\verb|.pk|~,或调用~\MF~自动生成;然后把~PK~转换成包含点阵字体的~Type 3,它的参数~\verb|-D|~可以用来控制该点阵字体的分辨率。用~\verb|ps2pdf|~处理含~Type 3~的~PS~时,输出的自然是含~Type 3~的~PDF。
-
-GSview~在低分辨率下可以很好地渲染~Type 3,Adobe Reader~或~Acrobat~却不能,因为它们使用的~Adobe Type Manager~不支持包含完整~PS~的~Type 3。含~Type 3~的~PDF~看起来会有些模糊,所以应尽量避免使用。
-
-\verb|dvips|~的另一个参数~\verb|-Ppdf|~把~Type 1~嵌入生成的~PS,这样再~\verb|ps2pdf|~就能生成含~Type 1~的~PDF。
-
-\verb|dvips|~不支持真正的(native)TrueType,用户只能把~TrueType~先转成~PK~或~Type 1,这样绕了个弯效果总会打些折扣。
-
-\verb|dvips|~的字体详细使用方法可查阅其手册\citep{Rokicki_2005}第~6~章,此处不赘述。
-
-\subsection{dvipdfm(x)}
-\verb|dvipdfm|~支持~PK~和~Type 1,它可以用一个~\verb|t1fonts.map|~文件建立~PK~文件和~Type 1~文件之间的映射,这样生成的~PDF~用的就是~Type 1。\verb|dvipdfm|~也不支持真正的~TrueType。
-
-\verb|dvipdfmx|~通过正确的设置可以使用真正的~TrueType,它对中日韩等东亚文字的支持也较好,所以它对我们来说是~Driver~的首选。
-
-\section{TrueType~字体安装配置}
-CJK~自带的~UTF-8~编码字体~gbsn~和~gkai只包含~GB2312~字符集,而~CTeX~只提供~GBK~编码字体,因此中文用户通常需要自己安装配置~UTF-8~编码的~TrueType~字体。
-
-在使用~TrueType~之前,用户通常需要作以下准备工作:
-\begin{enumerate}
- \item 用转换程序~\verb|ttf2tfm|~生成~TFM。
- \item 配置字体定义文件~\verb|.fd|。
- \item 配置~\verb|ttf2pk|~,因为~DVI~浏览器和~\verb|dvips|~都会自动调用~\verb|ttf2pk|~来生成~PK。
- \item 配置~\verb|dvipdfmx|。
-\end{enumerate}
-
-\subsection{目录和文件}
-通常每个发行包都会参照~TDS~建立自己的目录系统,把各种文件发在固定的位置。比如~MiKTeX~顶层目录如下,在本节后面的示例中我们将使用这些目录的缩写。
-\begin{code}
-Install: D:\edit\MiKTeX 2.7
-UserData: C:\Documents and Settings\Alpha\Local Settings\
- Application Data\MiKTeX\2.7
-UserConfig: C:\Documents and Settings\Alpha\
- Application Data\MiKTeX\2.7
-\end{code}
-
-目录多了有个缺点,文件不知道放在哪里好。MiKTeX~中有的配置文件居然在四个目录下各有一份,实在是令人发指。幸好我们可以用下面的命令检查配置文件的具体名字和路径。
-
-\begin{code}
-initexmf --edit-config-file=ttf2pk
-\end{code}
-
-\subsection{ttf2tfm}
-比如我们想把~\verb|SimSun18030.ttc|(18030~字符集的新宋体)转换为~UTF8~编码的字体文件,我们需要执行以下步骤。
-
-\begin{enumerate}
- \item 把需要的~\verb|.ttf|~文件复制到~\verb|UserData/fonts/truetype/chinese/|。
- \item 用下面的命令生成\verb|.tfm|~和~\verb|.enc|~文件。
- \item 把~\verb|*.tfm|~复制到~\verb|UserData/fonts/tfm/chinese/utf8song/|。
- \item 把~\verb|*.enc|~复制到~\verb|UserData/fonts/enc/chinese/utf8song/|。
-\end{enumerate}
-
-\begin{code}
-ttf2tfm SimSun18030.ttc -q -w utf8song@Unicode@
-\end{code}
-
-\subsection{字体定义文件}
-字体定义文件将字体引用名和实际的字体文件联系起来,比如我们在~\verb|CJK|~环境中引用~\verb|usong|~时,系统将会找到并使用~\verb|utf8song*.tfm|。
-
-\begin{code}
-%UserData\tex\latex\CJK\UTF8\C70usong.fd
-\ProvidesFile{c70usong.fd}
-%character set: GB18030
-%font encoding: Unicode
-\DeclareFontFamily{C70}{usong}{\hyphenchar \font\m@ne}
-\DeclareFontShape{C70}{usong}{m}{n}{<-> CJK * utf8song}{}
-\DeclareFontShape{C70}{usong}{m}{it}{<-> CJK * utf8song}{}
-\DeclareFontShape{C70}{usong}{bx}{n}{<-> CJKb * utf8song}{
- \CJKbold}
-\endinput
-\end{code}
-
-\subsection{配置~\texttt{ttf2pk}}
-MiKTeX~中~\verb|ttf2pk|~的配置文件是~\verb|ttf2pk.ini|~,在其它的发行包中可能是~\verb|ttf2pk.cfg|。
-
-\verb|ttf2pk.ini|~中有一个~\verb|.map|~文件列表,后者定义了~TrueType~应该按编码转为~PK~等信息。
-
-比如下面这个文件列表会让~\verb|ttf2pk|~读取~\verb|foo.map|~和~\verb|bar.map|。
-
-\begin{code}
-map foo.map
-map bar.map
-\end{code}
-
-如果系统找不到~\verb|ttf2pk.ini|,它会缺省使用~\verb|ttfonts.map|。
-\begin{code}
-%UserData\ttf2tfm\base\ttfonts.map
-utf8song@Unicode@ SimSun18030.ttc
-\end{code}
-
-\subsection{配置~\texttt{dvipdfmx}}
-配置~\verb|dvipdfmx|~是为了让~PDF~正确地嵌入~TrueType,否则生成的文件中的内容不能复制、粘贴。
-
-\begin{code}
-%UserConfig\dvipdfm\config\dvipdfmx.cfg
-f cid-x.map
-\end{code}
-
-\begin{code}
-%UserData\dvipdfm\config\cid-x.map
-utf8song@Unicode@ unicode SimSun18030.ttc
-\end{code}
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/graphics.tex b/Master/texmf-dist/doc/generic/lnotes/src/graphics.tex
deleted file mode 100644
index 03256a1fb42..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/graphics.tex
+++ /dev/null
@@ -1,1256 +0,0 @@
-\chapter{插图}
-\label{sec:graphics}
-
-\begin{quotation}
-A picture says more than a thousand words.
-\begin{flushright}
---- Shakespeare
-\end{flushright}
-\end{quotation}
-
-当年~Knuth~开发~\TeX~时,GIF、JPEG、PNG、EPS~等图形格式还没有问世,所以~DVI~不能直接支持这些格式。但是高手就是高手,Knuth~在~\TeX~上留了一个后门:\verb|\special|~命令,让后面的~Driver~决定怎样处理图形。
-
-这和当年老毛把港澳台,老邓把钓鱼岛都“留给后人解决”有异曲同工之妙。曾经有位出版社的编辑看上了包老师写的一个程序,要包老师改改当作教学辅助软件出版,但是包老师手头没有~DOS~中断的资料没办法加鼠标操作。该编辑说:你把鼠标驱动打包在软件里,让用户自己琢磨是怎么回事。
-
-下面我们会在~\ref{sec:graphics_format}~节介绍一下~\LaTeX~所用图形格式,\ref{sec:includegraphics}~节介绍怎样插入已有的图形,\ref{sec:mp}--\ref{sec:pgf}~节讨论怎样制作矢量图形。
-
-\section{图形格式}
-\label{sec:graphics_format}
-
-\LaTeX~支持点阵图形格式~JPEG~和~PNG,也支持矢量格式~EPS~和~PDF。对于示意图,我们应该首选矢量格式;包含大量自然色彩的图像(比如照片)应该选~JPEG,人工点阵图像应该选~PNG。
-
-\subsection{EPS}
-80~年代中后期,PS~风头之劲一时无两,人们自然会考虑把它作为文档中嵌入图形的标准格式。然而~PS~实在太强大,人们担心嵌入文档的~PS~会搞破坏,于是就产生了戴着手铐的~Encapsulated PostScript(EPS)。出于同样的原因,人们也担心嵌入~HTML~的~ActiveX、Java Applet、JavaScript~中混入恶意代码,所以才会对它们也有所限制。
-
-早年间~DVI~经常被转换为~PS,所以~EPS~就成了~\LaTeX~的标准图形格式。
-
-\subsection{Driver~们的口味}
-
-\subsubsection{dvips}
-\verb|dvips|~喜欢~PS,所以就爱屋及乌只支持嵌入~EPS。MiKTeX~看不惯这种垄断行为,就把~\verb|dvips|~破解,添加了对~JPEG~和~PNG~的支持。如果你反对这种黑客破解行径,只好找软件把其它图形格式转换为~EPS。
-
-\subsubsection{pdf\LaTeX}
-pdf\LaTeX~支持~JPEG、PNG和PDF,不支持~EPS。传说pdf\LaTeX~不支持~EPS~的原因是~PS~解释器的版权问题。包老师认为这种说法不可信,因为~1997~年~Hàn The Thành~发布~pdf\TeX~时~PS~已经被~PDF~赶超,Adobe~与其保护~PS~还不如保护~PDF。
-
-\LaTeX~有两个宏包~\verb|epstopdf|~和~\verb|pst-pdf|~可以实时地(on the fly)把~EPS~转换为~PDF\footnote{在这里on the fly是指在后台处理,用户不用操心。包老师不确定把它翻译为“实时”是否合适,因为~real time~通常被翻译为实时。对于用户无须干涉、知情的情况,有人说~user transparent,也有人说~black box,语言还真奇妙。}。然而前者有安全漏洞,后者用法繁琐,用户最好还是用其它软件事先把~EPS~转为~PDF。
-
-\subsubsection{dvipdfm}
-\verb|dvipdfm|~支持~JPEG、PNG、PDF,不支持~EPS,但是它可以实时地调用~Ghostscript~把~EPS~转为~PDF。所以从图形格式支持的角度来讲,\verb|dvipdfm|~比~\verb|dvips|~和~pdf\LaTeX~都好。
-
-那位同学说了,你这么多废话作甚,直接告诉我们用~\verb|dvipdfm|~不就完了。然而你别忘了~\verb|dvipdfm|~需要~DVI~作为输入,不幸的是用来生成~DVI~的~\verb|latex|~对~JPEG~和~PNG~有意见。
-
-综上所述,这些~driver~都不能把图形格式痛快地通吃,所以同学们别着急,且听包老师慢慢忽悠怎样转换和处理图形格式。
-
-\subsection{图形格式转换}
-
-注意把点阵图形转换为矢量图形并不能提高图形本身的质量,正所谓“garbage in, garbage out”。
-
-\subsubsection{JPEG~和~PNG~的范围框}
-
-作为中间格式的~DVI~不包含图形本身,它只记录图形的尺寸和文件名,因为具体的图形处理由后面的~driver~负责。DVI~中图形的尺寸来自它的范围框(bounding box),而~\verb|latex|~无法从点阵图形文件中提取这一信息,所以我们需要以某种方式把范围框信息告诉它。
-
-一种方法是打开图形文件,记下尺寸,插入图形时加上相应的参数。
-
-另一种方法用~\verb|ebb|~程序生成一个含范围框信息的文件。比如下例会生成~\verb|graph.bb|~文件,有了它插入图形时就不需要范围框参数。注意有时此程序算出的范围框不准,不知道是它的~bug~还是包老师的人品问题。
-\begin{code}
-ebb graph.jpg
-\end{code}
-
-\subsubsection{其它格式转为EPS}
-有很多程序都可以把点阵图形转换为~EPS,比如~\href{http://www.imagemagick.org/}{ImageMagick},以及~\href{http://www.tex.ac.uk/cgi-bin/texfaq2html?label=dvipsgraphics}{~a2ping/sam2p、bmeps、jpeg2ps、sam2p}~等。
-
-PS~从~Level 2~开始才支持点阵图形压缩,所以在把其它格式转为~EPS~时应尽量使用~Level 2~或~3,否则输出的~EPS~会很大。
-
-下面是一个~ImageMagick~中~\verb|convert|~程序的例子。
-\begin{code}
-convert photo.jpg eps2:photo.eps
-\end{code}
-
-另外还有一种~PS~虚拟打印机的方法,优点是可以把几乎所有文件“打印”成~EPS,缺点是输出的是~PS Level 1,即使驱动程序提供了其它~Level~的选项。
-
-\begin{enumerate}
-\item 找一个~PS~打印机驱动程序。Windows~安装盘附带很多打印机驱动,其中带~PS~字样的就是~PS~驱动。包老师选的是“HP Color LaserJet 8550-PS”,Adobe~提供的~PS~驱动效果不太好。其它驱动安装过程可能稍有不同。
-\item 安装时端口选“FILE”,或者后面打印时选择“Print to File”。高级选项里的~PS~选项选“Encapsulated PostScript (EPS)”。
-\item 打开点阵图形文件,打印到上面的虚拟打印机,输出的文件就是~EPS,但是它没有范围框。
-\item 用~GSview~打开上面生成的~EPS,不用理会没范围框的警告,Options~菜单里选上“EPS Clip”,用~File~菜单的“PS to EPS”生成含范围框的~EPS。
-\end{enumerate}
-
-\subsubsection{其它格式转为~PDF}
-
-\LaTeX~附带的~\verb|epstopdf|~程序\footnote{这个命令行程序和上面提到的~epstopdf~宏包是两样东西。}可以把~EPS~转为~PDF。类似地我们也可以安装一个~PDF~虚拟打印机,用它来把其它图形文件转为~PDF。
-
-\section{插入图形}
-\label{sec:includegraphics}
-
-\subsection{插入命令}
-如今万事俱备,只欠插入。上回讲到哪儿来着?Yeah,~Knuth~的后门~\verb|\special|。
-
-用低级命令~\verb|\special|~来插入图形很不爽,于是~\LaTeX~v2.09~增加了~\verb|epsf|~和~\verb|psfig|~宏包。之后~\LaTeXe~推出了更好的~\verb|graphics|~和~\verb|graphicx|~宏包,这两个宏包有个共同的命令:\verb|\includegraphics|。\verb|graphicx|~版本的语法更简单,功能更强大,所以一般推荐用它。
-
-插入图形的具体命令如下,如果是点阵图形需要加范围框参数(左上角和右下角坐标)。
-
-\begin{code}
-\includegraphics[bb=0 0 410 307]{photo.jpg}
-\end{code}
-
-若想省略文件后缀,可在插入图形前使用两个命令。前者指定一个后缀列表,让~\LaTeX~自行查找;后者告诉~\LaTeX~未知后缀的都是~EPS。
-\begin{code}
-\DeclareGraphicsExtensions{.eps,.mps,.pdf,.jpg,.png}
-\DeclareGraphicsRule{*}{eps}{*}{}
-\end{code}
-
-\subsection{缩放、旋转}
-\Fref{tab:scale_angle}~和\Fref{tab:clip}~的选项可以用来缩放、旋转和裁剪插图。
-
-\begin{table}[htbp]
-\caption{includegraphics~命令的缩放和旋转选项}
-\label{tab:scale_angle}
-\centering
-\begin{tabularx}{350pt}{lX}
- \toprule
- scale & 缩放比例 \\
- width & 宽度 \\
- height & 高度 \\
- totalheight & 范围框高度,旋转时它不等于高度 \\
- keepaspectratio & 如果不使用它而同时指定插图的宽度、高度,长宽比可能会失调;使用它时长宽比不变,宽度、高度都不超过指定参数 \\
- angle & 旋转角度 \\
- origin & 旋转原点 \\
- \bottomrule
-\end{tabularx}
-\end{table}
-
-\begin{table}[htbp]
-\caption{includegraphics~命令的裁剪选项}
-\label{tab:clip}
-\centering
-\begin{tabularx}{350pt}{lX}
- \toprule
- viewport & 可视区域的左上角和右下角坐标。\\
- trim & 左、下、右、上四边裁剪的数值。\\
- clip & 是否真正裁剪。缺省为false,不执行裁剪,多出的部分就那样放着;设置为true时执行裁剪。似乎是多此一举。\\
- \bottomrule
-\end{tabularx}
-\end{table}
-
-若想深入了解~\LaTeX~插入图形的功能,请参考~Keith Reckdahl~的《Using Imported Graphics in \LaTeX~ and pdf\LaTeX》\citep{Reckdahl_2006}(简称epslatex)。
-
-\subsection{figure环境}
-插图通常需要占据大块空白,所以在文字处理软件中用户经常需要调整插图的位置。\LaTeX~有一个~\verb|figure|~环境可以自动完成这样的任务,这种自动调整位置的环境称作浮动环境。
-
-\begin{code}
-\begin{figure}[htbp]%位置选项
-\centering
-\includegraphics[bb=0 0 410 307,scale=.8]{photo}
-\caption{10个月大的Anna}
-\label{fig:anna}
-\end{figure}
-\end{code}
-
-\begin{figure}[htbp]
-\centering
-\includegraphics[bb=0 0 410 307,scale=.8]{dscf4684}
-\caption{10个月大的Anna}
-\label{fig:anna}
-\end{figure}
-
-上述代码中,\verb|[htbp]|~选项用来指定插图排版的理想位置,这几个字母分别代表~here、top、bottom、float page,也就是固定位置、页顶、页尾、单独的浮动页。我们可以使用这几个字母的任意组合,一般不推荐单独使用~\verb|[h]|,因为那个位置也许很不合适,\LaTeX~会很生气。
-
-\verb|\centering|~用来使插图居中,\verb|\caption|~命令设置插图标题,\LaTeX~会自动给浮动环境的标题加上编号。注意~\verb|label|~应放在\verb|caption|~之后,否则引用时指向的是前一个插图。
-
-\subsection{插入多幅图形}
-\subsubsection{并排摆放,共享标题}
-当我们需要两幅图片并排摆放,并共享标题时,可以在~\verb|figure|~环境中使用两个~\verb|\includegraphics|~命令。
-
-\begin{fdemo}{
-\centering
-\includegraphics[scale=2]{examples/subfig_left.mps}
-\includegraphics[scale=2]{examples/subfig_right.mps}
-\captionof{figure}{反清复明}
-}
-\begin{figure}[htbp]
-\centering
-\includegraphics{left}
-\includegraphics{right}
-\caption{反清复明}
-\end{figure}
-\end{fdemo}
-
-\subsubsection{并排摆放,各有标题}
-如果想要两幅并排的图片各有自己的标题,可以在~\verb|figure|~环境中使用两个~\verb|minipage|~环境,每个环境里插入一个图。
-\begin{code}
-\begin{figure}[htbp]
-\centering
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics{left}
- \caption{清明}
-\end{minipage}
-\end{code}
-\begin{code}
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics{right}
- \caption{反复}
-\end{minipage}
-\end{figure}
-\end{code}
-
-\begin{figure}[htbp]
-\centering
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics[scale=2]{examples/subfig_left.mps}
- \caption{清明}
-\end{minipage}
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics[scale=2]{examples/subfig_right.mps}
- \caption{反复}
-\end{minipage}
-\end{figure}
-
-\subsubsection{并排摆放,共享标题,各有子标题}
-如果想要两幅并排的图片共享一个标题,并各有自己的子标题,可以使用~\verb|subfig|~宏包提供的~\verb|\subfloat|~命令。
-
-\verb|subfloat|~命令缺少宽度参数。虽然我们可以用~\verb|\hspace|~命令调整子图的距离,子标题却只能和子图本身一样宽,就会出现折行。
-\begin{code}
-\usepackage{subfig}
-\begin{figure}[htbp]
-\centering
-\subfloat[清明]{
- \label{fig:subfig_a}
- \includegraphics{left}
-}
-\hspace{80pt}
-\subfloat[反复]{
- \label{fig:subfig_b}
- \includegraphics{right}
-}
-\caption{反清复明}
-\end{figure}
-\end{code}
-
-每个子图可以有各自的引用,就象这个样子:\Fref{fig:subfig_a}、\Fref{fig:subfig_b}。
-\begin{figure}[htbp]
-\centering
-\subfloat[清明]{
- \label{fig:subfig_a}
- \includegraphics[scale=2]{examples/subfig_left.mps}
-}
-\hspace{80pt}
-\subfloat[反复]{
- \label{fig:subfig_b}
- \includegraphics[scale=2]{examples/subfig_right.mps}
-}
-\caption{反清复明}
-\end{figure}
-
-\subsubsection{改进的子图方法}
-为了避免子标题折行,我们可以在~\verb|\subfloat|~里再嵌套个~\verb|minipage|,因为后者是有宽度的。
-\begin{code}
-\begin{figure}[htbp]
-\centering
-\subfloat[清明]{
-\label{fig:improved_subfig_a}
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics{left}
-\end{minipage}
-}
-\subfloat[反复]{
-\label{fig:improved_subfig_b}
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics{right}
-\end{minipage}
-}
-\caption{反清复明}
-\end{figure}
-\end{code}
-
-\begin{figure}[htbp]
-\centering
-\subfloat[清明]{
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics[scale=2]{examples/subfig_left.mps}
-\end{minipage}
-}
-\subfloat[反复]{
-\begin{minipage}[t]{0.3\textwidth}
- \centering
- \includegraphics[scale=2]{examples/subfig_right.mps}
-\end{minipage}
-}
-\caption{反清复明}
-\end{figure}
-
-\section{图形绘制工具比较}
-与~\LaTeX~配套使用的绘图工具主要有三种:\MP、PSTricks~和~PGF,它们的特点如下。
-
-\begin{itemize}
-\item 工作方式。\MP~离线绘图,生成的~EPS~可以插入~\LaTeX~文档;PSTricks~和~PGF~都采用在线绘图的方式,也就是~\LaTeX~文档内直接使用绘图命令。
-\item 兼容性。\MP~生成的~MPS~需要先转为~PDF~才能被~pdf\LaTeX~使用;PSTricks~生成的~EPS和~pdf\LaTeX~不兼容;PGF~提供针对各种~driver~的接口,兼容性最好。
-\item 功能。PSTricks~有~PS~作后盾,功能最强;\MP~擅长处理数学内容;PGF~的流程图有独到之处。
-\end{itemize}
-
-限于篇幅,本文只对这三种工具进行简介。除了它们,用户也可以考虑一些面向~\LaTeX~的绘图前端,比如~Unix/Linux~下的~xfig~和~Windows~下的~TpX;或可以输出~EPS~的专用软件,比如~gnuplot~和~Matlab。
-
-\section{\MP}
-\label{sec:mp}
-
-1989~年~John D. Hobby\footnote{Hobby 1985年从斯坦福获博士学位,导师就是Knuth,现供职于贝尔实验室。}开始设计一种绘图语言及其编译器,也就是~\MP。\MP~从~\MF~那里获得了大量灵感和源代码,学生从导师那里顺点东西自然是手到擒来。\MP~和~\MF~语法类似,\MP~的主要优点在于是它输出的是~EPS,而且支持彩色;\MF~输出的是点阵格式,不支持彩色。Knuth~声称自己画图时只用~\MP。
-
-从~Hobby~主页上~\MP~的更新记录看,它的最后版本是~0.63,年份是~1994。目前~Taco Hoekwater\footnote{他也是LuaTeX开发者之一。}继续~\MP~的开发工作,最新版本是~1.005。
-
-本文只对~\MP~作简单介绍,若想深入了解请参阅~Hobby~的《A User's Manual for MetaPost》\citep{Hobby_2007}。
-
-\subsection{准备工作}
-用户一般需要把~\MP~源文件(.mp)用一个命令行程序~\verb|mpost|~编译为一种特殊的~EPS,也称作~MPS,然后再把~MPS~插入~\LaTeX~源文件中使用。
-\begin{figure}[htbp]
-\centering
-\begin{tikzpicture}
- \node[box] (mp) {.mp};
- \node[box, right=5 of mp] (mps) {.mps};
- \path (mp) edge [arrow] node[auto] {mpost} (mps);
-\end{tikzpicture}
-\caption{MetaPost~的编译}
-\label{fig:mp}
-\end{figure}
-
-一个~\MP~源文件可以包含多个图形,一般形式如下。代码中每行语句以~\verb|;|~结尾,注释行以~\verb|%|~起始。每个图形的绘图命令包含在一对起始和结尾声明之间。文件结尾也要有一个结尾声明。
-\begin{code}
-beginfig(1); %图形起始
-... %绘图命令
-endfig; %图形结尾
-
-beginfig(2);
-...
