diff options
Diffstat (limited to 'Master/texmf-dist/doc/fonts/amsfonts/amsfndoc.tex')
-rw-r--r-- | Master/texmf-dist/doc/fonts/amsfonts/amsfndoc.tex | 1471 |
1 files changed, 1471 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/fonts/amsfonts/amsfndoc.tex b/Master/texmf-dist/doc/fonts/amsfonts/amsfndoc.tex new file mode 100644 index 00000000000..371dbaebed6 --- /dev/null +++ b/Master/texmf-dist/doc/fonts/amsfonts/amsfndoc.tex @@ -0,0 +1,1471 @@ +%%% ==================================================================== +%%% @TeX-file{ +%%% filename = "amsfndoc.tex", +%%% version = "2.2d", +%%% date = "2002/01/19", +%%% time = "12:21:18 EST", +%%% checksum = "17515 1471 8131 61305" +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1994, 2001 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Publications Technical Group, +%%% P. O. Box 6248, +%%% Providence, RI 02940, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% keywords = "amsfonts, msam, msbm, eufm, eusm, Euler, +%%% blackboard bold, fraktur", +%%% supported = "yes", +%%% abstract = "This is part of the AMSFonts distribution. It is +%%% the plain TeX source file for the AMSFonts user's +%%% guide.", +%%% docstring = "The checksum field above contains a CRC-16 checksum +%%% as the first value, followed by the equivalent of +%%% the standard UNIX wc (word count) utility output of +%%% lines, words, and characters. This is produced by +%%% Robert Solovay's checksum utility.", +%%% } +%%% ==================================================================== + +\input amsfndoc.def +\extrafonts + +\maintitle User's Guide to AMSFonts Version 2.2d\\ + \fontsreleasedate< + +Standard distributions of \TeX{} ordinarily come with all the fonts +specified in \filename{plain.tex}, and they may also come with a number of +additional fonts intended for use with \LaTeX. Additional fonts +designed for use in mathematics and defined in \AmSTeX{} are not always +included among such font collections. For this reason, the \AMS{} has +compiled a collection, known as AMSFonts, which contains fonts of +symbols and several alphabets corresponding to symbols and alphabets +used in AMS publications, including electronic journals and the MathSci +online database. + +% Get toc from .aux file +\Contents + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{1} Contents of the AMSFonts collection + +The AMSFonts collection contains the \MF{} sources, \fn{.tfm} files and +bitmaps for the following fonts, in the sizes indicated: + +\begingroup +\raggedright +\parskip=0pt +\item{\bull} The Euler family, all but \fontname{euex} in 5, 6, 7, 8, 9, + and 10 point: +\itemitem{--} Fraktur (German), medium-weight and bold (\fontname{eufm} + and \fontname{eufb}) +\itemitem{--} ``roman'' cursive, medium-weight and bold (\fontname{eurm} + and \fontname{eurb}) +\itemitem{--} script, medium-weight and bold (\fontname{eusm} and + \fontname{eusb}) +\itemitem{--} Euler-compatible extension font (\fontname{euex}), + in 7, 8, 9, and 10 point + +\item{\bull} Additional sizes of some Computer Modern math fonts + (the 10-point fonts are included in standard \TeX\ distributions): +\itemitem{--} bold math italic (\fontname{cmmib}), in 5, 6, 7, 8, and 9 point +\itemitem{--} bold math symbols (\fontname{cmbsy}), in 5, 6, 7, 8, and 9 point +\itemitem{--} math extension font (\fontname{cmex}), in 7, 8, and 9 point + +\goodbreak +\item{\bull} Extra math symbols, in 5, 6, 7, 8, 9, and 10 point: +\itemitem{--} first series, medium-weight (\fontname{msam}) +\itemitem{--} second series, including Blackboard Bold, medium-weight + (\fontname{msbm}) + +\item{\bull} Cyrillic, developed at the University of Washington +\itemitem{--} lightface (\fontname{wncyr}), in 5, 6, 7, 8, 9, and 10 point +\itemitem{--} bold (\fontname{wncyb}), in 5, 6, 7, 8, 9, and 10 point +\itemitem{--} italic (\fontname{wncyi}), in 5, 6, 7, 8, 9, and 10 point +\itemitem{--} caps and small caps (\fontname{wncysc}), in 10 point +\itemitem{--} sans serif (\fontname{wncyss}), in 8, 9, and 10 point +\itemitem{--} virtual font property list (\filename{.vpl}) + files to enable the use of these fonts with alternate + encodings and transliteration schemes + +\item{\bull} Computer Modern caps and small caps (\fontname{cmcsc}), + in 8 and 9 point + (the 10-point font is included in standard \TeX\ distributions) + +\item{\bull} The ``dummy font'', used in \AmSTeX{} for syntax checking, + which consists only of metrics (\filename{dummy.tfm}), no character shapes + +\item{\bull} Packages for using these fonts with \LaTeX{}: +\itemitem{--} \filename{amsfonts}, a package for using the fonts + \fontname{msam}, \fontname{msbm}, and \fontname{eufm} in \LaTeX{} +\itemitem{--} \filename{amssymb}, a package for defining en masse + (instead of