-endfig;
-...
-end; %文件结尾
-\end{code}
-
-假如上面的源文件名字是~\verb|fig.mp|,我们可以执行以下编译命令。
-\begin{code}
-mpost fig(.mp)
-\end{code}
-
-编译后就会生成“fig.1、fig.2、$\cdots$”~等文件,每个文件的后缀就是相应的图形起始声明的编号。所以此编号在一个源文件中应保持唯一,否则后生成的文件就会覆盖前面的。
-
-这样的文件名管理起来很麻烦,插入它们时也不能省略后缀,因为~\LaTeX~不能识别它们。用~\verb|\DeclareGraphicsExtensions|~来逐一声明后缀看起来很傻,自己改文件名更傻,\verb|\DeclareGraphicsRule|~也显得不够严谨。
-
-然而~\MP~已经考虑到这个问题,为此提供了一个文件名模板命令。把下面的代码加到源文件头部,编译输出的文件名就会是“fig-01.mps、fig-02.mps、$\cdots$”。
-\begin{code}
-filenametemplate "%j-%2c.mps"; %加在源文件头部
-\end{code}
-
-我们也可以把这个命令加在每个图形的起始声明之前,指定个性化的输出文件名,这样可能更便于记忆。
-\begin{code}
-filenametemplate "flowchart.mps" %加在每个图形前面
-\end{code}
-
-MPS~可以用~GSview~查看,我们也可以用以下命令把它转为~PDF~再用~Adobe Reader~查看。
-
-\begin{code}
-epstopdf flowchart.mps
-\end{code}
-
-\subsection{基本图形对象}
-为了节省空间,本节后面的示例会略去图形起始声明和结尾声明等不重要的细节。
-
-\subsubsection{直线}
-
-绘图命令~\verb|draw|~把几个点以直线段连接起来。\MP~中的缺省长度单位是~bp,用户也可以使用\Fref{tab:unit}~中的其它单位。我们还可以定义一个缩放系数,把坐标都转换成此系数的倍数,这样以后想缩放图形时只要改这个系数即可。
-
-注意~\MP~中的变量赋值符号是~\verb|:=|,而~\verb|=|~用于方程式。变量在同一源文件中只须定义一次,其后的图形中都可以使用。
-
-\begin{fdemo}{\includegraphics{examples/line.mps}}
-draw (0,0)--(40,0)--(20,20)--(0,0);
-u:=10pt; %缩放系数
-draw (5u,0)--(9u,0)--(7u,2u)--cycle;
-\end{fdemo}
-
-几段直线或曲线可以构成一条路径(path),在路径末尾加个~\verb|cycle|~就能构成封闭路径(closed path)。上例中的两个三角形看起来都是封闭的,但是前面这个其实不是真正的封闭路径。
-
-\subsection{点和线宽}
-\verb|drawdot|~命令可以在指定坐标画一个点,为了使它醒目些我们可以换支粗一点的画笔。\MP~中的画笔缺省是直径~0.5pt~的圆形,拿它画出来的线宽就是~0.5pt。
-
-\begin{fdemo}{\includegraphics{examples/dot.mps}}
-draw (0,0)--(10u,4u);
-pickup pencircle scaled 2pt;
-drawdot (0,0);
-drawdot (10u,4u);
-\end{fdemo}
-
-上面的~\verb|pickup|~是一种全局操作,也就是说它会影响到之后所有的绘图命令,我们也可以用~\verb|withpen|~为单个绘图命令设置画笔。
-
-\begin{code}
-draw (0,0)--(10u,4u) withpen pencircle scaled 2pt;
-\end{code}
-
-\subsubsection{曲线}
-曲线和直线的命令相近,只是把连接两个点的~\verb|--|~换成了~\verb|..|。如果共用一些坐标,直线和曲线也可以混在一条语句里画。
-
-\begin{fdemo}{\includegraphics{examples/curve.mps}}
-draw (0,.5u)..(5u,3u)..(10u,1.5u)..
- (7u,0)..(5u,1.5u)..(7u,1.5u);
-\end{fdemo}
-
-\MP~的曲线用三次贝塞尔(Cubic B\'ezier)算法实现。用户可以在命令中增加~direction(方向)、Tension(张力)和~Curl(曲率)等控制,限于篇幅本文不赘述。
-
-\subsubsection{预定义图形}
-~\verb|fullcircle|~命令以原点为圆心画一个单位圆,类似的预定义图形还有~\verb|halfcircle、quartercircle、unitsquare|~等。注意单位正方形的参考点在左下而不在其中心。
-
-通过不同的横向和纵向缩放系数,我们可以把圆形和正方形变成椭圆和长方形。
-
-\begin{code}
-draw fullcircle scaled 2u;
-draw halfcircle scaled 2u shifted (3u,0);
-draw quartercircle scaled 2u shifted (5u,0);
-draw fullcircle xscaled 4u yscaled 2u shifted (9u,0);
-draw unitsquare scaled 2u shifted (12u,-u);
-draw unitsquare xscaled 4u yscaled 2u shifted (15u,-u);
-\end{code}
-
-\begin{out}
-\includegraphics{examples/predefined.mps}
-\end{out}
-
-\subsection{图形控制}
-
-\subsubsection{线型和箭头}
-在绘制图形时,我们不仅可以变换线宽,也可以使用多种线型。
-\begin{code}
-draw (0,0)--(10u,0) dashed withdots;
-draw (0,1u)--(10u,1u) dashed withdots scaled 2;
-draw (0,2u)--(10u,2u) dashed evenly;
-draw (0,3u)--(10u,3u) dashed evenly scaled 2;
-\end{code}
-
-\begin{out}
-\includegraphics{examples/dashed.mps}
-\end{out}
-
-箭头和直线、曲线的语法相近,注意画反向箭头时需要把两个坐标用一对~\verb|()|~括起来。
-
-\begin{fdemo}{\includegraphics{examples/arrow.mps}}
-drawarrow (0,4u)--(9u,4u);
-drawarrow reverse ((0,2u)--(9u,2u));
-drawdblarrow (0,0)--(9u,0);
-\end{fdemo}
-
-\subsubsection{颜色和填充}
-\MP~预定义的颜色有黑、白、红、绿、蓝,它们的~RGB~值分别为(0,0,0)、(1,1,1)、(1,0,0)、(0,1,0)、(0,0,1),缺省色就是黑色。
-
-绘图命令一般都可以通过~\verb|withcolor|~参数来使用各种颜色。封闭路径可以用~\verb|fill|~命令填充。
-
-\begin{fdemo}{\includegraphics{examples/color.mps}}
-draw (0,4u)--(9u,4u) withcolor red;
-draw (0,2u)--(9u,2u) withcolor green;
-draw (0,0)--(9u,0) withcolor blue;
-\end{fdemo}
-
-\begin{code}
-fill p scaled u;
-fill p scaled u shifted (3u,0) withcolor red;
-fill p scaled u shifted (6u,0) withcolor green;
-fill p scaled u shifted (9u,0) withcolor blue;
-\end{code}
-
-\begin{out}
-\includegraphics{examples/fill.mps}
-\end{out}
-
-另一个命令~\verb|filldraw|~可以看作是~\verb|fill+draw|,它除了填充外还会把路径用指定的画笔画一遍。然而不幸的是画边缘和填充内部只能用同一种颜色,所以它的用处不大。
-
-除了为每个绘图命令单独指定颜色,我们也可以使用一个全局命令,使得其后的绘图命令都使用某种颜色。
-\begin{code}
-drawoption(withcolor blue);
-\end{code}
-
-下面的方法可以用来定义基本色以外的颜色,用基本色混色或直接用RGB值效果是一样的。
-
-\begin{code}
-color c[];
-c1 := .9red + .6green + .3blue;
-c2 := (.9,.6,.3);
-\end{code}
-
-\subsubsection{图形变换}
-我们可以对路径进行缩放、平移、旋转等变换操作,横向和纵向缩放可以分开进行。由于旋转是围绕原点进行的,所以要注意平移和旋转的顺序。下例中定义了一个~\verb|path|~变量,以便后面重用。
-
-\begin{code}
-path p;
-p := (0,0)--(2,0)--(1,1.732)--cycle;
-draw p scaled u;
-draw p xscaled 2u yscaled u shifted (3u,0);
-draw p scaled u rotated 60 shifted (8u,0);
-\end{code}
-
-\begin{out}
-\includegraphics{examples/transform.mps}
-\end{out}
-
-\subsubsection{标注}
-\verb|\label|~命令可以在指定的点附近加文字标注。\MP~也可以用一对~\verb|btex|~和~\verb|etex|~来嵌入一些~\TeX~内容,比如数学标注。
-
-\begin{code}
-draw unitsquare xscaled 10u yscaled 4u;
-label.top("top", (5u,4u));
-label.bot("bottom", (5u,0));
-label.lft("left", (0,2u));
-label.rt("right", (10u,2u));
-\end{code}
-\begin{code}
-label.ulft("upper left", (0,4u));
-label.urt("upper right", (10u,4u));
-label.llft("lower left", (0,0));
-label.lrt("lower right", (10u,0));
-label.rt(btex $E=mc^2$ etex, (3u,2u));
-\end{code}
-
-\begin{out}
-\includegraphics{examples/label.mps}
-\end{out}
-
-因为用缺省方法编译生成的~MPS~不嵌入字体,当~\MP~包含文字时,GSview~就不能正常查看。这时我们可以给编译命令加个参数,生成的~MPS~就会包含字体信息。注意这种方法生成的~MPS~虽然~GSview~能查看,\verb|dvipdfmx|~却不能正常处理。
-
-\begin{code}
-mpost \prologues:=2; input fig.mp
-\end{code}
-
-\subsection{编程功能}
-
-\subsubsection{数据类型和变量}
-\MP~中有10~种基本数据类型:numeric、pair、path、pen、~color~、cmykcolor、transform、string、boolean、picture。我们已经接触过其中几种,比如缩放系数~u~就是一个~numeric,一个点的坐标是一个~pair,几个点用直线或曲线连起来是一个~path,pencircle~是一种~pen,black~是一种~color,scaled、rotated、shifted~都是~transform。
-
-numeric~类型变量的精度是~1/65536,它的绝对值不能超过~4096,在计算过程中数值可以达到~32768。这样的规定也应归功于当年的电脑硬件,不过对于科技文档插图而言,4096~一般还是够用的。
-
-除了缺省的~numeric,其它变量在使用之前都需要用数据类型来显式声明。相同类型的变量可以在一行语句中声明,但是带下标的变量不能放在同一行(这个规定很蹊跷)。
-\begin{code}
-numeric x,y,z; %正确
-numeric x1,x2,x3; %错误
-numeric x[]; %正确
-\end{code}
-
-\subsubsection{数学运算}
-\MP~中可以使用普通的运算符,比如~\verb|+ - * /|;也提供一些特殊的运算符,比如~\verb|a++b|~表示$\sqrt{a^2+b^2}$,\verb|a+-+b|~表示$\sqrt{a^2-b^2}$;另外\Fref{tab:math_function}~列出一些常用数学函数。
-
-\begin{table}[htbp]
-\caption{数学函数}
-\label{tab:math_function}
-\centering
-\begin{tabular}{llll}
- \toprule
- abs & 绝对值 & mexp & 指数 \\
- round & 四舍五入 & mlog & 对数 \\
- ceiling & 向上圆整 & sind & 正弦 \\
- floor & 向下圆整 & cosd & 余弦 \\
- mod & 模余 & normaldeviate & 正态分布随机数 \\
- sqrt & 开方 & uniformdeviate & 均匀分布随机数 \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\subsubsection{循环}
-当执行重复任务时,循环语句可以让程序变得简洁。注意下例中的循环语句是一条命令,之所以分成三行写是为了看起来清晰点。
-
-\begin{fdemo}{\includegraphics{examples/loop.mps}}
-draw (0,0) %注意这里没有分号
-for x=1 upto 3:
- ..(x*x,x)*u
-endfor;
-\end{fdemo}
-
-循环语句缺省步长是~1,我们也可以改用其它步长。\verb|upto|~其实就是~\verb|step 1 until|~的缩写方式。
-\begin{code}
-for x=1 step .5 until 3:
-\end{code}
-
-\section{PSTricks}
-\label{sec:pstricks}
-
-PSTricks~是一个基于~PS~的宏包,有了它用户就可以直接在~\LaTeX~文档中插入绘图命令。PSTricks~早期的作者是~Timothy Van Zandt\footnote{法国Insead大学经济系教授。},初始开发年月不详,他于~1997~年退居二线,之后由~Denis Girou、Sebastian Rahtz\footnote{牛津大学计算机系网管。}、Herbert Voß~等维护。
-
-本文只介绍~PSTricks~的基本功能,若想深入了解请参阅~Van Zandt~的《PSTricks User's Guide》\citep{Zandt_2007}。另外\Fref{tab:pst_add}~列出了一些可以和~PsTricks~配合使用的辅助宏包。
-
-\begin{table}[htbp]
-\caption{PSTricks~辅助宏包}
-\label{tab:pst_add}
-\centering
-\begin{tabular}{llll}
- \toprule
- multido & 循环语句 & pst-eucl & 几何函数 \\
- pst-plot & 函数绘图 & pst-math & 弧度三角函数 \\
- pst-plot3d & 三维绘图 & pstricks-add & 极坐标 \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\subsection{准备工作}
-首先要引入~PSTricks~宏包。PSTricks~中缺省长度单位是~1cm,我们也可以设置自己的单位。
-\psset{unit=10pt}
-\begin{code}
-\usepackage{pstricks}
-\psset{unit=10pt}
-\end{code}
-
-绘图命令一般要放在~\verb|pspicture|~环境里,这样~\LaTeX~就会给图形预留一个矩形区域,注意这个矩形要能容纳所有图形对象。为了节省空间,在本节后面的示例代码中,~\verb|pspicture|~环境将被略去。
-
-\begin{code}
-\begin{pspicture}(0,0)(4,2)
-...
-\end{pspicture}
-\end{code}
-
-另外需要注意的是,嵌入~\LaTeX~的~PSTricks~生成的是~PS,\verb|dvips|~可以处理,\verb|dvipdfm|~和pdf\LaTeX~则不能。所以如果使用后两种~driver,需要先行生成~EPS。
-
-第一种方法是把~PSTricks~代码放进一个空白的\LaTeX~页面,用它生成一个简单的~DVI。
-
-\begin{code}
-\documentclass{article}
-\usepackage{pstricks}
-\pagestyle{empty} %页面样式为空
-
-\begin{document}
-\psset{unit=10pt}
-\colorbox{white}{%
- \begin{pspicture}(0,0)(4,2)%
- \psdot(0,0)%
- \psdots(0,2)(2,2)(4,2)%
- \end{pspicture}%
-}
-\end{document}
-\end{code}
-
-然后用以下命令把~DVI~转为~EPS,\verb|-E|~参数即代表~EPS。上面代码中的~colorbox~使得生成的~EPS~有正确的范围框。
-
-\begin{code}
-dvips pst_dots(.dvi) -E -o dots.eps
-\end{code}
-
-第二种方法是用~\verb|pst-eps|~宏包,它能够在线处理~PSTricks~代码并生成~EPS,这样用户就可以在同一文件中使用该~EPS。
-
-然而~\verb|dvipdfmx|~不能正确处理~\verb|pst-eps|~生成的~EPS。它和~\verb|\rput|、\verb|\uput|~命令,\verb|pst-plot|~宏包中的~\verb|\psaxes|~命令都不兼容。类似的~\verb|ps4pdf|~宏包和~\verb|tabularx|~宏包不兼容。
-
-\begin{comment}
-\usepackage{pst-eps}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=4,bbury=2,makeeps=all]
-{dots.eps}{
- \psdot(0,0)
- \psdots(0,2)(2,2)(4,2)
-}
-\includegraphics{dots.eps}
-\end{comment}
-
-\subsection{基本图形对象}
-\subsubsection{点}
-我们可以用以下命令画一个或多个点。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=4,bbury=2,makeeps=all]
-{examples/dot.eps}{
- \psdot(0,0)
- \psdots(0,2)(2,2)(4,2)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_dot.eps}}
-\psdot(0,0)
-\psdots(0,2)(2,2)(4,2)
-\end{fdemo}
-
-\subsubsection{直线、多边形、矩形}
-\verb|\psline|~命令把多个点用直线段连接起来,线段之间的连接缺省为尖角,也可以设置圆角。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=2,makeeps=all]
-{examples/line.eps}{
- \psline(0,0)(2,2)(4,0)
- \psline[linearc=.3](5,0)(7,2)(9,0)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_line.eps}}
-\psline(0,0)(2,2)(4,0)
-\psline[linearc=.3](5,0)(7,2)(9,0)
-\end{fdemo}
-
-\verb|\pspolygon|~命令和~\verb|\psline|~类似,但是它会形成封闭路径。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=2,makeeps=all]
-{examples/polygon.eps}{
- \pspolygon(0,0)(2,2)(4,0)
- \pspolygon[linearc=.3](5,0)(7,2)(9,0)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_polygon.eps}}
-\pspolygon(0,0)(2,2)(4,0)
-\pspolygon[linearc=.3](5,0)(7,2)(9,0)
-\end{fdemo}
-
-矩形用~\verb|\psframe|~命令,其参数就是矩形左下角和右上角的坐标。矩形也可以设置圆角。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=2,makeeps=all]
-{examples/frame.eps}{
- \psframe(0,0)(4,2)
- \psframe[framearc=.3](5,0)(9,2)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_frame.eps}}
-\psframe(0,0)(4,2)
-\psframe[framearc=.3](5,0)(9,2)
-\end{fdemo}
-
-\subsubsection{圆、椭圆、圆弧、扇形}
-圆形用~\verb|\pscircle|~命令,参数是圆心和半径。椭圆用~\verb|\psellipse|~命令,参数是中心、长径、短径。注意这两个命令的半径参数用不同的括号,可能是作者的笔误。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=7,bbury=2,makeeps=all]
-{examples/circle.eps}{
- \pscircle(1,1){1}
- \psellipse(5,1)(2,1)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_circle.eps}}
-\pscircle(1,1){1}
-\psellipse(5,1)(2,1)
-\end{fdemo}
-
-圆弧用~\verb|\psarc|~命令,其参数是圆心、半径、起止角度,逆时针作图。~\verb|\psarcn|~类似,只是顺时针作图。扇形用~\verb|\pswedge|~命令。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=11,bbury=2,makeeps=all]
-{examples/arc.eps}{
- \psarc(1,0){2}{0}{120}
- \psarcn(5,0){2}{120}{0}
- \pswedge(9,0){2}{0}{120}
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_arc.eps}}
-\psarc(1,0){2}{0}{120}
-\psarcn(5,0){2}{120}{0}
-\pswedge(9,0){2}{0}{120}
-\end{fdemo}
-
-\subsubsection{曲线}
-\verb|\pscurve|~命令把一系列点用平滑曲线连接起来;它的变形版本~\verb|\psecurve|~命令不显示曲线的两个端点;另一变形命令~\verb|\psccurve|~则把曲线封闭起来。
-
-参数~\verb|showpoints=true|~用来显示曲线的构成点,此参数也可用于其它绘图命令。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=15,bbury=2,makeeps=all]
-{examples/curve.eps}{
- \pscurve[showpoints=true](0,1)(1,2)(3,0)(4,2)(1,0)
- \psecurve[showpoints=true](5,1)(6,2)(8,0)(9,2)(5,0)
- \psccurve[showpoints=true](11,1)(12,2)(14,0)(15,2)(12,0)
-}
-\end{comment}
-
-\begin{code}
-\pscurve[showpoints=true](0,1)(1,2)(3,0)(4,2)(1,0)
-\psecurve[showpoints=true](5,1)(6,2)(8,0)(9,2)(5,0)
-\psccurve[showpoints=true](11,1)(12,2)(14,0)(15,2)(12,0)
-\end{code}
-\begin{out}
-\includegraphics{examples/pst_curve.eps}
-\end{out}
-
-\verb|\psbezier|~命令输出一条贝塞尔曲线,其参数就是曲线的控制点。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=6,bbury=2,makeeps=all]
-{examples/bezier.eps}{
- \psbezier[showpoints=true]
- (0,0)(2,2)(4,0)(6,2)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_bezier.eps}}
-\psbezier[showpoints=true]
- (0,0)(2,2)(4,0)(6,2)
-\end{fdemo}
-
-抛物线用~\verb|\psparabola|~命令,它有两个参数,第一个是抛物线通过的一点,第二个是抛物线的顶点。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=2,bbury=2,makeeps=all]
-{examples/parabola.eps}{
- \psparabola[showpoints=true]
- (2,2)(1,0)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_parabola.eps}}
-\psparabola[showpoints=true]
- (2,2)(1,0)
-\end{fdemo}
-
-\subsubsection{网格和坐标}
-科技制图通常会用到坐标网格。\verb|\psgrid|~命令输出一个矩形网格,它有三个参数点。网格坐标标注在通过第一个点的两条直线上,第二和第三个点是矩形的两个对角顶点。当第一个参数省略时,坐标标注在通过第一个顶点的两条矩形边上。
-\begin{comment}
-\psset{unit=10pt}
-\PSTtoEPS[bbllx=-1,bblly=-1,bburx=8.4,bbury=2.4,makeeps=all]
-{examples/grid.eps}{
- \psgrid(0,0)(-1,-1)(3,2)
- \psgrid(5,0)(8,2)
-}
-\end{comment}
-
-\begin{code}
-\psgrid(0,0)(-1,-1)(3,2)
-\psgrid(5,0)(8,2)
-\end{code}
-\begin{out}
-\includegraphics{examples/pst_grid.eps}
-\end{out}
-
-\verb|pst-plot|~宏包提供的~\verb|\psaxes|~命令输出坐标轴。它的参数和~\verb|\psgrid|~的类似,刻度和标注都可以灵活地设置,也可以把坐标轴改成一个矩形框的形式。
-\begin{code}
-\psset{unit=10pt}
-\psaxes{<->}(0,0)(-1,-1)(3,2)
-\psaxes[tickstyle=top,labels=none]{->}(5,0)(8,2)
-\psaxes[axesstyle=frame,tickstyle=top]{->}(10,0)(13,2)
-\end{code}
-\begin{out}
-\includegraphics{examples/pst_axis.eps}
-\end{out}
-
-\subsection{图形控制}
-\subsubsection{线型和箭头}
-PSTricks~中的缺省线宽是~0.8pt,缺省线型是实线。以下参数可以控制单个绘图命令的线宽和线型。
-\begin{comment}
-\psset{unit=10pt}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=4,makeeps=all]
-{examples/linestyle.eps}{
- \psline[linewidth=1.5pt](0,4)(9,4)
- \psline[linestyle=dotted](0,2)(9,2)
- \psline[linestyle=dashed](0,0)(9,0)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_linestyle.eps}}
-\psline[linewidth=1.5pt](0,4)(9,4)
-\psline[linestyle=dotted](0,2)(9,2)
-\psline[linestyle=dashed](0,0)(9,0)
-\end{fdemo}
-
-我们也可以用命令~\verb|\psset|~命令来设置全局参数。
-\begin{code}
-\psset{linewidth=1pt,linestyle=dashed}
-\end{code}
-
-以下参数可以控制绘图命令的箭头。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=4,makeeps=all]
-{examples/arrow.eps}{
- \psline{->}(0,4)(9,4)
- \psline{<-}(0,2)(9,2)
- \psline{<->}(0,0)(9,0)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_arrow.eps}}
-\psline{->}(0,4)(9,4)
-\psline{<-}(0,2)(9,2)
-\psline{<->}(0,0)(9,0)
-\end{fdemo}
-
-\subsubsection{颜色和填充}
-PSTricks~预定义的颜色有~black、darkgray、gray、lightgray、white~等灰度颜色,也有~red、green、blue、cyan、magenta、yellow~等彩色。我们也可以自定义灰度颜色和彩色。
-
-\begin{code}
-\newgray{mygray}{.3}
-\newrgbcolor{mycolor}{.3 .4 .5}
-\end{code}
-
-以下参数可以控制单个绘图命令的颜色,我们也可以用~\verb|\psset|~命令设置全局参数。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=4,makeeps=all]
-{examples/color.eps}{
- \psline[linecolor=red](0,4)(9,4)
- \psline[linecolor=green](0,2)(9,2)
- \psline[linecolor=blue](0,0)(9,0)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_color.eps}}
-\psline[linecolor=red](0,4)(9,4)
-\psline[linecolor=green](0,2)(9,2)
-\psline[linecolor=blue](0,0)(9,0)
-\end{fdemo}
-
-以下参数可以控制单个绘图命令的填充模式和填充颜色,注意只有封闭路径才可以填充。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=11,bbury=2,makeeps=all]
-{examples/fill.eps}{
- \pscircle[fillstyle=solid,fillcolor=red](1,1){1}
- \pscircle[fillstyle=vlines](4,1){1}
- \pscircle[fillstyle=hlines](7,1){1}
- \pscircle[fillstyle=crosshatch](10,1){1}
-}
-\end{comment}
-
-\begin{code}
-\pscircle[fillstyle=solid,fillcolor=red](1,1){1}
-\pscircle[fillstyle=vlines](4,1){1}
-\pscircle[fillstyle=hlines](7,1){1}
-\pscircle[fillstyle=crosshatch](10,1){1}
-\end{code}
-\begin{out}
-\includegraphics{examples/pst_fill.eps}
-\end{out}
-
-\subsection{对象布局}
-\subsubsection{平移}
-参数~\verb|origin|~可以让一个图形对象平移到指定的坐标点,我们也可以用~\verb|\psset|~命令设置全局平移参数。
-\begin{comment}
-\PSTtoEPS[bbllx=0,bblly=0,bburx=7,bbury=2,makeeps=all]
-{examples/origin.eps}{
- \psframe(0,0)(3,2)
- \psframe[origin={4,0}](0,0)(3,2)
-}
-\end{comment}
-
-\begin{fdemo}{\includegraphics{examples/pst_origin.eps}}
-\psframe(0,0)(3,2)
-\psframe[origin={4,0}](0,0)(3,2)
-\end{fdemo}
-
-\subsubsection{旋转}
-\verb|\rput|~命令可以对一个图形对象同时进行旋转和平移操作。它有两个参数,第一个是旋转角度,第二个是平移到的坐标点。
-\begin{fdemo}{\includegraphics{examples/pst_rput.eps}}
-\psframe(0,0)(3,2)
-\rput{30}(5,0){\psframe(0,0)(3,2)}
-\end{fdemo}
-
-\subsubsection{文字标注}
-\verb|\rput|~命令还可以在指定的坐标点标注文字,这时它的第一个参数是坐标点相对于标注的位置。其取值可以是纵向的~t、b(上下),或横向的~l、r(左右),也可以是纵向和横向位置的组合。
-\begin{fdemo}{\includegraphics{examples/pst_label.eps}}
-\pspolygon(0,0)(4,0)(2,3)
-\rput[r](0,0){A}
-\rput[l](4,0){B}
-\rput[b](2,3){C}
-\end{fdemo}
-
-\verb|\rput|~生成的标注就在坐标点上,有时会感觉离图形太近。另一个命令~\verb|\uput|~则生成缺省距离指定坐标点~5pt的标注,它的第一个参数是标注相对于坐标点的角度。
-\begin{fdemo}{\includegraphics{examples/pst_uput.eps}}
-\pspolygon(0,0)(4,0)(2,3)
-\uput[l](0,0){A}
-\uput[r](4,0){B}
-\uput[u](2,3){C}
-\end{fdemo}
-
-\verb|\uput|~的角度参数可以是任意角度,也可以是字母,参见。注意~\verb|\uput|~的角度参数和~\verb|\rput|~命令的参考点位置参数的定义几乎正好相反,这也许反映了作者洒脱的风格。
-
-\begin{table}[htbp]
-\caption{uput~命令的角度参数}
-\label{tab:uput}
-\centering
-\begin{tabular}{lrlr}
- \toprule
- r & 0$^\circ$ & ur & 45$^\circ$ \\
- u & 90$^\circ$ & ul & 135$^\circ$ \\
- l & 180$^\circ$ & dl & 225$^\circ$ \\
- d & 270$^\circ$ & dr & 315$^\circ$ \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{PGF}
-\label{sec:pgf}
-PGF~和~Beamer~的作者都是~Till Tantau\footnote{德国Lübeck大学计算机研究所教授。}。Tantau~当初开发~Beamer~是为了应付~2003~年他的博士学位论文答辩,之后它在~CTAN~上流行开来。2005~年~PGF~从~Beamer~项目中分离出来,成为一个独立的宏包。
-
-本文只对~PGF~作简单介绍,若想深入了解请参阅~Tantau~的《TikZ and PGF Manual》\citep{Tantau_2008}。
-
-\subsection{准备工作}
-一般人们并不直接使用~PGF~命令,而是通过它前端~TikZ~来调用~PGF。在引用~\verb|tikz|~宏包之前,用户需要设置~PGF~系统~driver。
-\begin{code}
-\def\pgfsysdriver{pgfsys-dvipdfmx.def}
-\usepackage{tikz}
-\end{code}
-
-PGF~的缺省长度单位是~1cm,我们也可以改用其它单位。注意这样预定义的长度单位有时会失效,这可能是~PGF~的~bug。
-\begin{code}
-\pgfsetxvec{\pgfpoint{10pt}{0}}
-\pgfsetyvec{\pgfpoint{0}{10pt}}
-\end{code}
-
-TikZ~提供一个~\verb|tikz|~命令和一个~\verb|tikzpicture|~环境,具体绘图指令可以放在~\verb|tikz|~后面,也可以放在~\verb|tikzpicture|~中间。两种方法效果相同,用户可以任意选择。为了节省空间,本节的示例将省略部分环境代码。
-\begin{code}
-\tikz ... %绘图命令
-\begin{tikzpicture}
-... %绘图命令
-\end{tikzpicture}
-\end{code}
-
-\subsection{基本图形对象}
-\subsubsection{直线、多边形、矩形}
-TikZ~中直线的语法和~\MP~类似,加~\verb|cycle|~参数才能构成真正的封闭路径。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw (0,0)--(4,0)--(2,2)--(0,0);
-\draw (5,0)--(9,0)--(7,2)--cycle;
-\end{tikzpicture}
-}
-\draw (0,0)--(4,0)--(2,3)--(0,0);
-\draw (5,0)--(9,0)--(7,3)--cycle;
-\end{fdemo}
-
-矩形命令如下,它的两个参数是矩形的两个对角顶点。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw (0,0) rectangle (4,2);
-\end{tikzpicture}
-}
-\draw (0,0) rectangle (4,2);
-\end{fdemo}
-
-\subsubsection{圆、椭圆、弧}
-圆和椭圆命令如下,圆的参数是圆心和半径,椭圆的参数是中心、长径、短径。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw (1,1) circle (1);
-\draw (5,1) ellipse (2 and 1);
-\end{tikzpicture}
-}
-\draw (1,1) circle (1);
-\draw (5,1) ellipse (2 and 1);
-\end{fdemo}
-
-圆弧和椭圆弧命令如下,圆弧的参数是起始点,起始角度、终止角度、半径;椭圆弧则把半径换成了长径和短径。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw (2,1) arc (0:270:1);
-\draw (7,1) arc (0:270:2 and 1);
-\end{tikzpicture}
-}
-\draw (2,1) arc (0:270:1);
-\draw (7,1) arc (0:270:2 and 1);
-\end{fdemo}
-
-\subsubsection{曲线和抛物线}
-曲线命令如下,中间的参数是控制点。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw (0,0) .. controls (2,2)
- and (4,2) .. (4,0);
-\filldraw (0,0) circle (.1)
- (2,2) circle (.1)
- (4,2) circle (.1)
- (4,0) circle (.1);
-\end{tikzpicture}
-}
-\draw (0,0) .. controls (2,2)
- and (4,2) .. (4,0);
-\end{fdemo}
-
-抛物线命令如下,除了起止点还可以指定顶点。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw (-1,1) parabola bend (0,0) (1.414,2);
-\filldraw (-1,1) circle (.1)
- (0,0) circle (.1)
- (1.414,2) circle (.1);
-\end{tikzpicture}
-}
-\draw (-1,1) parabola
- bend (0,0) (1.414,2);
-\end{fdemo}
-
-\subsection{图形控制}
-\subsubsection{线型和箭头}
-绘图命令可以设置线型和箭头参数。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw[line width=2pt] (0,3)--(9,3);
-\draw[->] (0,2)--(9,2);
-\draw[<-] (0,1)--(9,1);
-\draw[<->] (0,0)--(9,0);
-\end{tikzpicture}
-}
-\draw[line width=2pt] (0,0)--(9,0);
-\draw[->] (0,1)--(9,1);
-\draw[<-] (0,2)--(9,2);
-\draw[<->] (0,3)--(9,3);
-\end{fdemo}
-
-\subsubsection{颜色、填充、阴影}
-颜色参数的用法如下。PGF~可以使用~\verb|xcolor|~宏包\citep{Kern_2007}中定义的所有颜色。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw[red] (0,4)--(9,4);
-\draw[green] (0,2)--(9,2);
-\draw[blue] (0,0)--(9,0);
-\end{tikzpicture}
-}
-\draw[red] (0,4)--(9,4);
-\draw[green] (0,2)--(9,2);
-\draw[blue] (0,0)--(9,0);
-\end{fdemo}
-
-封闭路径可以用颜色填充,\verb|\filldraw|~命令可以分别指定边框色和填充色。
-\begin{fdemo}{
-\begin{tikzpicture}
-\fill[red] (1,1) circle (1);
-\filldraw[fill=lightgray,draw=black]
- (4,1) circle (1);
-\end{tikzpicture}
-}
-\fill[red] (1,1) circle (1);
-\filldraw[fill=lightgray,draw=black]
- (4,1) circle (1);
-\end{fdemo}
-
-\verb|\shade|~命令可以产生渐变和光影效果,缺省是从上到下,灰色渐变为白色。我们也可以使用其它方向和颜色的渐变。
-\begin{code}
-\shade (0,0) rectangle (2,2);
-\shade[left color=red,right color=orange] (3,0) rectangle (5,2);
-\shade[inner color=red,outer color=orange] (6,0) rectangle (8,2);
-\shade[ball color=blue] (10,1) circle (1);
-\end{code}
-
-\begin{out}
-\begin{tikzpicture}
-\shade (0,0) rectangle (2,2);
-\shade[left color=red,right color=orange] (3,0) rectangle (5,2);
-\shade[inner color=red,outer color=orange] (6,0) rectangle (8,2);
-\shade[ball color=blue] (10,1) circle (1);
-\end{tikzpicture}
-\end{out}
-
-\subsubsection{图形变换}
-对图形对象可以进行平移和旋转操作,注意如果两种操作同时进行,它们是有顺序的。注意预定义的长度单位在这里对平移参数失效。
-\begin{code}
-\draw (0,0) rectangle (2,2);
-\draw[xshift=30pt] (0,0) rectangle (2,2);
-\draw[xshift=75pt,rotate=45] (0,0) rectangle (2,2);
-\end{code}
-
-\begin{out}
-\begin{tikzpicture}
-\draw (0,0) rectangle (2,2);
-\draw[xshift=30pt] (0,0) rectangle (2,2);
-\draw[xshift=75pt,rotate=45] (0,0) rectangle (2,2);
-\end{tikzpicture}
-\end{out}
-
-\subsection{样式}
-PGF~比~\MP~和~PSTricks~多了一个有趣的概念:样式(style),它的思路和~HTML~的~CSS~相近。我们可以先定义两种样式,
-\tikzset{
- myline/.style={line width=2pt},
- myblueline/.style={myline,blue}
-}
-\begin{code}
-\tikzset{
- myline/.style={line width=2pt},
- myblueline/.style={myline,blue}
-}
-\end{code}
-
-然后就可以在绘图命令中这样使用样式。
-\begin{fdemo}{
-\begin{tikzpicture}
-\draw[myline] (0,2)--(9,2);
-\draw[myblueline] (0,0)--(9,0);
-\end{tikzpicture}
-}
-\draw[myline] (0,2)--(9,2);
-\draw[myblueline] (0,0)--(9,0);
-\end{fdemo}
-
-除了用~\verb|\tikzset|~命令定义样式,我们也可以在~\verb|tikzpicture|~环境头部声明样式。前者是全局性的,后者则是局部性的。
-\begin{code}
-\begin{tikzpicture}[
- thickline/.style=2pt,
- bluethickline/.style={thickline,color=blue}
-]
-...
-\end{tikzpicture}
-\end{code}
-
-注意在样式中预定义长度单位有时会失效,所以最好使用绝对单位。
-
-\subsection{流程图}
-\subsubsection{节点}
-PGF~中的节点(node)可以是简单的标签,也可以有各种形状的边框,还可以有各种复杂的属性。比如下例中的节点样式:\verb|box|,它的边框是矩形,有圆角;它有最小宽度、高度、文字和边框的距离,边框和填充颜色等属性。
-
-\begin{code}
-\tikzset{
- box/.style={rectangle, rounded corners=6pt,
- minimum width=50pt, minimum height=20pt, inner sep=6pt,
- draw=gray,thick, fill=lightgray}
-}
-\end{code}
-
-除了上述类别属性,节点还可以有名字、位置等属性。在下例中,我们先画了三个有名字的文本框;然后用箭头把文本框连接起来,注意连接时要引用文本框的名字;接着在箭头上加了标签。
-\begin{code}
-\node[box] (tex) at(0,0) {.tex}; %文本框
-\node[box] (dvi) at(10,0) {.dvi}; %文本框
-\node[box] (pdf) at(20,0) {.pdf}; %文本框
-\draw[->] (tex)--(dvi); %箭头
-\draw[->] (dvi)--(pdf); %箭头
-\node at (5,1) {latex}; %标签
-\node at (15,1) {dvipdfmx}; %标签
-\end{code}
-
-\begin{out}
-\begin{tikzpicture}
-\node[box] (tex) at(0,0) {.tex};
-\node[box] (dvi) at(10,0) {.dvi};
-\node[box] (pdf) at(20,0) {.pdf};
-\draw[->] (tex)--(dvi);
-\draw[->] (dvi)--(pdf);
-\node at (5,1) {latex};
-\node at (15,1) {dvipdfmx};
-\end{tikzpicture}
-\end{out}
-
-在上例中的节点都使用了绝对位置,PGF~中还可以使用更灵活一点的相对位置。比如在下例中,dvi~节点在~tex~节点右边~50pt~处(我们前面定义的基本长度单位是~10pt),而~pdf~节点又在~dvi~节点右边~50pt~处。
-
-箭头可以换为专门用来连接节点的~\verb|edge|~;标签也改成相对位置,箭头上方~5pt~处。
-\begin{code}
-\node[box] (tex) {.tex};
-\node[box,right=5 of tex] (dvi) {.dvi};
-\node[box,right=6 of dvi] (pdf) {.pdf};
-\path (tex) edge[->] node[above=.5] {latex} (dvi)
- (dvi) edge[->] node[above=.5] {dvipdfmx} (pdf);
-\end{code}
-
-\begin{out}
-\begin{tikzpicture}
-\node[box] (tex) {.tex};
-\node[box,right=5 of tex] (dvi) {.dvi};
-\node[box,right=6 of dvi] (pdf) {.pdf};
-\path (tex) edge[->] node[above=.5] {latex} (dvi)
- (dvi) edge[->] node[above=.5] {dvipdfmx} (pdf);
-\end{tikzpicture}
-\end{out}
-
-\subsubsection{树}
-下面是一棵简单的树。我们可以用一个参数控制相邻节点的距离,预定义长度单位对此参数也会失效。
-\begin{code}
-\begin{tikzpicture}[sibling distance=80pt]
-\node[box] {TeX}
- child {node[box] {Plain\TeX}}
- child {node[box] {\LaTeX}
- child {node[box] {MiKTeX}}
- child {node[box] {TeX Live}}
- child {node[box] {MacTeX}}
- };
-\end{tikzpicture}
-\end{code}
-
-\begin{out}
-\begin{tikzpicture}[sibling distance=80pt]
-\node[box] {TeX}
- child {node[box] {Plain\TeX}}
- child {node[box] {\LaTeX}
- child {node[box] {MiKTeX}}
- child {node[box] {TeX Live}}
- child {node[box] {MacTeX}}
- };
-\end{tikzpicture}
-\end{out}
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/i18n.tex b/Master/texmf-dist/doc/generic/lnotes/src/i18n.tex
deleted file mode 100644
index bdc974649f3..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/i18n.tex
+++ /dev/null
@@ -1,73 +0,0 @@
-\chapter{中文}
-
-\section{字符集和编码}
-\label{sec:encoding}
-
-众所周知电脑内部采用二进制编码,因为它易于用电子电路实现。所有字符(包括字母、数字、符号、控制码等)在电脑内部都是用二进制表示的,字符集(Character Set)的二进制编码被称为字符编码(Character Encoding),有时人们也会混用这两个术语。
-
-1963~年发布的~American Standard Code for Information Interchange(~ASCII)是最早出现的字符编码,它用~7~位(bit)表示了~$2^7=128$个字符,只能勉强覆盖英文字符。
-
-美国人发明了电脑,英语被优先考虑是很自然的事情。随着电脑技术的传播,人们呼吁把字符编码扩充到~8~位也就是一个字节(byte),于是国际标准化组织(International Organization for Standardization,ISO)推出了~ISO 8859。$2^8=256$个字符显然也不能满足需要,所以~8859~被分为十几个部分,从~8859-1(西欧语言)、8859-2(中欧语言),直到~8859-16(东南欧语言),覆盖了大部分使用拉丁字母的语言文字。
-
-在~ISO~标准完全定型之前,IBM~就有一系列自己的字符编码,他们称之为代码页(Code Page),其中著名的有~1981~年就被用于~IBM PC~的~437(扩展~ASCII)、850(西欧语言)、852(东欧语言)。IBM~代码页通常被用于控制台(Console)环境,也就是~MS-DOS~或~Unix Shell~那样的命令行环境。
-
-微软将~IBM~代码页称为~OEM~代码页,自己定义的称为~ANSI~代码页,后者中著名的有1252(西欧语言)、1250(东欧语言)、936(GBK~简体中文)、950(Big5~繁体中文)、932(SJIS~日文)、949(EUC-KR~韩文)等。
-
-1981~年,中国大陆推出了第一个自己的字符集标准~GB2312,它是一个~$94*94$~的表,包括~7445~个字符(含~6763~个汉字)。GB2312~通常采用双字节的EUC-CN编码,所以后者也常常被称为~GB2312~编码;其实~GB2312~还有另一种编码方式~HZ,只是不常用。GB2312~不包含朱镕基的“镕”字,政府、新闻、出版、印刷等行业和部门在使用中感到十分不便,于是它在~1993~年被扩展为~GBK,后者包括~21886~个字符(含~21003~个汉字),没有形成正式标准。2000~年发布的~GB18030~包含~70244~个字符(含~27533~个汉字),采用四字节编码。GB18030~之前还出现过一个~GB13000,没有形成气候。
-
-1990~年ISO~推出了通用字符集(Universal Character Set,UCS),即~ISO 10646,意图一统江湖。它有两种编码:双字节的~UCS-2~和四字节的~UCS-4。
-
-ISO~之外还有个希望一统江湖的组织:统一码联盟(The Unicode Consortium),它于~1991~年推出了~Unicode 1.0。后来两家组织意识到没必要做重复工作,于是开始合并双方的成果,携手奔小康。从~Unicode 2.0~开始,Unicode~采用了与~ISO 10646-1~相同的编码。
-
-Unicode~主要有三种编码:UTF-8、UTF-16、UTF-32。UTF-8~使用一至四个~8~位编码。互联网工程任务组(Internet Engineering Task Force,~IETF)要求所有网络协议都支持~UTF-8,互联网电子邮件联盟(Internet Mail Consortium,IMC)也建议所有电子邮件软件都支持~UTF-8,所以它已成为互联网上的事实标准。UTF-16~用一或两个~16~位编码,基本上是~UCS-2~的超集,和~ASCII~不兼容。UTF-32~用一个~32~位编码,它是~UCS-4~的一个子集。
-
-\section{中文解决方案}
-\TeX~是基于单字节编码的,因为~Knuth~当初开发~\TeX~时没考虑那么远,也没有现成的标准可以借鉴。
-
-\LaTeX~对中文的支持主要有两种方法:张林波\footnote{中科院计算数学所某实验室主任。}开发的~\href{ftp://ftp.cc.ac.cn/pub/cct/}{CCT}~和~Werner Lemberg\footnote{1968~年生于奥地利,从维也纳音乐学院获得作曲、指挥、钢琴、乐团管理、歌手教练等五个专业文凭,后自学中文和数学。曾任职于奥地利和德国多家剧院和乐团,现任德国科布伦茨某剧院指挥。}开发的~CJK~宏包。早期~CCT~比较流行,新的~CCT~也可以和~CJK~配合使用,网上可以找到的最后更新是~2003~年的。CJK~是当前主流,它不仅支持中日韩等东亚文字,还支持几十种其他不同语言的多种编码。
-
-支持简体中文的~\LaTeX~发行版有吴凌云\footnote{中科院应用数学所研究员。}的~CTeX~和李树钧\footnote{德国哈根函授大学研究员。}的~ChinaTeX,繁体中文的有吴聪敏\footnote{台湾大学电机系学士,美国罗彻斯特大学经济学博士,现任台湾大学经济系教授。}、吴聪慧兄弟的~cwTeX~和蔡奇伟\footnote{美国犹他大学计算机博士,现任台湾静宜大学资讯工程系教授。}的~PUTeX。后面两个台湾的发行版包老师不熟悉,前面两个大陆的发行版都包含~MikTeX、CCT、CJK、WinEdt~等。
-
-\section{CJK的使用}
-CJK~的作者写的使用说明比较凌乱和晦涩,读者可以参阅李果正的《我的CJK》\citep{Lee_2004a}。
-
-CJK~有两个基本宏包:\verb|CJK|~和~\verb|CJKutf8|,后者面向~UTF-8~编码。CJK~环境的一般使用方法如下:
-
-\begin{code}
-\usepackage{CJK(utf8)}
-...
-\begin{document}
-\begin{CJK}{<encoding>}{<family>}
-...
-\end{CJK}
-\end{document}
-\end{code}
-
-简体中文常用编码是~GBK~和~UTF8~。family~是指宋体、楷体、隶书等,具体引用要看电脑上安装了什么字体。麻烦的是~GBK~和~UTF8~字体不通用,也就是说每种编码需要自己的字体。CJK~自带的~UTF8~简体字体有~gbsn(宋体)和~gkai(楷体)。CTeX~提供的~GBK~字体有~song(宋体)、fs(仿宋)、kai(楷体)、hei(黑体)、li(隶书)、~you(幼圆)等。
-
-注意使用~\verb|CJKutf8|~宏包时,\verb|CJK|~环境的编码最好是~UTF8,否则可能遭遇不测。
-
-下面是一个简单的~GBK~示例和一个~UTF8~示例,注意用编辑器保存时要选则相应的编码格式,比如前者用~ANSI,后者用~UTF-8。
-\begin{code}
-\documentclass{article}
-\usepackage{CJK}
-\begin{document}
-\begin{CJK}{GBK}{song}
-这是一个CJK例子,使用了GBK编码和song字体。
-\end{CJK}
-\end{document}
-\end{code}
-
-\begin{code}
-\documentclass{article}
-\usepackage{CJKutf8}
-\begin{document}
-\begin{CJK}{UTF8}{gbsn}
-这是一个CJK例子,使用了UTF-8编码和gbsn字体。
-\end{CJK}
-\end{document}
-\end{code}
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/introduction.tex b/Master/texmf-dist/doc/generic/lnotes/src/introduction.tex
deleted file mode 100644
index 3a2aa35e00b..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/introduction.tex
+++ /dev/null
@@ -1,111 +0,0 @@
-\chapter{简介}
-
-\begin{quotation}
-滚滚长江东逝水,浪花淘尽英雄。是非成败转头空。青山依旧在,几度夕阳红。
-
-白发渔樵江渚上,惯看秋月春风。一壶浊酒喜相逢。古今多少事,都付笑谈中。
-\begin{flushright}
----~杨慎《临江仙》
-\end{flushright}
-\end{quotation}
-
-\section{历史回顾}
-
-\LaTeX~是一种面向数学和其它科技文档的电子排版系统。一般人们提到的~\LaTeX~是一个总称,它包括~\TeX、\LaTeX、\AmS-\LaTeX~等\footnote{一般认为~\TeX~是一种引擎,\LaTeX~是一种格式,而~\AmS-\LaTeX~等是宏集。此处目的是简介,故不展开讨论。}。
-
-\TeX~的开发始于~1977~年~5~月,Donald E. Knuth\footnote{斯坦福大学计算机系教授,已退休。}开发它的初衷是用于《The Art of Computer Programming》的排版。1962~年~Knuth~开始写一本关于编译器设计的书,原计划是~12~章的单行本。不久~Knuth~觉得此书涉及的领域应该扩大,于是越写越多,如滔滔江水连绵不绝,又如黄河泛滥一发不可收拾。1965~年完成的初稿居然有~3000~页,全是手写的!据出版商估计,这些手稿印刷出来需要~2000~页,出书的计划只好改为七卷,每卷一或两章。1976~年~Knuth~改写第二卷的第二版时,很郁闷地发现第一卷的铅版不见了,而当时电子排版刚刚兴起,质量还差强人意。于是~Knuth~仰天长啸:“我要扼住命运的咽喉”,决定自己开发一个全新的系统,这就是~\TeX。
-
-1978~年~\TeX~第一版发布后好评如潮,Knuth~趁热打铁在~1982~年发布了第二版。人们现在使用的~\TeX~基本就是第二版,中间只有一些小的改进。1990~年~\TeX~ v3.0~发布后,Knuth~宣布除了修正~bug~外停止~\TeX~的开发,因为他要集中精力完成那本巨著的后几卷\footnote{已出版的前三卷是:《Fundamental Algorithms》、《Seminumerical Algorithms》、《Sorting and Searching》;第四卷《Combinatorial Algorithms》和第五卷《Syntactic Algorithms》正在写作中,预计~2015~年出版;第六卷《Theory of Context-free Languages》和第七卷《Compiler Techniques》尚未安排上工作日程。}。此后每发布一个修正版,版本号就增加一位小数,使得它趋近于$\pi$(目前是~3.141592)。Knuth~希望将来他离世时,\TeX~的版本号永远固定下来,从此人们不再改动他的代码。他开发的另一个软件~\MF~也作类似处理,它的版本号趋近于$e$,目前是~2.71828。
-
-\TeX~是一种语言也是一个宏处理器,这使得它很好很强大,但是它同时又很繁琐,让人难以接近。因此~Knuth~提供了一个对~\TeX~进行了封装的宏集~Plain \TeX,里面有一些高级命令,有了它最终用户就无须直接面对枯燥无味的~\TeX。
-
-然而~Plain \TeX~还是不够高级,所以~Leslie Lamport\footnote{现供职于微软研究院。}在~80~年代初期开发了另一个基于~\TeX~的宏集~\LaTeX。1992~年~\LaTeX~ v2.09~发布后,Lamport~退居二线,之后的开发活动由~Frank Mittelbach~领导的~The LaTeX Team~接管。此小组发布的最后版本是~1994~年的~\LaTeXe,他们同时还在进行~\LaTeX~3~的开发,只是正式版看起来遥遥无期。
-
-起初,美国数学学会(American Mathematical Society,AMS)看着\TeX~是好的,就派~Michael Spivak~写了~\AmS-\TeX,这项基于~Plain \TeX~的开发活动进行了两年(1983--1985)。后来与时俱进的~AMS~又看着~\LaTeX~是好的,就想转移阵地,但是他们的字体遇到了麻烦。恰好~Mittelbach~和~Rainer Schöpf(后者也是~LaTeX Team~的成员)刚刚发布了~New Font Selection Scheme for \LaTeX(NFSS),AMS~看着还不错,就拜托他们把~AMSFonts加入~\LaTeX,继而在~1989~年请他们开发~\AmS-\LaTeX。\AmS-\LaTeX~发布于~1990~年,之后它被整合为~\AmS~宏包,像其它宏包一样可以直接运行于~\LaTeX。
-
-\section{优点和缺点}
-当前的文字处理系统大致可以分为两种:标记语言(Markup Language)式的,比如\LaTeX;所见即所得(WYSIWYG)式的,比如~MS Word\footnote{其实~Word~也有自己的标记语言域代码(field code),只是一般用户不了解。}。
-
-一般而言,\LaTeX~相对于所见即所得系统有如下优点:
-\begin{itemize}
- \item 高质量\ 它制作的版面看起来更专业,数学公式尤其赏心悦目。
- \item 结构化\ 它的文档结构清晰。
- \item 批处理\ 它的源文件是文本文件,便于批处理,虽然解释(parse)源文件可能很费劲。
- \item 跨平台\ 它几乎可以运行于所有电脑硬件和操作系统平台。
- \item 免费\ 多数~\LaTeX~软件都是免费的,虽然也有一些商业软件。
-\end{itemize}
-
-相应地,\LaTeX~的工作流程、设计原则,资源的缺乏,以及开发人员的历史局限性等种种原因也导致了一些缺陷:
-\begin{itemize}
- \item 制作过程繁琐,有时需要反复编译,不能直接或实时看到结果。
- \item 宏包鱼龙混杂,水准参差不齐,风格不够统一。
- \item 排版风格比较统一,但因而缺乏灵活性。
- \item 用户支持不够好,文档不完善。
- \item 对国际语言和字体的支持很差。
-\end{itemize}
-
-抛开~MS Word~不谈,即使跟同为标记语言的~HTML/Web~系统相比,\LaTeX~也有一些不足之处。比如~Web~浏览器对~HTML~内容的渲染(render)比~DVI~浏览器对~\LaTeX~内容的渲染要快上许多,基本上可以算是实时。虽然~HTML~内容可能没有~LaTeX~那么复杂,但是~DVI~毕竟是已经被~\LaTeX~编译过的格式。
-
-还有一点令人困惑的是,有一部分~\LaTeX~阵营的人士习惯于称对方为“邪恶的”或“出卖灵魂的”,如果昂贵的微软系统应当为人诟病,那么更贵的苹果系统为何却被人追捧?
-
-2000~年有记者在采访~Lamport~时问:“为什么当前没有高质量的所见即所得排版系统?”他回答道:“门槛太高了,一个所见即所得系统要做到~\LaTeX~当前的水平,工作量之大不是单枪匹马所能完成\footnote{\TeX/\LaTeX~也不单单是那几个大腕儿完成的,他们背后还有众多默默无闻的小人物,比如当年~Knuth~手下的大批学生。此所谓一将功成万骨枯。}。微软那样的大公司可以做,但是市场太小了。我偶尔也会想加入“Dark Side”,让微软给我一组人马来开发一个这样的系统。”(包老师注:他果然于次年加入微软。)
-
-窃以为这两大阵营其实是萝卜青菜的关系,与其抱残守缺、互相攻讦,不如各取所需;甚至可以捐弃前嫌、取长补短,共建和谐社会。
-
-\section{软件准备}
-\label{sec:latexsoft}
-
-\LaTeX~是一个软件系统,同时也是一套标准。遵照这些标准,实现了(implement)所要求功能的软件集合被称为发行版(distribution)。与此类似的例子有~Java~和~Linux,比如SUN、IBM、BEA~等公司都有自己的~Java~虚拟机(JVM),它们都被称作~Java~的实现;而Linux~有~Red Hat/~Fedora、Ubuntu、SuSE~等众多的发行版。
-
-\begin{table}[htbp]
-\caption{\LaTeX~发行版与编辑器}
-\label{tab:latexsoft}
-\centering
-\begin{tabular}{lll}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & \href{http://www.miktex.org/}{MikTeX} & \href{http://www.toolscenter.org/}{TeXnicCenter}、\href{http://www.winedt.com/}{WinEdt} \\
- Unix/Linux & \href{http://www.tug.org/texlive/}{TeX Live} & \href{http://www.gnu.org/software/emacs/emacs.html}{Emacs}、\href{http://vim.sourceforge.net/}{vim}、\href{http://kile.sourceforge.net/}{Kile} \\
- Mac OS & \href{http://www.tug.org/mactex/}{MacTeX} & \href{http://www.uoregon.edu/~koch/texshop/}{TeXShop} \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\LaTeX~发行版只提供了一个~\LaTeX~后台处理机制,用户还需要一个前台编辑器来编辑它的源文件。常用的~\LaTeX~发行版和编辑器见\fref{tab:latexsoft}。在使用~\LaTeX~的过程中可能还需要其它一些软件,将在后面相关章节中分别介绍。
-
-\section{学习方法}
-\begin{quotation}
-在科学上没有平坦的大道,只有那些不畏劳苦沿着陡峭山路攀登的人,才有希望达到光辉的顶点。
-\begin{flushright}
----~卡尔·马克思
-\end{flushright}
-\end{quotation}
-
-\begin{quotation}
-无他,唯手熟尔。
-\begin{flushright}
----~卖油翁
-\end{flushright}
-\end{quotation}
-
-\begin{quotation}
-用心。
-\begin{flushright}
----~斯蒂芬·周
-\end{flushright}
-\end{quotation}
-
-限于篇幅和水平,本文只能提供一个概览外加一些八卦。比较严谨的入门资料有~Tobias Oetiker~的《A (Not So) Short Introduction to \LaTeXe》\citep{Oetiker_2008}(简称lshort);若想对~\LaTeX~有更深入全面的了解,可以拜读~Mittelbach~的《The \LaTeX~ Companion》\citep{Mittelbach_2004}。
-
-中文资料可参考李果正的《大家来学~\LaTeX》\citep{Lee_2004},lshort~有吴凌云等人翻译的中文版本\footnote{此译本首发于~CTeX~论坛,但是需要注册才能看见链接,所以请读者自行搜索。}。
-
-\href{http://www.ctan.org/}{Comprehensive TeX Archive Network}(CTAN)和~\href{http://www.tug.org/}{TeX Users Group}~(TUG)提供了权威、丰富的资源。
-
-\href{http://www.text.ac.uk/}{英国TUG}~和~\href{http://www.ctex.org}{CTeX}~分别提供了常见问题集(FAQ)\citep{UKTUG_FAQ,CTeX_FAQ},一般问题多会在这里找到答案。
-
-中文~\TeX~论坛有\href{http://www.smth.org/bbsdoc.php?board=TeX}{水木清华~BBS TeX~版}、\href{http://bbs.ctex.org/}{CTeX~论坛}。
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/lnotes.tex b/Master/texmf-dist/doc/generic/lnotes/src/lnotes.tex
deleted file mode 100644
index a3ac25d30eb..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/lnotes.tex
+++ /dev/null
@@ -1,296 +0,0 @@
-\documentclass[11pt]{book}
-
-%\usepackage{lnote}
-
-\usepackage{CJKutf8,CJKnumb}
-%\usepackage{CJKpunct} %a homemade package
-
-\usepackage{fancyhdr}
-\usepackage{titlesec}
-
-\usepackage{indentfirst}
-\usepackage{paralist}
-\usepackage{verbatim}
-
-\usepackage[plain]{fancyref}
-\usepackage[bookmarksnumbered,dvipdfmx,unicode, pdfborder=1,breaklinks,colorlinks,linkcolor=RoyalBlue3,urlcolor=blue]{hyperref}
-\usepackage{makeidx}
-
-\usepackage{mflogo,texnames}
-\usepackage{textcomp}
-
-\usepackage{amsmath,amsfonts,amsthm}
-
-\usepackage[x11names]{xcolor} %must before tikz, x11names defines RoyalBlue3
-\usepackage{graphicx}
-%\usepackage{ps4pdf} %conflict with tabularx
-\usepackage{pstricks,pst-plot,pst-eps}
-\usepackage{subfig}
-\def\pgfsysdriver{pgfsys-dvipdfmx.def} %put before tikz
-\usepackage{tikz}
-
-\usepackage{booktabs,tabularx,multirow,colortbl,longtable}
-
-\usepackage{chapterbib}
-\usepackage[sectionbib,super,square,sort&compress]{natbib}
-
-
-%中文设置
-\newcommand{\song}{\CJKfamily{usong}}
-\newcommand{\fang}{\CJKfamily{ufang}}
-\newcommand{\kai}{\CJKfamily{ukai}}
-\newcommand{\hei}{\CJKfamily{uhei}}
-
-%\AtBeginDvi{\special{pdf:tounicode GBK-EUC-UCS2}} %not necessary if use UTF8.
-
-%行距
-\renewcommand{\baselinestretch}{1.25}
-
-%页眉页脚
-\pagestyle{fancy}
-\fancyhf{}
-\fancyhead[LE,RO]{\thepage}
-\fancyhead[RE]{\leftmark}
-\fancyhead[LO]{\rightmark}
-\fancypagestyle{plain}{%设置plain页格式
- \fancyhf{}
- \renewcommand{\headrulewidth}{0pt}
-}
-
-%章节
-\renewcommand{\chaptername}{第\CJKnumber{\thechapter}章}
-\newcommand{\sectionname}{节}
-\renewcommand{\figurename}{图}
-\renewcommand{\tablename}{表}
-\renewcommand{\bibname}{参考文献}
-\renewcommand{\contentsname}{目~录}
-\renewcommand{\listfigurename}{图~目~录}
-\renewcommand{\listtablename}{表~目~录}
-\renewcommand{\indexname}{索~引}
-\titleformat{\chapter}[block]{\center\Huge}{\chaptername}{20pt}{}
-
-\makeindex
-
-%空白页
-\makeatletter
-\def\cleardoublepage{
- \clearpage\if@twoside\ifodd\c@page\else
- \hbox{}
- \vspace*{\fill}
- \begin{center}
- 看什么看,没见过空白页?
- \end{center}
- \vspace{\fill}
- \thispagestyle{empty}
- \newpage
- \if@twocolumn\hbox{}\newpage\fi\fi\fi
-}
-\makeatother
-
-%Code demo
-\makeatletter
-\newenvironment{mycode}{
- \noindent
- \newsavebox{\mybox}
- \begin{lrbox}{\mybox}
- \begin{minipage}[c]{.945\textwidth}
- \begin{verbatim}
-}{
- \end{verbatim}
- \end{minipage}
- \end{lrbox}%
- \setlength{\fboxsep}{8pt}
- \colorbox{demo@bgcolor}{\usebox{\mybox}}
- \setlength{\fboxsep}{\oldfboxsep}
-}
-
-\newenvironment{myoutput}{
- \noindent
- \begin{lrbox}{\@tempboxa}
- \begin{minipage}[c]{.945\textwidth}
-}{
- \end{minipage}
- \end{lrbox}%
- \setlength{\fboxsep}{8pt}
- \fbox{\usebox{\@tempboxa}}
- \setlength{\fboxsep}{\oldfboxsep}
-}
-\makeatother
-
-
-\definecolor{demo@bgcolor}{gray}{.8}
-\let\oldfboxsep\fboxsep
-\newwrite\file
-\newsavebox{\mybox}
-
-\makeatletter
-\def\demo@start{
- \begingroup% Lets Keep the Changes Local
- \@bsphack
- \immediate\openout \file \jobname.exa
- \let\do\@makeother\dospecials
- \catcode`\^^M\active
- \def\verbatim@processline{
- \immediate\write\file{\the\verbatim@line}
- }
- \verbatim@start
-}
-
-\def\demo@end{\immediate\closeout\file\@esphack\endgroup}
-
-\def\demo@code#1#2{%
- \setlength{\fboxsep}{8pt}%
- \colorbox{#1}{%
- \begin{minipage}[c]{#2}
- \setlength{\fboxsep}{\oldfboxsep}
- \small\verbatiminput{\jobname.exa}
- \end{minipage}%
- }%
-}
-
-\def\demo@out#1{%
- \setlength{\fboxsep}{8pt}%
- \fbox{%
- \begin{minipage}[c]{#1}
- \setlength{\fboxsep}{\oldfboxsep}
- \small\input{\jobname.exa}
- \end{minipage}%
- }%
-}
-
-\newenvironment{code}{
- \demo@start
-}{
- \demo@end
- \list{}{\itemindent-\leftmargin}
- \item
- \demo@code{demo@bgcolor}{.95\textwidth}
- \endlist
-}
-
-\newenvironment{halfcode}{
- \demo@start
-}{
- \demo@end
- \list{}{\itemindent-\leftmargin}
- \item
- \demo@code{demo@bgcolor}{.52\textwidth}
- \endlist
-}
-
-\newenvironment{out}{
- \demo@start
-}{
- \demo@end
- \list{}{\itemindent-\leftmargin}
- \item
- \demo@out{.95\textwidth}
- \endlist
-}
-
-\newenvironment{demo}{
- \demo@start
-}{
- \demo@end
- \list{}{\itemindent-\leftmargin}
- \item
- \makebox[\textwidth][c]{%
- \demo@code{demo@bgcolor}{.52\textwidth}%
- \hspace{10pt}%
- \demo@out{.36\textwidth}%
- }
- \endlist
-}
-
-\newenvironment{fdemo}[1]{
- \begin{lrbox}{\mybox}%
- \setlength{\fboxsep}{8pt}%
- \fbox{%
- \begin{minipage}[c]{.36\textwidth}
- \setlength{\fboxsep}{\oldfboxsep}
- \small{#1}
- \end{minipage}%
- }%
- \end{lrbox}
- \demo@start
-}{
- \demo@end
- \list{}{\itemindent-\leftmargin}
- \item
- \makebox[\textwidth][c]{%
- \demo@code{demo@bgcolor}{0.52\textwidth}%
- \hspace{10pt}%
- \usebox{\mybox}%
- }
- \endlist
-}
-\makeatother
-
-\def\reflect#1{{\setbox0=\hbox{#1}\rlap{\kern0.5\wd0
- \special{x:gsave}\special{x:scale -1 1}}\box0 \special{x:grestore}}}
-\def\XeTeX{\leavevmode
- \setbox0=\hbox{X\lower.5ex\hbox{\kern-.15em\reflect{E}}\kern-.1667em \TeX}%
- \dp0=0pt\ht0=0pt\box0 }
-
-%图形设置
-\DeclareGraphicsExtensions{.eps,.mps,.pdf,.jpg,.png}
-
-\usetikzlibrary{arrows,decorations,positioning}
-\pgfsetxvec{\pgfpoint{10pt}{0}}
-\pgfsetyvec{\pgfpoint{0}{10pt}}
-\tikzset{
- box/.style={rectangle,rounded corners=6pt,
- minimum width=40pt, minimum height=20pt, inner sep=6pt,
- draw=gray,thick,fill=lightgray},
- arrow/.style={->, shorten >=1pt, >=stealth', semithick},
- larrow/.style={->, shorten >=1pt, >=stealth', semithick},
- bloop/.style={semithick, to path={-- ++(0,-35pt) -| (\tikztotarget)}},
- rloop/.style={semithick, to path={-- ++(10pt,0) |- (\tikztotarget)}}
-}
-
-\begin{document}
-\begin{CJK*}{UTF8}{usong}
-\CJKindent %can only be used in the CJK environment
-\CJKtilde
-
-\frontmatter
-
-\title{\Huge\LaTeX~ Notes v~1.20}
-\author{Alpha Huang\footnote{\url{http://www.dralpha.com/}}}
-\date{2008年7月26日}
-\maketitle
-
-
-%\setcitestyle{numbers,square}
-
-%前言页眉
-\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
-
-\include{preface}
-\tableofcontents
-
-\mainmatter
-%正文页眉
-\renewcommand{\chaptermark}[1]{\markboth{\chaptername\ #1}{}}
-\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
-
-\include{introduction}
-\include{basics}
-\include{math}
-\include{graphics}
-\include{tables}
-\include{misc}
-\include{i18n}
-\include{fonts}
-
-\backmatter
-\include{postcript}
-
-%chapter*{索引}
-%\printindex
-
-\newpage
-
-\end{CJK*}
-
-\end{document} \ No newline at end of file
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/math.tex b/Master/texmf-dist/doc/generic/lnotes/src/math.tex
deleted file mode 100644
index a15beaffbac..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/math.tex
+++ /dev/null
@@ -1,350 +0,0 @@
-\chapter{数学}
-
-\begin{quotation}
-今有上禾三秉,中禾二秉,下禾一秉,实三十九斗;上禾二秉,中禾三秉,下禾一秉,实三十四斗;上禾一秉,中禾二秉,下禾三秉,实二十六斗。问上、中、下禾实一秉各几何?
-\begin{gather*}
-\begin{split}
- 3x+2y+z &= 39 \\
- 2x+3y+z &= 34 \\
- x+2y+3z &= 26 \\
-\end{split}
-\end{gather*}
-\begin{flushright}
---- 《九章算术》
-\end{flushright}
-\end{quotation}
-
-%\begin{quotation}
-%邺下谚曰:博士买驴,书券三纸,未有驴字。
-%\begin{flushright}
-%--- 颜之推《颜氏家训·勉学》
-%\end{flushright}
-%\end{quotation}
-
-为了使用~\AmS-\LaTeX~提供的数学功能,我们首先需要在文档的序言部分加载~\verb|amsmath|~宏包,其详细用法可参阅《amsmath User's Guide》\citep{AMS_2002}。更全面的数学内容排版可参阅~George Grätzer\footnote{匈牙利裔,加拿大~Manitoba~大学数学系教授。}的《More Math into \LaTeX, 4th Edition》\citep{Gratzer_2007}。
-%\begin{code}
-%\usepackage[options]{amsmath}
-%\end{code}
-
-\section{数学模式}
-\LaTeX~中的数学模式有两种形式:inline~和~display。前者是指在正文插入行间数学公式,后者独立排列,可以有或没有编号。
-
-行间公式用一对~\verb|$...$|~来输入,独立公式用~\verb|equation|~或~\verb|equation*|~环境来输入,有~\verb|*|~的版本不生成公式编号。
-
-前文提到~\verb|\fbox|~命令可以给文本内容加个方框,数学模式下也有类似的命令~\verb|\boxed|。
-
-\begin{demo}
-爱因斯坦的$E=mc^2$方程
-\begin{equation}
- E=mc^2
-\end{equation}
-\[ E=mc^2 \]
-\[ \boxed{E=mc^2} \]
-\end{demo}
-
-\section{基本原素}
-\subsection{字母}
-
-英文字母在数学模式下可以直接输入,希腊字母则需要用\Fref{tab:greek}~中的命令输入,注意大写希腊字母的命令首字母也是大写。
-
-\begin{table}[htbp]
-\caption{希腊字母}
-\label{tab:greek}
-\centering
-\begin{tabular}{llllllll}
- \toprule
- $\alpha$ & \verb|\alpha| & $\theta$ & \verb|\theta| &
- $o$ & \verb|o| & $\tau$ & \verb|\tau| \\
- $\beta$ & \verb|\beta| & $\vartheta$ & \verb|\vartheta| &
- $\pi$ & \verb|\pi| & $\upsilon$ & \verb|\upsilon| \\
- $\gamma$ & \verb|\gamma| & $\iota$ & \verb|\iota| &
- $\varpi$ & \verb|\varpi| & $\phi$ & \verb|\phi| \\
- $\delta$ & \verb|\delta| & $\kappa$ & \verb|\kappa| &
- $\rho$ & \verb|\rho| & $\varphi$ & \verb|\varphi| \\
- $\epsilon$ & \verb|\epsilon| & $\lambda$ & \verb|\lambda| &
- $\varrho$ & \verb|\varrho| & $\chi$ & \verb|\chi| \\
- $\varepsilon$ & \verb|\varepsilon| & $\mu$ & \verb|\mu| &
- $\sigma$ & \verb|\sigma| & $\psi$ & \verb|\psi| \\
- $\zeta$ & \verb|\zeta| & $\nu$ & \verb|\nu| &
- $\varsigma$ & \verb|\varsigma| & $\omega$ & \verb|\omega| \\
- $\eta$ & \verb|\eta| & $\xi$ & \verb|\xi| &
- & & & \\
- $\Gamma$ & \verb|\Gamma| & $\Lambda$ & \verb|\Lambda| &
- $\Sigma$ & \verb|\Sigma| & $\Psi$ & \verb|\Psi| \\
- $\Delta$ & \verb|\Delta| & $\Xi$ & \verb|\Xi| &
- $\Upsilon$ & \verb|\Upsilon| & $\Omega$ & \verb|\Omega| \\
- $\Theta$ & \verb|\Theta| & $\Pi$ & \verb|\Pi| &
- $\Phi$ & \verb|\Phi| & & \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\subsection{指数、下标、根号}
-指数或上标用~\verb|^|~表示,下标用~\verb|_|~表示,根号用~\verb|\sqrt|~表示。上下标如果多于一个字母或符号,需要用一对~\verb|{}|~括起来。
-\begin{demo}
-\[x_{ij}^2\quad \sqrt[2]{x}\]
-\end{demo}
-
-\subsection{分数}
-分数用~\verb|\frac|~命令表示,它会自动调整字号,比如在行间公式中小一点,在独立公式则大一点。\verb|\dfrac|~命令把分数的字号显式设置为独立公式中的大小,\verb|\tfrac|~命令则把字号设为行间公式中的大小。
-\begin{demo}
-$\frac{1}{2} \dfrac{1}{2}$
-\[\frac{1}{2} \tfrac{1}{2}\]
-\end{demo}
-
-\subsection{运算符}
-有些小的运算符(operator)例如~\verb|+ - * /|~等可以直接输入,另一些则需要特殊命令。完整的数学符号参见~Scott Pakin~的《The Comprehensive \LaTeX~ Symbol List》\citep{Pakin_2008}。
-\begin{code}
-\[\pm \times \div \cdot \cap \cup \geq \leq \neq \approx \equiv\]
-\end{code}
-
-\begin{out}
-\[\pm\quad \times\quad \div\quad \cdot\quad \cap\quad \cup\quad \geq\quad \leq\quad \neq\quad \approx\quad \equiv\]
-\end{out}
-
-和、积、极限、积分等大运算符用~\verb|\sum \prod \lim \int|~等表示。它们的上下标在行间公式中被压缩,以适应行高。。
-
-\begin{code}
-$\sum_{i=1}^n i \prod_{i=1}^n \lim_{x\to0}x^2 \int_a^b x^2 dx\$
-\[\sum_{i=1}^n i \prod_{i=1}^n \lim_{x\to0}x^2 \int_a^b x^2 dx\]
-\end{code}
-
-\begin{out}
-$\sum_{i=1}^n i\quad \prod_{i=1}^n\ \lim_{x\to0}x^2\ \int_a^b x^2\mathrm{d}x$
-\[\sum_{i=1}^n i\quad \prod_{i=1}^n\ \lim_{x\to0}x^2\ \int_a^b x^2\mathrm{d}x\]
-\end{out}
-
-多重积分如果用多个~\verb|\int|~来输入的话,积分号间距过宽。正确的方法是用~\verb|\iint \iiint \iiiint \idotsint|~等命令输入。从下例中可以看出两种方法的差异。
-
-\begin{out}
-\[\iint\quad \iiint\quad \iiiint\quad \idotsint\]
-\[\int\int\quad \int\int\int\quad \int\int\int\int\quad \int\dots\int\]
-\end{out}
-
-\subsection{分隔符}
-各种括号用~\verb|() [] \{\} \langle\rangle|~等命令表示,注意花括号通常用来输入命令和环境的参数,所以在数学公式中它们前面要加~\verb|\|。因为~\LaTeX~中的~\verb+|和\|+~的应用过于随意,~amsamth~宏包推荐用~\verb|\lvert\rvert|~和~\verb|\lVert\rVert|~取而代之。
-
-我们可以在上述分隔符前面加~\verb|\big \Big \bigg \Bigg|~等命令来调整大小。\LaTeX~原有的方法是在分隔符前面加~\verb|\left \right|~来自动调整大小,但是效果不佳,所以~amsmath~不推荐用这种方法。
-
-\begin{out}
-\[\Bigg(\bigg(\Big(\big((x+y)\big)\Big)\bigg)\Bigg)\quad
-\Bigg[\bigg[\Big[\big[[x+y]\big]\Big]\bigg]\Bigg]\quad
-\Bigg\{\bigg\{\Big\{\big\{\{x+y\}\big\}\Big\}\bigg\}\Bigg\}\]
-\[\Bigg\langle\bigg\langle\Big\langle\big\langle\langle x+y \rangle\big\rangle\Big\rangle\bigg\rangle\Bigg\rangle\quad
-\Bigg\lvert\bigg\lvert\Big\lvert\big\lvert\lvert x+y \rvert\big\rvert\Big\rvert\bigg\rvert\Bigg\rvert\quad
-\Bigg\lVert\bigg\lVert\Big\lVert\big\lVert\lVert x+y \rVert\big\rVert\Big\rVert\bigg\rVert\Bigg\rVert\]
-\end{out}
-
-\subsection{箭头}
-\Fref{tab:arrow}~列出了部分箭头的输入方法。另外还有两个命令生成的箭头可以根据上下标自动调整长度。
-
-\begin{table}[htbp]
-\caption{箭头}
-\label{tab:arrow}
-\centering
-\begin{tabular}{llll}
- \toprule
- $\leftarrow$ & \verb|\leftarrow| & $\longleftarrow$ & \verb|\longleftarrow| \\
- $\rightarrow$ & \verb|\rightarrow| & $\longrightarrow$ & \verb|\longrightarrow| \\
- $\leftrightarrow$ & \verb|\leftrightarrow| & $\longleftrightarrow$ & \verb|\longleftrightarrow| \\
- $\Leftarrow$ & \verb|\Leftarrow| & $\Longleftarrow$ & \verb|\Longleftarrow| \\
- $\Rightarrow$ & \verb|\Rightarrow| & $\Longrightarrow$ & \verb|\Longrightarrow| \\
- $\Leftrightarrow$ & \verb|\Leftrightarrow| & $\Longleftrightarrow$ & \verb|\Longleftrightarrow| \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\begin{demo}
-\[\xleftarrow{x+y+z}\quad
-\xrightarrow[x<y]{a*b*c}\]
-\end{demo}
-
-\subsection{标注}
-\Fref{tab:accent}~列出一些短的注音符号(accent),\Fref{tab:notation}~则列出一些长的标注符号。
-
-\begin{table}[htbp]
-\caption{数学注音符号}
-\label{tab:accent}
-\centering
-\begin{tabular}{llllllll}
- \toprule
- $\acute{x}$ & \verb|\acute{x}| & $\tilde{x}$ & \verb|\tilde{x}| & $\mathring{x}$ & \verb|\mathring{x}| \\
- $\grave{x}$ & \verb|\grave{x}| & $\breve{x}$ & \verb|\breve{x}| & $\dot{x}$ & \verb|\dot{x}| \\
- $\bar{x}$ & \verb|\bar{x}| & $\check{x}$ & \verb|\check{x}| & $\ddot{x}$ & \verb|\ddot{x}| \\
- $\vec{x}$ & \verb|\vec{x}| & $\hat{x}$ & \verb|\hat{x}| & $\dddot{x}$ & \verb|\dddot{x}| \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\begin{table}[htbp]
-\caption{长标注符号}
-\label{tab:notation}
-\centering
-\begin{tabular}{llll}
- \toprule
- $\overline{xxx}$ & \verb|\overline{xxx}| & $\overleftrightarrow{xxx}$ & \verb|\overleftrightarrow{xxx}| \\
- $\underline{xxx}$ & \verb|\underline{xxx}| & $\underleftrightarrow{xxx}$ & \verb|\underleftrightarrow{xxx}| \\
- $\overleftarrow{xxx}$ & \verb|\overleftarrow{xxx}| & $\overbrace{xxx}$ & \verb|\overbrace{xxx}| \\
- $\underleftarrow{xxx}$ & \verb|\underleftarrow{xxx}| & $\underbrace{xxx}$ & \verb|\underbrace{xxx}| \\
- $\overrightarrow{xxx}$ & \verb|\overrightarrow{xxx}| & $\widetilde{xxx}$ & \verb|\widetilde{xxx}| \\
- $\underrightarrow{xxx}$ & \verb|\underrightarrow{xxx}| & $\widehat{xxx}$ & \verb|\widehat{xxx}| \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\subsection{省略号}
-省略号用~\verb|\dots \cdots \vdots \ddots|~等命令表示,注意~\verb|\cdots|~和~\verb|\dots|~的差别。
-\begin{out}
-\[\dots\quad \cdots\quad \vdots\quad \ddots\]
-\end{out}
-
-\subsection{空白间距}
-在数学模式中,我们可以用\Fref{tab:quad}中的命令生成不同的间距,注意负间距命令~\verb|\!|~可以用来减小间距。
-
-\begin{table}[htbp]
-\caption{空白间距}
-\label{tab:quad}
-\centering
-\begin{tabular}{llll}
- \toprule
- \verb|\,| & 3/18 em & \verb|\quad| & 1 em \\
- \verb|\:| & 4/18 em & \verb|\qquad| & 2 em \\
- \verb|\;| & 5/18 em & \verb|\!| & -3/18 em \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{矩阵和行列式}
-数学模式下可以用~\verb|array|~环境来生成行列表。参数~\verb|{ccc}|~用于设置每列的对齐方式,\verb|l、c、r|~分别表示左中右;\verb|\\|~和~\verb|&|~用来分隔行和列。
-
-\begin{demo}
-\[\begin{array}{ccc}
-x_1 & x_2 & \dots \\
-x_3 & x_4 & \dots \\
-\vdots & \vdots & \ddots \\
-\end{array}\]
-\end{demo}
-
-\verb|amsmath|~有几个类似的环境:\verb|pmatrix、bmatrix、Bmatrix、vmatrix|~和~
-\verb|Vmatrix|,它们和~\verb|array|~的主要区别是会在表两端加上~$()\; []\; \{\}\; ||\; \|\|$~等分隔符,其次这些环境没有列对齐方式参数。
-
-行间公式可以用~\verb|smallmatrix|~环境来生成排列紧密的小矩阵。
-
-\section{多行公式}
-有时一个公式太长一行放不下,或几个公式需要写成一组,这时我们就要用到~\verb|amsmath|~提供的几个适合多行公式的环境。
-
-\subsection{长公式}
-对于多行不需要对齐的长公式,我们可以用~\verb|multline|~环境。
-\begin{demo}
-\begin{multline}
-x=a+b+c+\\
-d+e+f+g
-\end{multline}
-\end{demo}
-
-需要对齐的长公式可以用~\verb|split|~环境,它本身不能单独使用,因此也称作次环境,必须包含在~\verb|equation|~或其它数学环境内。\verb|split|~环境用~\verb|\\|~和~\verb|&|~来分行和设置对齐位置。
-\begin{demo}
-\[ \begin{split}
-x=&a+b+c+\\
- &d+e+f+g
-\end{split} \]
-\end{demo}
-
-\subsection{公式组}
-不需要对齐的公式组用~\verb|gather|环境,需要对齐的用~\verb|align|。
-\begin{demo}
-\begin{gather}
-a=b+c+d\\
-x=y+z
-\end{gather}
-\end{demo}
-
-\begin{demo}
-\begin{align}
-a&=b+c+d\\
-x&=y+z
-\end{align}
-\end{demo}
-
-\verb|multline、gather、align|~等环境都有带~\verb|*|~的版本,它们不生成公式编号。
-
-有多种条件的公式组用~\verb|cases|~次环境。
-\begin{demo}
-\[ y=\begin{cases}
--x & x<0\\
-x & x\geq0
-\end{cases} \]
-\end{demo}
-
-\section{定理和证明}
-\LaTeX~提供了一个~\verb|\newtheorem|~命令来定义定理之类的环境,其语法如下。
-\begin{code}
-\newtheorem{环境名}[编号延续]{显示名}[编号层次]
-\end{code}
-
-在下例中,我们定义了四个环境:定义、定理、引理和推论,它们都在一个~\verb|section|~内编号,而引理和推论会延续定理的编号。
-\begin{code}
-\newtheorem{defination}{定义}[section]
-\newtheorem{theorem}{定理}[section]
-\newtheorem{lemma}[theorem]{引理}
-\newtheorem{corollary}[theorem]{推论}
-\end{code}
-
-\newtheorem{defination}{定义}[section]
-\newtheorem{theorem}{定理}[section]
-\newtheorem{lemma}[theorem]{引理}
-\newtheorem{corollary}[theorem]{推论}
-
-定义了上述环境之后,我们就可以象下面这样使用它们。
-\begin{demo}
-\begin{defination}
-Java是一种跨平台的编程语言。
-\end{defination}
-\end{demo}
-
-\begin{demo}
-\begin{theorem}
-咖啡因会使人的大脑兴奋。
-\end{theorem}
-\end{demo}
-
-\begin{demo}
-\begin{lemma}
-茶和咖啡都会使人兴奋。
-\end{lemma}
-\end{demo}
-
-\begin{demo}
-\begin{corollary}
-晚上喝咖啡会导致失眠。
-\end{corollary}
-\end{demo}
-
-\verb|proof|环境可以用来输入下面这样的证明,它会在证明结尾输入一个~QED~符号\footnote{拉丁语~quod erat demonstrandum~的缩写。}。
-
-\begin{demo}
-\begin{proof}[命题``物质无限可分''的证明]
-一尺之棰,日取其半,万世不竭。
-\end{proof}
-\end{demo}
-
-\section{数学字体}
-和文本模式类似,数学模式下可以用\Fref{tab:math_font}~中的命令选择不同字体,其中有些字体需要加载~\verb|amsfonts|~宏包。
-
-\begin{table}[htbp]
-\caption{数学字体}
-\label{tab:math_font}
-\centering
-\begin{tabular}{ccccccc}
- \toprule
- 缺省 & \verb|\mathbf| & \verb|\mathit| & \verb|\mathsf| &
- \verb|\mathcal| & \verb|\mathbb| \\
- XNZRC & $\mathbf{XNZRC}$ & $\mathit{XNZRC}$ & $\mathsf{XNZRC}$ &
- $\mathcal{XNZRC}$ & $\mathbb{XNZRC}$ \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/misc.tex b/Master/texmf-dist/doc/generic/lnotes/src/misc.tex
deleted file mode 100644
index eed39c5f1a4..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/misc.tex
+++ /dev/null
@@ -1,322 +0,0 @@
-\chapter{杂项}
-
-\section{超链接}
-\label{sec:hyperlink}
-
-\verb|hyperref|~宏包\citep{Rahtz_2006}提供了一些超链接功能。它给文档内部的交叉引用和参考文献自动加上了超链接,还提供了几个命令。
-
-\verb|\hyperref|~命令对已经定义的label进行简单包装,加上文字描述。
-
-\begin{code}
-\usepackage{hyperref}
-...
-\label{sec:hyperlink}
-...
-例如\ref{sec:hyperlink}是编号形式的链接,而\hyperref[sec:hyperlink]{这个链接}是文字形式的链接,都指向本节开始。
-\end{code}
-
-\begin{out}
-例如\ref{sec:hyperlink}是编号形式的超链接,而\hyperref[sec:hyperlink]{这个链接}则是文字形式,都指向本节开始。
-\end{out}
-
-\verb|\url|~和~\verb|\href|~命令可以用来定义外部链接,后者有文字描述。
-
-\begin{code}
-\url{http://www.dralpha.com/}
-\href{http://www.dralpha.com/}{包老师的主页}
-\end{code}
-
-\begin{out}
-\url{http://www.dralpha.com/}
-
-\href{http://www.dralpha.com/}{包老师的主页}
-\end{out}
-
-%hyperref选项
-
-\section{长文档}
-当文档很长时,我们可以把它分为多个文件,然后在主控文档的正文中引用它们。注意~\verb|\include|~命令会新起一页,如果不想要新页可以改用~\verb|\input|~命令。
-\begin{code}
-%master.tex
-\begin{document}
-\include{chapter1.tex}
-\include{chapter2.tex}
-...
-\end{document}
-\end{code}
-
-当文档很长时,编译一遍也会很花时间,我们可以用~\verb|syntonly|~宏包。这样编译时就只检查语法,而不生成结果文件。
-\begin{code}
-\usepackage{syntonly}
-...
-\syntaxonly
-\end{code}
-
-\section{参考文献}
-在文档中,我们经常要引用参考文献(bibliography)。\LaTeX~提供的~\verb|thebibliography|~环境和~\verb|\bibtem|~命令可以用来定义参考文献条目及其列表显示格式,\verb|cite|~命令用来在正文中引用参考文献条目。这种方法把内容和格式混在一起,用户需要为每个条目设置格式,很繁琐且易出错。
-
-\subsection{BibTeX}
-1985年,~Oren Patashnik\footnote{Wiki~上说他是~Knuth~的学生,我发现他不在~Knuth~的博士生列表上,而在姚期智的博士生列表上,也许他是~Knuth~的硕士生。}和~Lamport~开发了~\BibTeX\citep{Patashnik_1988},其详细使用方法请参阅~Nicolas Markey~的《Tame the BeaST: The B to X of BibTeX》\citep{Markey_2005}
-
-\BibTeX~把参考文献的数据放在一个~\verb|.bib|~文件中,显示格式放在~\verb|.bst|~文件中。普通用户一般不需要改动~\verb|.bst|,只须维护~\verb|.bib|~数据库。
-
-一个~\verb|.bib|~文件可以包含多个参考文献条目(entry),每个条目有类型、关键字,以及题目、作者、年份等字段。常用条目类型有~article、~book、conference、manual、misc、techreport~等。每种类型都有一些自己的规定字段和可选字段,字段之间用逗号分开。数据库中每个条目的关键字要保持唯一,因为引用时要用到它们。
-
-下例显示了一个条目,它的类型是~\verb|manual|,关键字是~\verb|Markey_2005|。~\verb|.bib|~文件可以用普通文本编辑器来编辑,也可以用专门的文献管理软件来提高效率。包老师推荐~\href{http://jabref.sourceforge.net/}{JabRef}。
-
-\begin{code}
-@MANUAL{Markey_2005,
- title = {Tame the BeaST: The B to X of BibTeX},
- author = {Nicolas Markey},
- year = {2005},
- url = {http://www.ctan.org/tex-archive/info/bibtex/
- tamethebeast/}
-}
-\end{code}
-
-有了数据库,我们可以象下面这样引用一个条目。
-\begin{demo}
-请参阅\cite{Markey_2005}。
-\end{demo}
-
-前文中我们提到含有交叉引用的文档需要编译两遍。含有参考文献的文档更麻烦,它需要依次执行~\verb|latex、bibtex、latex、latex|~等四次编译操作。
-
-\begin{enumerate}
- \item 第一遍~\verb|latex|~只把条目的关键字写到中间文件~\verb|.aux|~中去。
- \item \verb|bibtex|~根据\verb|.aux、.bib、.bst|~生成一个~\verb|.bbl|~文件,即参考文献列表。它的内容就是~\verb|thebibliography|~环境和一些~\verb|\bibtem|~命令。
- \item 第二遍~\verb|latex|~把交叉引用写到~\verb|.aux|~中去。
- \item 第三遍~\verb|latex|~则在正文中正确地显示引用。
-\end{enumerate}
-
-\begin{figure}[htbp]
-\centering
-\begin{tikzpicture}
- \node[box] (tex) {.tex};
- \node[box, right=4 of tex] (aux) {.aux};
- \node[box, right=6 of aux] (bbl) {.bbl};
- \node[box, above=1.5 of aux] (bib) {.bib};
- \node[box, below=1.5 of aux] (bst) {.bst};
- \path (tex) edge [arrow] node[auto] {latex} (aux)
- (aux) edge [arrow] node[auto] {bibtex} (bbl)
- (bib.east) edge [rloop] (bst);
-\end{tikzpicture}
-\caption{\BibTeX~的编译}
-\label{fig:bibtex}
-\end{figure}
-
-注意在长文档中使用参考文献时,应该用~\verb|latex|~编译主控文档,而用~\verb|bibtex|~编译子文档。
-
-\begin{code}
-latex master(.tex)
-bibtex chapter1(.tex)
-latex master(.tex)
-latex master(.tex)
-\end{code}
-
-\subsection{natbib}
-参考文献的引用通常有两种样式:作者-年份和数字。\LaTeX~本身只支持数字样式,而~\verb|natbib|~宏包\citep{Daly_2007}则同时支持这两种样式。
-
-使用~\verb|natbib|~宏包时,我们首先要引用宏包;其次设置文献列表样式和引用样式,每种列表样式都有自己的缺省引用样式,所以后者可选;然后指定参考文献数据库。
-\begin{code}
-\usepackage{natbib}
-...
-\begin{document}
-\bibliographystyle{plainnat}
-\setcitestyle{square,aysep={},yysep={;}}
-\bibliography{mybib.bib}
-...
-\end{document}
-\end{code}
-
-\verb|natbib|~提供了三种列表样式:plainnat、abbrvnat、unsrtnat。前两种都是作者-年份样式,文献列表按作者-年份排序,后者会使用一些缩写(比如作者的~first name);unsrtnat~是数字样式,文献列表按引用顺序排序。
-
-\verb|\setcitestyle|~命令可以用来改变引用样式的设置,其选项见~\Fref{tab:citestyle}。
-
-\begin{table}[htbp]
-\caption{参考文献引用样式选项}
-\label{tab:citestyle}
-\centering
-\begin{tabular}{ll}
- \toprule
- 引用模式 & authoryear、numbers、super \\
- 括号 & round、square、open={char},close={char} \\
- 引用条目分隔符 & 分号、逗号、citesep={char} \\
- 作者年份分隔符 & aysep={char} \\
- 共同作者年份分隔符 & yysep={char} \\
- 注解分隔符 & notesep={text} \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-注意在长文档中,每个含参考文献的子文档都需要分别设置列表样式,并指定数据库。
-
-\verb|natbib|~提供了多种引用命令,其中最基本的是~\verb|\citet|~和~\verb|\citep|~,它们在不同引用模式下效果不同。一般不推荐使用~\LaTeX~本身提供的~\verb|\cite|,因为它在作者-年份模式下和~\verb|\citet|~一样,在数字模式下和~\verb|\citep|~一样。
-
-作者-年份模式下引用命令的效果如下。
-\setcitestyle{authoryear}
-\begin{demo}
-参阅\cite{Daly_2007}\\
-参阅\citet{Daly_2007}\\
-参阅\citep{Daly_2007}
-\end{demo}
-
-数字模式下引用命令的效果如下。
-\setcitestyle{numbers}
-\begin{demo}
-参阅\cite{Daly_2007}\\
-参阅\citet{Daly_2007}\\
-参阅\citep{Daly_2007}
-\end{demo}
-
-上标模式下引用命令的效果如下。
-\setcitestyle{super}
-\begin{demo}
-参阅\cite{Daly_2007}\\
-参阅\citet{Daly_2007}\\
-参阅\citep{Daly_2007}
-\end{demo}
-
-另外还有一些引用命令,如~\verb|\citetext、\citenum、\citeauthor|、~\verb|\citeyear|~等,此处不赘述。
-
-\section{索引}
-\verb|makeidx|~宏包提供了索引功能。应用它时,我们首先需要在文档序言部分引用宏包,并使用~\verb|makeindex|~命令;其次在正文中需要索引的地方定义索引,注意索引关键字在全文中须保持唯一;最后在合适的地方(一般是文档末尾)打印索引。
-
-\begin{code}
-\usepackage{makeidx}
-\makeindex
-...
-\begin{document}
-\index{索引关键字}
-...
-\printindex
-\end{document}
-\end{code}
-
-当编译含索引的文档时,用户需要执行~\verb|latex、makeindex、latex|~等三次编译操作。
-
-\begin{enumerate}
- \item 第一遍~\verb|latex|~把索引条目写到一个~\verb|.idx|~文件中去。
- \item \verb|makeindex|~把~\verb|.idx|~排序后写到一个~\verb|.ind|~文件中去。
- \item 第二遍~\verb|latex|~在~\verb|\printindex|~命令的地方引用~\verb|.ind|~的内容,生成正确的DVI。
-\end{enumerate}
-
-\begin{figure}[htbp]
-\centering
-\begin{tikzpicture}
- \node[box] (tex) {.tex};
- \node[box, right=4 of tex] (idx) {.idx};
- \node[box, right=7 of idx] (ind) {.ind};
- \node[box, right=6 of ind] (dvi) {.dvi};
- \node[box, above=1.5 of ind] (tex1) {.tex};
- \node[right=1 of ind] (point) {};
- \path (tex) edge [arrow] node[auto] {latex} (idx)
- (idx) edge [arrow] node[auto] {makeindex} (ind)
- (ind) edge [arrow] node[auto] {latex} (dvi)
- (tex1.east) edge [rloop] (point);
-\end{tikzpicture}
-\caption{索引的编译}
-\label{fig:makeidx}
-\end{figure}
-
-\section{页面布局}
-在~\LaTeX~中用户可以通过~\verb|\pagestyle|~和~\verb|\pagenumbering|~命令来设置页眉(header)、页脚(footer)的样式和内容。页面样式有以下四种。
-
-\begin{table}[htbp]
-\caption{\LaTeX~页面样式}
-\centering
-\begin{tabular}{ll}
- \toprule
- \texttt{empty} & 页眉、页脚空白 \\
- \texttt{plain} & 页眉空白,页脚含居中页码 \\
- \texttt{headings} & 页脚空白,页眉含章节名和页码 \\
- \texttt{myheadings} & 页脚空白,页眉含页码和用户自定义信息 \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\verb|fancyhdr|\citep{Oostrum_2004}宏包提供了更灵活的控制。我们可以用以下代码定制页眉、页脚的内容,以及页眉下方、页脚上方的横线。
-
-\begin{code}
-\usepackage{fancyhdr}
-...
-\pagestyle{fancy} %fancyhdr宏包新增的页面风格
-\lhead{左擎苍}
-\chead{三个代表}
-\rhead{右牵黄}
-\lfoot{左青龙}
-\cfoot{八荣八耻}
-\rfoot{右白虎}
-\renewcommand{\headrulewidth}{0.4pt}
-\renewcommand{\footrulewidth}{0.4pt}
-\end{code}
-
-\ \\
-\begin{tikzpicture}
-\draw (0,0) rectangle (36,10);
-\node at(2,9) {左擎苍};
-\node at(18,9) {三个代表};
-\node at(34,9) {右牵黄};
-\draw (.5,8)--(35.5,8);
-\node at(18,5) {和谐社会};
-\draw (.5,2)--(35.5,2);
-\node at(2,1) {左青龙};
-\node at(18,1) {八荣八耻};
-\node at(34,1) {右白虎};
-\end{tikzpicture}
-
-用户可以在页眉、页脚中使用一些~\LaTeX~变量,比如分别代表页码和章节编号的~\verb|\thepage、\thechapter、\thesection|;代表章节起始单词(Chapter、Section等)的~\verb|\chaptername、\sectionname|~等。
-
-这些变量组合起来可以构成复合标记~\verb|\leftmark|~和~\verb|\rightmark|~。当文档奇偶页面布局不同时,我们可以使用以下方法为奇偶页分别设置页眉、页脚。\verb|fancyhdr|~宏包会自动把每章起始页的样式设为~\verb|plain|,若想去掉页脚中间的页码,可以重定义~\verb|plain|~样式。
-
-\begin{code}
-\pagestyle{fancy}
-\fancyhf{} %清空页眉页脚
-\fancyhead[LE,RO]{\thepage} %偶数页左,奇数页右
-\fancyhead[RE]{\leftmark} %偶数页右
-\fancyhead[LO]{\rightmark} %奇数页左
-\fancypagestyle{plain}{ %重定义plain页面样式
- \fancyhf{}
- \renewcommand{\headrulewidth}{0pt}
-}
-\end{code}
-
-\ \\
-\begin{tikzpicture}
-\draw (0,0) rectangle (36,10);
-\node at(2.5,9) {3.2 节名};
-\node at(35,9) {17};
-\draw (.5,8)--(35.5,8);
-\node at(18,5) {奇数页};
-\end{tikzpicture}
-
-\ \\
-\begin{tikzpicture}
-\draw (0,0) rectangle (36,10);
-\node at(1,9) {18};
-\node at(32,9) {Chapter 3 章名};
-\draw (.5,8)--(35.5,8);
-\node at(18,5) {偶数页};
-\end{tikzpicture}
-
-Lamport当初设计~\LaTeX~时把页面布局变量的定义方式搞得比较晦涩,用户在重定义~\verb|\leftmark|~和~\verb|\rightmark|~时,不能直接用~\verb|\renewcommand|~的方法,而要用另外两个命令。
-
-\begin{code}
-\markboth{main-mark}{sub-mark}
-\markright{sub-mark}
-\end{code}
-
-\verb|\leftmark|~即~main-mark,是一种高层次标记,在~article~文档类中它包含~section~的信息,在~report~和~book~则包含~chapter~的信息;\verb|rightmark|~则是一种低层次标记,在~article~中包含~subsection~信息,在~report~和~book~中包含~section~信息。
-
-比如在~\verb|book|~文档类中,章节标记是通过下面的方法定义的,其中的~\verb|#1|~指的是章节的名字。
-
-\begin{code}
-\renewcommand\chaptermark[1]{\markboth{\chaptername \thechapter.
- #1}{}}
-\renewcommand\sectionmark[1]{\markright{\thesection. #1}}
-\end{code}
-
-%\section{演示文档}
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/postcript.tex b/Master/texmf-dist/doc/generic/lnotes/src/postcript.tex
deleted file mode 100644
index 0cbbe6a4727..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/postcript.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\chapter{跋}
-
-首先向一路披荆斩棘看到这里的读者表示祝贺,至少在精神上你已经成为一名合格的~\LaTeX{}er。从此你生是~\LaTeX~的人,死是~\LaTeX~的鬼。Once Black, never back。没有坚持到这里的同学自然已经重新投向“邪恶”的~MS Word,毕竟那里点个按钮就可以插入图形,点个下拉框就可以选择字体。
-
-当然~\LaTeX{}er也有简单的出路,就是只使用缺省设置,尽量少用插图;不必理会点阵、矢量,也不必理会~Type 1、Type 3、TrueType、OpenType。因为内容高于形式,你把文章的版面、字体搞得再漂亮,它也不会因此成为《红楼梦》;而《红楼梦》即使是手抄本,也依然是不朽的名著。
-
-包老师曾经以为~\LaTeX~和~Word~的关系就好像是《笑傲江湖》中华山的气宗和剑宗,头十年剑宗进步快,中间十年打个平手,再往后气宗就遥遥领先。至于令狐冲的无招胜有招,风清扬的神龙见首不见尾又是另一重境界,普通人恐怕只能望其颈背。
-
-费尽九牛二虎之力熬到本文杀青的时候,才发现从前的想法很傻很天真。让我们挥一挥衣袖,不带走一片云,卧薪尝胆忍辱负重,耐心等待~\XeTeX~和~Lua\TeX。 \ No newline at end of file
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/preface.tex b/Master/texmf-dist/doc/generic/lnotes/src/preface.tex
deleted file mode 100644
index b77fc449369..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/preface.tex
+++ /dev/null
@@ -1,31 +0,0 @@
-\chapter{序}
-
-\begin{quotation}
-满纸荒唐言,一把辛酸泪!都云作者痴,谁解其中味?\footnote{当年作博士论文时虽不曾增删五次披阅十载,也被折磨得欲仙欲死,故与室友戏言将此五绝加入序言。多年以后的今天终于实现了此夙愿。}
-\begin{flushright}
---- 曹雪芹
-\end{flushright}
-\end{quotation}
-
-最早听说~\LaTeX~大约是~2002~年,一位同事演示了用它排版的一篇文章和几幅图。包老师\footnote{吾有多重人格,比如本色的是阿黄,下围棋的是隐忍灰衣人,道貌岸然的是包老师。}不以为然,因为那些东西用~Microsoft Word~和~Visio~也可以做到,而且可以做得更快。再次听说它是王垠同学在闹退学,传说他玩~Linux~和~\LaTeX~而走火入魔。
-
-大约是~2005~年底,看了一下~lshort,用~\LaTeX~记了些数学笔记,开始有点感觉。包老师生性愚钝,所以喜欢相对简单的东西。HTML、Java~都用手写,FrontPage、Dreamweaver、JBuilder~之类笨重的家伙看两眼就扔了,所以喜欢上~\LaTeX~只是时间问题。
-
-次年老妻要写博士论文,拿出~Word~底稿让我排版。大家都知道~Word~太简单了,谁都能用,但是不是谁都能用好。人称电脑杀手的老妻制作的~Word~文档自然使出了各种奇门遁甲,加上她实验室、学校和家里电脑里的三个~EndNote~版本互不兼容,实在难以驯服。我只好重起炉灶,拿她的博士论文当小白鼠,试验一下~\LaTeX~的威力。
-
-就这样接触了两三年,总算略窥门径,感觉~\LaTeX~实在是博大精深,浩如烟海。而人到中年大脑储存空间和处理能力都有点捉襟见肘,故时常作些笔记。一来对常用资料和问题进行汇编索引,便于查询;二来也记录一些心得。
-
-日前老妻吵着要学~\LaTeX,便想这份笔记对初学者或有些许借鉴意义,于是系统地整理了一番,添油加醋包装上市。
-
-原本打算分九章,以纪念《九章算术》,实际上第八章完成时已如强弩之末,最后一章还须另择黄道吉日。
-
-本文第一章谈谈历史背景;第二章介绍入门基础;第三至五章讲解数学、插图、表格等对象的用法;第六章是一些特殊功能;第七、八章讨论中文和字体的处理;第九章附加定制内容。
-
-从难易程度上看前两章较简单,插图、字体两章较难。一般认为~\LaTeX~相对于微软的傻瓜型软件比较难学,所以这里采取循序渐进,温水煮青蛙的方法。
-
-初则示弱,麻痹读者;再则巧言令色,请君入瓮;三则舌绽莲花,诱敌深入;彼入得罄中则摧动机关,关门打狗;继而严刑拷打,痛加折磨;待其意乱情迷彷徨无计之时,给予当头棒喝醍醐灌顶,虽戛然而止亦余音绕梁。
-
-鄙人才疏学浅功力不逮,面对汗牛充栋罄竹难书\footnote{此处用法循阿扁古例。}的资料,未免考虑不周挂一漏万,或有误导,敬请海涵。若有高手高手高高手略拨闲暇指点一二,在下感激不尽\footnote{\href{mailto:huang.xingang@gmail.com}{huang.xingang@gmail.com}}
-。
-
-借此感谢一下老妻,如果不是伊天天看韩剧,包老师也不会有时间灌水和整理这份笔记。
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/reading.bib b/Master/texmf-dist/doc/generic/lnotes/src/reading.bib
deleted file mode 100644
index 9abb90c95b8..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/reading.bib
+++ /dev/null
@@ -1,914 +0,0 @@
-% This file was created with JabRef 2.3.1.
-% Encoding: UTF8
-
-@MISC{CTeX_FAQ,
- author = {中国TeX用户组},
- title = {{CTeX}常见问题集},
- year = {2005},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctex.org/CTeXFAQ/}
-}
-
-@MANUAL{Lee_2004,
- title = {大家来学LaTeX},
- author = {李果正},
- year = {2004},
- owner = {Alpha},
- review = {good},
- timestamp = {2008.04.11},
- url = {http://edt1023.sayya.org/tex/latex123/}
-}
-
-@MANUAL{Lee_2004a,
- title = {我的CJK},
- author = {李果正},
- year = {2004},
- owner = {Alpha},
- timestamp = {2008.05.12},
- url = {http://edt1023.sayya.org/tex/mycjk/}
-}
-
-@BOOK{Zhang_1997,
- title = {数学的思想、方法和应用},
- publisher = {北京大学},
- year = {1997},
- author = {张顺燕},
- review = {good}
-}
-
-@MANUAL{AMS_2002,
- title = {amsmath User's Guide},
- author = {AMS},
- year = {2002},
- owner = {Alpha},
- review = {good},
- timestamp = {2008.04.01},
- url = {http://www.ams.org/tex/amslatex.html}
-}
-
-@MANUAL{AMS_short_2002,
- title = {Short Math Guide for LaTeX},
- author = {AMS},
- year = {2002},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ams.org/tex/amslatex.html}
-}
-
-@BOOK{ATT_1989,
- title = {Unix System V/386 Release 3.2: User's Guide},
- publisher = {Prentice Hall},
- year = {1989},
- author = {AT\&T},
- review = {common}
-}
-
-@BOOK{Baker_1984,
- title = {A Concise Introduction to the Theory of Numbers},
- publisher = {Cambridge University},
- year = {1984},
- author = {Alan Baker},
- owner = {Alpha},
- review = {hard},
- timestamp = {2007.06.05}
-}
-
-@BOOK{Baker_1997,
- title = {Practical Stylist with Readings and Handbook, 8th Edition},
- publisher = {Longman},
- year = {1997},
- author = {Sheridan Baker},
- owner = {Alpha},
- timestamp = {2008.05.20},
- url = {http://www.amazon.com/exec/obidos/tg/detail/-/0321011821/}
-}
-
-@BOOK{Benz_2005,
- title = {Morningstar Guide to Mutual Funds},
- publisher = {Wiley},
- year = {2005},
- author = {Christine Benz},
- owner = {Alpha},
- review = {common},
- timestamp = {2007.11.29}
-}
-
-@BOOK{Black_2001,
- title = {The Complete Photo Guide to Home Improvement},
- publisher = {Black \& Decker},
- year = {2001},
- editor = {Philip Schmidt},
- author = {Black},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.10.30}
-}
-
-@BOOK{Brighton_2003,
- title = {Introducing Artificial Intelligence},
- publisher = {Totem},
- year = {2003},
- author = {Brighton, Henry and Selina, Howard},
- review = {Good}
-}
-
-@BOOK{Camerson_1998,
- title = {Sets, Logic and Categories},
- publisher = {Springer},
- year = {1998},
- author = {Peter J. Camerson},
- owner = {Alpha},
- review = {common},
- timestamp = {2007.07.27}
-}
-
-@BOOK{Campbell_2006,
- title = {Zero to Zillionaire},
- publisher = {Sourcebooks},
- year = {2006},
- author = {Chellie Campbell},
- owner = {Alpha},
- review = {bad},
- timestamp = {2007.05.18}
-}
-
-@MANUAL{Carlisle_2004,
- title = {The longtable Package},
- author = {David Carlisle},
- year = {2004},
- owner = {Alpha},
- timestamp = {2008.05.13},
- url = {http://www.ctan.org/pkg/longtable}
-}
-
-@MANUAL{Carlisle_2001,
- title = {The colortbl Package},
- author = {David Carlisle},
- year = {2001},
- owner = {Alpha},
- timestamp = {2008.05.13},
- url = {http://tug.ctan.org/tex-archive/macros/latex/contrib/colortbl/}
-}
-
-@BOOK{Castro_2006,
- title = {HTML, XHTML, and CSS, 6th Edition},
- publisher = {Peachpit},
- year = {2006},
- author = {Elizabeth Castro},
- owner = {Alpha},
- review = {Good for beginners},
- timestamp = {2008.02.06}
-}
-
-@MANUAL{Daly_2007,
- title = {Natural Sciences Citations and References},
- author = {Patrick W. Daly},
- year = {2007},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.mps.mpg.de/software/latex/localtex/localltx.html}
-}
-
-@BOOK{Ducharme_1994,
- title = {The Operating Systems Handbook: Unix, Openvms, Os/400, Vm, and MVS},
- publisher = {McGraw-Hill},
- year = {1994},
- author = {Ducharme, Bob},
- review = {good}
-}
-
-@BOOK{Dunphy_1991,
- title = {The Unix Industry: Evolution, Concepts, Architecture, Applications,
- and Standards},
- publisher = {QED},
- year = {1991},
- author = {Dunphy, Ed},
- review = {poor}
-}
-
-@BOOK{Elmaghraby_1978,
- title = {Activity Networks},
- publisher = {John Wiley \& Sons},
- year = {1978},
- author = {Elmaghraby, Salah Eldin},
- review = {good}
-}
-
-@BOOK{Black_2005,
- title = {Home Improvement 101},
- publisher = {Black \& Decker},
- year = {2005},
- author = {Jerri Farris and Thomas Lemmer},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.10.30}
-}
-
-@MANUAL{Fear_2005,
- title = {Publication Quality Tables in LaTeX},
- author = {Simon Fear},
- year = {2005},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/macros/latex/contrib/booktabs/}
-}
-
-@BOOK{Flanagan_2006,
- title = {JavaScript: The Definitive Guide, 5th Edition},
- publisher = {O'Reilly},
- year = {2006},
- author = {David Flanagan},
- owner = {Alpha},
- review = {good but complex},
- timestamp = {2008.02.08}
-}
-
-@BOOK{Gamow_1988,
- title = {One Two Three... Infinity: Facts and Speculations of Science},
- publisher = {Dover},
- year = {1988},
- author = {Gamow, George},
- review = {good}
-}
-
-@BOOK{Geisst_2000,
- title = {100 Years of Wall Street},
- publisher = {McGraw-Hill},
- year = {2000},
- author = {Charles R. Geisst},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.30}
-}
-
-@MISC{UKTUG_FAQ,
- author = {UK TeX User Group},
- title = {{UK List of TeX Frequently Asked Questions}},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.tex.ac.uk/faq/}
-}
-
-@BOOK{Gratzer_2007,
- title = {More Math into LaTeX},
- publisher = {Springer},
- year = {2007},
- author = {George Grätzer},
- edition = {4th},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.amazon.com/exec/obidos/tg/detail/-/0387322892/}
-}
-
-@BOOK{Mobil_2006,
- title = {Mobil Travel Guide: Northern Plains 2007},
- publisher = {Mobil Travel Guide},
- year = {2006},
- author = {Mobil Travel Guide},
- owner = {Alpha},
- review = {common},
- timestamp = {2007.12.09}
-}
-
-@BOOK{Gulbransen_2000,
- title = {Complete Idiot's Guide to XML},
- publisher = {Alpha},
- year = {2000},
- author = {Gulbransen, David},
- review = {good}
-}
-
-@BOOK{Hardy_1979,
- title = {An Introduction to the Theory of Numbers},
- publisher = {Oxford University},
- year = {1979},
- author = {G.H. Hardy and E.M. Wright},
- owner = {Alpha},
- review = {hard},
- timestamp = {2007.06.05}
-}
-
-@BOOK{Harrison_1997,
- title = {A Survival Guide to Critical Path Analysis},
- publisher = {Butterworth-Heinemann},
- year = {1997},
- author = {Harrison, Andrew},
- review = {Simple but good}
-}
-
-@BOOK{Higham_1998,
- title = {Handbook of Writing for the Mathematical Sciences},
- publisher = {Society for Industrial and Applied Mathematics},
- year = {1998},
- author = {Nicholas J. Higham},
- owner = {Alpha},
- review = {great},
- timestamp = {2008.05.20},
- url = {http://www.siam.org/books/ot63/}
-}
-
-@MANUAL{Hobby_2007,
- title = {MetaPost: A User's Manual},
- author = {John D. Hobby},
- year = {2007},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/graphics/metapost/}
-}
-
-@BOOK{Johnson_1998,
- title = {Elements of Logic via Numbers and Sets},
- publisher = {Springer},
- year = {1998},
- author = {D.L. Johnson},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.07.27}
-}
-
-@BOOK{Jones_2007,
- title = {Elementary Number Theory},
- publisher = {Springer},
- year = {1998},
- author = {Gareth A. Jones and J. Mary Jones},
- owner = {Alpha},
- review = {good, detailed},
- timestamp = {2007.07.17}
-}
-
-@BOOK{Kennedy_2007,
- title = {Resumes for Dummies},
- publisher = {Wiley},
- year = {2007},
- author = {Joyce Lain Kennedy},
- owner = {Alpha},
- review = {common},
- timestamp = {2008.02.06}
-}
-
-@MANUAL{Kern_2007,
- title = {Extending LaTeX's Color Facilities: The xcolor Package},
- author = {Uwe Kern},
- organization = {CTAN},
- year = {2007},
- owner = {Alpha},
- timestamp = {2008.04.30},
- url = {http://www.ukern.de/tex/xcolor.html}
-}
-
-@BOOK{Kidd_1994,
- title = {Agile Manufacturing: Forging New Frontiers},
- publisher = {Pearson Education},
- year = {1994},
- author = {Kidd, Paul T.}
-}
-
-@BOOK{Kline_1990,
- title = {Mathematical Thought from Ancient to Modern Times},
- publisher = {Oxford University},
- year = {1990},
- author = {Kline, Morris},
- review = {good but too long. 2004/09/20}
-}
-
-@MANUAL{Markey_2005,
- title = {Tame the BeaST: The B to X of BibTeX},
- author = {Nicolas Markey},
- organization = {CTAN},
- year = {2005},
- owner = {Alpha},
- timestamp = {2008.05.07},
- url = {http://www.ctan.org/tex-archive/info/bibtex/tamethebeast/}
-}
-
-@BOOK{Meyer_2001,
- title = {Matrix Analysis and Applied Linear Algebra},
- publisher = {Society for Industrial and Applied Mathematics},
- year = {2001},
- author = {Carl D. Meyer},
- owner = {Alpha},
- review = {great},
- timestamp = {2008.05.21},
- url = {http://www.matrixanalysis.com/}
-}
-
-@BOOK{Miller_2005,
- title = {Furniture: World Styles From Classical to Contemporary},
- publisher = {DK Adult},
- year = {2005},
- author = {Judith Miller},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.11.29}
-}
-
-@BOOK{Better_2004,
- title = {Decks Step-by-Step},
- publisher = {Better Homes \& Gardens},
- year = {2004},
- author = {Martin Miller},
- owner = {Alpha},
- timestamp = {2007.10.30}
-}
-
-@BOOK{Mitchell_2003,
- title = {Trees of North America},
- publisher = {Thunder Bay},
- year = {2003},
- author = {Alan Mitchell and David More},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.12.09}
-}
-
-@BOOK{Mittelbach_2004,
- title = {The LaTeX Companion (Tools and Techniques for Computer Typesetting)},
- publisher = {Addison-Wesley},
- year = {2004},
- author = {Frank Mittelbach and Michel Goossens and Johannes Braams and David
- Carlisle and Chris Rowley},
- edition = {2nd},
- owner = {Alpha},
- review = {good},
- timestamp = {2008.04.01},
- url = {http://www.amazon.com/exec/obidos/tg/detail/-/0201362996/}
-}
-
-@BOOK{Moder_1995,
- title = {Project Management with CPM, Pert \& Precedence Diagramming},
- publisher = {Blitz},
- year = {1995},
- author = {Moder, Joseph J. and Phillips, Cecil R. and Davis, Edward W.},
- review = {good}
-}
-
-@BOOK{Morley_1999,
- title = {The History of Furniture},
- publisher = {Bulfinch},
- year = {1999},
- author = {John Morley},
- owner = {Alpha},
- review = {common},
- timestamp = {2007.11.29}
-}
-
-@BOOK{Nisenfeld_1989,
- title = {Artificial Intelligence Handbook: Applications},
- publisher = {Instrumentation Systems},
- year = {1989},
- author = {Nisenfeld, A. Eli}
-}
-
-@MANUAL{Oetiker_2008,
- title = {A (Not So) Short Introduction to LaTeX2e},
- author = {Tobias Oetiker},
- year = {2008},
- owner = {Alpha},
- review = {good},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/info/lshort/english/}
-}
-
-@MANUAL{Oostrum_2004,
- title = {Page Layout in LaTeX},
- author = {Piet van Oostrum},
- year = {2004},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://tug.ctan.org/tex-archive/macros/latex/contrib/fancyhdr/}
-}
-
-@BOOK{Ore_1967,
- title = {Invitation to Number Theory},
- publisher = {Mathematical Association of America},
- year = {1967},
- author = {Oystein Ore},
- owner = {Alpha},
- review = {good, fun},
- timestamp = {2007.07.11}
-}
-
-@MANUAL{Pakin_2008,
- title = {The Comprehensive LaTeX Symbol List},
- author = {Scott Pakin},
- year = {2008},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/info/symbols/comprehensive/}
-}
-
-@MANUAL{Patashnik_1988,
- title = {BibTeXing},
- author = {Oren Patashnik},
- year = {1988},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/}
-}
-
-@BOOK{Pogue_1997,
- title = {Classical Music for Dummies},
- publisher = {Hungry Minds},
- year = {1997},
- author = {David Pogue and Scott Speck},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.12.09}
-}
-
-@MANUAL{Rahtz_2006,
- title = {Hypertext Marks in LaTeX: A Manual for hyperref},
- author = {Sebastian Rahtz and Heiko Oberdiek},
- year = {2006},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.tug.org/applications/hyperref/}
-}
-
-@MANUAL{Reckdahl_2006,
- title = {Using Imported Graphics in LaTeX and pdfLaTeX},
- author = {Keith Reckdahl},
- year = {2006},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/info/epslatex/english/}
-}
-
-@BOOK{Robbins_2006,
- title = {Web Design in a Nutshell, 3rd Edition},
- publisher = {O'Reilly},
- year = {2006},
- author = {Jennifer Niederst Robbins},
- owner = {Alpha},
- review = {great},
- timestamp = {2008.02.19}
-}
-
-@BOOK{Robinson_2003,
- title = {An Introduction to Abstract Algebra},
- publisher = {Walter De Gruyter},
- year = {2003},
- author = {Derek J.S. Robinson},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.07.28}
-}
-
-@MANUAL{Rokicki_2005,
- title = {Dvips: A DVI-to-PostScript Translator},
- author = {Tomas Rokicki},
- year = {2005},
- owner = {Alpha},
- timestamp = {2008.05.12},
- url = {http://tug.org/texinfohtml/dvips.html}
-}
-
-@BOOK{Ross_2000,
- title = {Introduction to Probalility Models},
- publisher = {Harcort},
- year = {2000},
- author = {Ross, Sheldon M.},
- edition = {7th Edition},
- review = {good}
-}
-
-@BOOK{Rowling_2005,
- title = {Harry Potter and the Half-Blood Prince},
- publisher = {Bloomsbury},
- year = {2005},
- author = {J. K. Rowling},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Rowling_2003,
- title = {Harry Potter and the Order of the Phoenix},
- publisher = {Bloomsbury},
- year = {2003},
- author = {J. K. Rowling},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Rowling_2000,
- title = {Harry Potter and the Goblet of Fire},
- publisher = {Bloomsbury},
- year = {2000},
- author = {J. K. Rowling},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Rowling_1999,
- title = {Harry Potter and the Prisoner of Azkaban},
- publisher = {Bloomsbury},
- year = {1999},
- author = {J. K. Rowling},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Rowling_1998,
- title = {Harry Potter and the Chamber of Secrets},
- publisher = {Bloomsbury},
- year = {1998},
- author = {J. K. Rowling},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Rowling_1997,
- title = {Harry Potter and the Philosopher's Stone},
- publisher = {Bloomsbury},
- year = {1997},
- author = {J. K. Rowling},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Sardar_1999,
- title = {Introducing Mathematics},
- publisher = {Icon},
- year = {1999},
- author = {Sardar, Ziauddin and Ravetz, Jerry and Loon, Borin Van},
- review = {great}
-}
-
-@BOOK{Schulman_1992,
- title = {Introduction to UNIX},
- publisher = {Que},
- year = {1992},
- author = {Schulman, Mark},
- review = {good}
-}
-
-@BOOK{Sheldon_2000,
- title = {The Sky is Falling},
- publisher = {HarperCollins},
- year = {2000},
- author = {Sidney Sheldon},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.07.05}
-}
-
-@BOOK{Sidney_1997,
- title = {The Best laid Plans},
- publisher = {Warner Books},
- year = {1997},
- author = {Sidney Sheldon},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Sidney_1992,
- title = {The Stars Shine Down},
- publisher = {Warner Books},
- year = {1992},
- author = {Sidney Sheldon},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Sheldon_1985,
- title = {If Tomorrow Comes},
- publisher = {Morrow},
- year = {1985},
- author = {Sidney Sheldon},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.07.02}
-}
-
-@BOOK{Smith_1998,
- title = {Introductory Mathematics: Algebra and Analysis},
- publisher = {Springer},
- year = {1998},
- author = {Geoff Smith},
- owner = {Alpha},
- review = {good, light},
- timestamp = {2007.07.13}
-}
-
-@BOOK{Solow_1990,
- title = {How to Read and Do Proofs},
- publisher = {Wiley},
- year = {1990},
- author = {Daniel Solow},
- edition = {2nd},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.07.25}
-}
-
-@BOOK{Strang_2005,
- title = {Linear Algebra and Its Applications, 4th Edition},
- publisher = {Brooks Cole},
- year = {2005},
- author = {Giblert Strang},
- owner = {Alpha},
- timestamp = {2008.06.09},
- url = {http://www.amazon.com/exec/obidos/tg/detail/-/0030105676/}
-}
-
-@BOOK{Strang_2003,
- title = {Introduction to Linear Algebra, 3rd Edition},
- publisher = {Wellesley Cambridge},
- year = {2003},
- author = {Giblert Strang},
- owner = {Alpha},
- review = {common},
- timestamp = {2008.06.09},
- url = {http://www.amazon.com/exec/obidos/tg/detail/-/0961408898/}
-}
-
-@BOOK{Strunk_2005,
- title = {Elements of Style Illustrated},
- publisher = {Penguin},
- year = {2005},
- author = {William Strunk and Elwyn B. White},
- owner = {Alpha},
- timestamp = {2008.06.10},
- url = {http://en.wikipedia.org/wiki/Elements_of_Style}
-}
-
-@MANUAL{Tantau_2008,
- title = {TikZ and PGF Manual},
- author = {Till Tantau},
- year = {2008},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://sourceforge.net/projects/pgf/}
-}
-
-@MANUAL{Tantau_2007,
- title = {User Guide to Beamer},
- author = {Till Tantau},
- year = {2007},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://latex-beamer.sourceforge.net/}
-}
-
-@BOOK{Tolkien_ROK_1988,
- title = {The Return of The King},
- publisher = {Houghton Mifflin},
- year = {1988},
- author = {J.R.R. Tolkien},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Tolkien_TT_1988,
- title = {The Two Towers},
- publisher = {Houghton Mifflin},
- year = {1988},
- author = {J.R.R. Tolkien},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Tolkien_Hobbit_1976,
- title = {The Hobbit},
- publisher = {Ballantine},
- year = {1976},
- author = {Tolkien, J.R.R.},
- review = {good}
-}
-
-@BOOK{Tolkien_FOR_1988,
- title = {The Fellowship of the Ring},
- publisher = {Houghton Mifflin},
- year = {1988},
- author = {J. R. R. Tolkien},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.05.16}
-}
-
-@BOOK{Tuthill_1990,
- title = {Knowledge Engineering: Concepts and Practices for Knowledge-Based
- Systems},
- publisher = {Tab Professional \& Reference},
- year = {1990},
- author = {Tuthill, G. Steven}
-}
-
-@BOOK{Tyson_2004,
- title = {Mutual Funds for Dummies},
- publisher = {Wiley},
- year = {2004},
- author = {Eric Tyson},
- owner = {Alpha},
- review = {common},
- timestamp = {2007.05.17}
-}
-
-@BOOK{Tyson_2001,
- title = {Home Buying for Dummies},
- publisher = {Wiley},
- year = {2001},
- author = {Eric Tyson},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.06.03}
-}
-
-@BOOK{Valade_2004,
- title = {PHP and MySQL for Dummies},
- publisher = {John Wiley \& Sons},
- year = {2004},
- author = {Valade, Janet},
- edition = {2nd Edtion}
-}
-
-@BOOK{Wallis_2000,
- title = {A Beginner's Guide to Graph Theory},
- publisher = {Birkhauser},
- year = {2000},
- author = {Wallis, W.D.},
- edition = {1st Edition}
-}
-
-@BOOK{Wels_2001,
- title = {Domain Names for Dummies},
- publisher = {Hungry Minds},
- year = {2001},
- author = {Susan Wels},
- owner = {Alpha},
- review = {good},
- timestamp = {2008.02.06}
-}
-
-@MANUAL{Wicks_1999,
- title = {Dvipdfm User's Manual},
- author = {Mark A. Wicks},
- year = {1999},
- owner = {Alpha},
- timestamp = {2008.05.12},
- url = {http://gaspra.kettering.edu/dvipdfm/}
-}
-
-@BOOK{Winston_1984,
- title = {Artificial Intelligence},
- publisher = {Addison-Wesley},
- year = {1984},
- author = {Winston, Patrick Henry},
- edition = {2nd Edittion},
- review = {good}
-}
-
-@BOOK{Wolf_2005,
- title = {A Tour through Mathematical Logic},
- publisher = {Mathematical Association of America},
- year = {2005},
- author = {Robert S. Wolf},
- owner = {Alpha},
- review = {good},
- timestamp = {2007.07.18}
-}
-
-@BOOK{Yen_1998,
- title = {Fuzzy Logic: Intelligence, Control, and Information},
- publisher = {Prentice Hall},
- year = {1998},
- author = {Yen, John and Langari, Reza}
-}
-
-@MANUAL{Zandt_2007,
- title = {PSTricks User's Guide},
- author = {Timothy van Zandt},
- year = {2007},
- owner = {Alpha},
- timestamp = {2008.04.01},
- url = {http://www.ctan.org/tex-archive/graphics/pstricks/base/doc/}
-}
-
-@BOOK{Zhang_1999,
- title = {State Space Search: Algorithms, Complexity, Extensions, and Applications},
- publisher = {Springer},
- year = {1999},
- author = {Zhang, Weixiong}
-}
-
-@BOOK{Chicago_2003,
- title = {Chicago Manual of Style, 15th Edition},
- publisher = {University of Chicago},
- year = {2003},
- editor = {UCP},
- owner = {Alpha},
- timestamp = {2008.06.10},
- url = {http://en.wikipedia.org/wiki/Chicago_Manual_of_Style}
-}
-
diff --git a/Master/texmf-dist/doc/generic/lnotes/src/tables.tex b/Master/texmf-dist/doc/generic/lnotes/src/tables.tex
deleted file mode 100644
index 84e2a94c52e..00000000000
--- a/Master/texmf-dist/doc/generic/lnotes/src/tables.tex
+++ /dev/null
@@ -1,345 +0,0 @@
-\chapter{表格}
-\label{sec:tables}
-
-\section{简单表格}
-\verb|tabular|~环境提供了最简单的表格功能。它用~\verb|\hline|~命令代表横线,\verb+|+~代表竖线,用~\verb|&|~来分栏。每个栏位的对齐方式可以用~l、c、r(左中右)来控制。
-\begin{code}
-\begin{tabular}{|l|c|r|}
- \hline
- 操作系统 & 发行版 & 编辑器 \\
- \hline
- Windows & MikTeX & TeXnicCenter \\
- \hline
- Unix/Linux & TeX Live & Emacs \\
- \hline
- Mac OS & MacTeX & TeXShop \\
- \hline
-\end{tabular}
-\end{code}
-
-\begin{tabular}{|l|c|r|}
- \hline
- 操作系统 & 发行版 & 编辑器 \\
- \hline
- Windows & MikTeX & TeXnicCenter \\
- \hline
- Unix/Linux & TeX Live & Emacs \\
- \hline
- Mac OS & MacTeX & TeXShop \\
- \hline
-\end{tabular}
-\ \\
-
-和针对插图的~\verb|figure|~环境类似,\LaTeX~还有另一个针对表格的浮动环境~\verb|table|。我们可以用它给上面的示例穿件马甲,顺便把表格简化为科技文献中常用的三线表。
-
-\begin{code}
-\begin{table}[htbp]
-\caption{浮动环境中的三线表}
-\label{tab:threesome}
-\centering
-\begin{tabular}{lll}
- \hline
- 操作系统 & 发行版 & 编辑器 \\
- \hline
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \hline
-\end{tabular}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{浮动环境中的三线表}
-\label{tab:threesome}
-\centering
-\begin{tabular}{lll}
- \hline
- 操作系统 & 发行版 & 编辑器 \\
- \hline
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \hline
-\end{tabular}
-\end{table}
-
-完美主义者可能觉得上面示例中的三条线一样粗不够美观,这时可以使用~\verb|booktabs|~宏包\citep{Fear_2005}的几个命令。
-
-\begin{code}
-\begin{table}[htbp]
-\caption{浮动环境中的三线表}
-\centering
-\begin{tabular}{lll}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
-\end{code}
-
-\begin{code}
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{\texttt{booktabs}~宏包的效果}
-\centering
-\begin{tabular}{lll}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{表格宽度}
-有时我们需要控制某栏位宽度,可以将其对齐方式参数从~\verb|l、c、r|~改为~\verb|p{宽度}|~。
-\begin{code}
-\begin{table}[htbp]
-\caption{控制栏位宽度}
-\centering
-\begin{tabular}{p{100pt}p{100pt}p{100pt}}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{控制栏位宽度}
-\centering
-\begin{tabular}{p{100pt}p{100pt}p{100pt}}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-若想控制整个表格的宽度可以使用~\verb|tabularx|~宏包,\verb|X|~参数表示某栏可以折行。
-
-\begin{code}
-\begin{table}[htbp]
-\caption{控制表格宽度}
-\centering
-\begin{tabularx}{350pt}{lXlX}
- \toprule
- 李白 & 平林漠漠烟如织,寒山一带伤心碧。暝色入高楼,有人楼上愁。玉梯空伫立,宿鸟归飞急。何处是归程,长亭更短亭。&
- 泰戈尔 & 夏天的飞鸟,飞到我的窗前唱歌,又飞去了。秋天的黄叶,它们没有什么可唱,只叹息一声,飞落在那里。\\
- \bottomrule
-\end{tabularx}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{控制表格宽度}
-\centering
-\begin{tabularx}{350pt}{lXlX}
- \toprule
- 李白 & 平林漠漠烟如织,寒山一带伤心碧。暝色入高楼,有人楼上愁。玉阶空伫立,宿鸟归飞急。何处是归程,长亭更短亭。&
- 泰戈尔 & 夏天的飞鸟,飞到我的窗前唱歌,又飞去了。秋天的黄叶,它们没有什么可唱,只叹息一声,飞落在那里。\\
- \bottomrule
-\end{tabularx}
-\end{table}
-
-\section{跨行、跨列表格}
-有时某栏需要横跨几列,我们可以使用~\verb|\multicolumn|~命令。它的前两个参数指定横跨列数和对齐方式。\verb|booktabs|~宏包的~\verb|\cmidrule|~命令用于横跨几列的横线。
-\begin{code}
-\begin{table}[htbp]
-\caption{跨栏表格}
-\centering
-\begin{tabular}{lll}
- \toprule
- & \multicolumn{2}{c}{常用工具} \\
- \cmidrule{2-3}
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{跨栏表格}
-\centering
-\begin{tabular}{lll}
- \toprule
- & \multicolumn{2}{c}{常用工具} \\
- \cmidrule{2-3}
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-跨行表格需要使用~\verb|multirow|~宏包,\verb|\multirow|~命令的前两个参数是竖跨的行数和宽度。
-\begin{code}
-\usepackage{multirow}
-...
-\begin{table}[htbp]
-\caption{跨行表格}
-\centering
-\begin{tabular}{lllc}
-\end{code}
-\begin{code}
- \toprule
- 操作系统 & 发行版 & 编辑器 & 用户体验\\
- \midrule
- Windows & MikTeX & TeXnicCenter &
- \multirow{3}{*}{\centering 爽} \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{跨行表格}
-\centering
-\begin{tabular}{lllc}
- \toprule
- 操作系统 & 发行版 & 编辑器 & 用户体验 \\
- \midrule
- Windows & MikTeX & TeXnicCenter &
- \multirow{3}{*}{\centering 爽} \\
- Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{彩色表格}
-彩色表格需要使用~\verb|colortbl|~宏包\citep{Carlisle_2001}提供的一些命令:\verb|\columncolor|、~\verb|\rowcolor|、\verb|\cellcolor|~等。
-\begin{code}
-\usepackage{colortbl}
-...
-\begin{table}[htbp]
-\caption{彩色表格}
-\centering
-\begin{tabular}{lll}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
-\end{code}
-\begin{code}
- \rowcolor[gray]{.8} Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-\end{code}
-
-\begin{table}[htbp]
-\caption{彩色表格}
-\centering
-\begin{tabular}{lll}
- \toprule
- 操作系统 & 发行版 & 编辑器 \\
- \midrule
- Windows & MikTeX & TeXnicCenter \\
- \rowcolor[gray]{.8} Unix/Linux & TeX Live & Emacs \\
- Mac OS & MacTeX & TeXShop \\
- \bottomrule
-\end{tabular}
-\end{table}
-
-\section{长表格}
-有时表格太长要跨页,可以使用~\verb|longtable|~宏包\citep{Carlisle_2004}。\verb|\endfirsthead|、~\verb|\endhead|~命令用来定义首页表头和通用表头,\verb|\endfoot|、\verb|\endlastfoot|~命令用来定义通用表尾和末页表尾。
-\begin{code}
-\usepackage{longtable}
-...
-\begin{longtable}{ll}
-\caption{长表格} \\
- \toprule
- 作者 & 作品 \\
- \midrule
- \endfirsthead
- \midrule
- 作者 & 作品 \\
- \midrule
- \endhead
- \midrule
- \multicolumn{2}{r}{接下页\dots} \\
-\end{code}
-\begin{code}
- \endfoot
- \bottomrule
- \endlastfoot
- 白居易 & 汉皇重色思倾国,\\
- & 御宇多年求不得。\\
- & 杨家有女初长成,\\
- & 养在深闺人未识。\\
- & 天生丽质难自弃,\\
- & 一朝选在君王侧。\\
- & 回眸一笑百媚生,\\
- & 六宫粉黛无颜色。\\
- & 春寒赐浴华清池,\\
- & 温泉水滑洗凝脂。\\
- & 侍儿扶起娇无力,\\
- & 始是新承恩泽时。\\
- & 云鬓花颜金步摇,\\
- & 芙蓉帐暖度春宵。\\
- & 春宵苦短日高起,\\
- & 从此君王不早朝。\\
-\end{longtable}
-\end{code}
-
-\begin{longtable}{ll}
-\caption{长表格} \\
- \toprule
- 作者 & 作品 \\
- \midrule
- \endfirsthead
- \midrule
- 作者 & 作品 \\
- \midrule
- \endhead
- \midrule
- \multicolumn{2}{r}{接下页\dots} \\
- \endfoot
- \bottomrule
- \endlastfoot
- 白居易 & 汉皇重色思倾国,\\
- & 御宇多年求不得。\\
- & 杨家有女初长成,\\
- & 养在深闺人未识。\\
- & 天生丽质难自弃,\\
- & 一朝选在君王侧。\\
- & 回眸一笑百媚生,\\
- & 六宫粉黛无颜色。\\
- & 春寒赐浴华清池,\\
- & 温泉水滑洗凝脂。\\
- & 侍儿扶起娇无力,\\
- & 始是新承恩泽时。\\
- & 云鬓花颜金步摇,\\
- & 芙蓉帐暖度春宵。\\
- & 春宵苦短日高起,\\
- & 从此君王不早朝。\\
-\end{longtable}
-
-\bibliographystyle{unsrtnat}
-\bibliography{reading}
-\newpage