selectively) command names for all the math symbols + in the fonts \fontname{msam} and \fontname{msbm} +\itemitem{--} \filename{eucal}, a package for using the Euler script font + \fontname{eusm} +%\itemitem{--} \filename{eurom}, a package for using the Euler cursive +% (roman) font \fontname{eurm} +\itemitem{--} \filename{cmmib57}, a package for adapting the font + definitions for \fn{cmmib} and \fn{cmbsy} to scale from sizes 5,7,10 + instead of sizes 5,6,7,8,9,10 when the Y\&Y/Blue Sky PostScript outline + fonts are used +\itemitem{--} \filename{*.fd}, font definition files +\item{} For details, see Section 3 on using AMSFonts with \LaTeX{}. + +\item{\bull} Macro files for using these fonts with plain \TeX{}: +\itemitem{--} \filename{amssym.tex}, a file defining names for the symbols + in fonts \fontname{msam} and \fontname{msbm} +\itemitem{--} \filename{amssym.def}, a file that loads the fonts + \fontname{msam}, \fontname{msbm} and \fontname{eufm} and defines some + control sequences required by \filename{amssym.tex} +\itemitem{--} \filename{cyracc.def}, a file containing definitions needed for + proper access to characters in the cyrillic fonts + +\item{\bull} Documentation files: +\itemitem{--} \filename{amsfndoc.tex}, the source file for this User's Guide +\itemitem{--} \filename{amsfndoc.cyr}, the source file for the table showing + cyrillic input conventions, input by \filename{amsfndoc.tex} +\itemitem{--} \filename{amsfndoc.fnt}, the source file for the tables of + the principal 10-point fonts in the AMSFonts collection, input by + \filename{amsfndoc.tex}; this file may also be \TeX{}ed by itself +\itemitem{--} \filename{amsfndoc.def}, the macros used to format this + User's Guide +\itemitem{--} \filename{amsfndoc.ins}, the source file for the appendixes + to this User's Guide, input by + \filename{amsfndoc.tex}; this file may also be \TeX{}ed by itself +\itemitem{--} \filename{amsfonts.faq}, a file of Frequently Asked + Questions about AMSFonts +\itemitem{--} \filename{amsfonts.bug}, a chronicle of bug fixes and list + of known bugs still outstanding +\endgraf +\endgroup % end \raggedright + +\noindent +Each font at a particular size is provided in seven standard \TeX{} +magnifications, magsteps 0~through~5, including magstephalf (except the +{\it Textures}\slash Macintosh package, which includes +only magnifications 0 and 1; see the installation instructions). + +The philosophy under which the Euler fonts were implemented was different +from that used for Computer Modern, and the result is a lower degree of +``meta-ness''. For that reason, the appearance of these fonts is not +very good at small sizes when output on low-resolution devices, in +particular on screens. Even so, the fonts are included in AMSFonts in all +the sizes and magnifications offered, on the assumption that the printed +output will be prepared on a device of higher resolution (at least 300dpi) +where this effect will not be noticeable. + +Font charts are given in \fontchartapp. + + +\subsection{1.1} Font naming conventions + +Developers of fonts for use with \TeX, at least those using \MF, +generally try to make the names distinctive, so that a user will know +the origin of the font by the font name. For most of the fonts in the +AMSFonts collection, the first two letters identify the font source, +as follows: + +\begingroup +\raggedright +\parskip=0pt +\item{\bull} ``{\tt cm}'': These fonts are based directly on the + specifications for Knuth's Computer Modern fonts, as described + in Volume~E of \CandT{} [DEK86E]. +\item{\bull} ``{\tt eu}'': These are members of the Euler family, + described below. +\item{\bull} ``{\tt ms}'': These fonts of math symbols were developed + by or under the direction of the AMS staff. +\item{\bull} ``{\tt wn}'': These cyrillic fonts were developed at or + under the direction of the University of Washington Humanities and + Arts Computing Center, and are distributed with their permission. +\endgraf +\endgroup + +\noindent +The font called \fn{dummy} is a special case; it was developed +as part of the Stanford University \TeX{} Project, and follows no +particular naming convention. + +For information on Computer Modern fonts other than those specifically named +here, and on other fonts in general, the newsgroup {\tt comp.text.tex} +is a good source. For some other suggestions, see \furtherinfo. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{2} History of these fonts + +When the AMS began using \TeX{} to produce its publications, the available +complement of symbols was found to be inadequate. Several alphabets +used extensively as symbols were not available either. While +development of the symbols could be undertaken by in-house personnel, +using the existing \TeX{} symbol font as a model, the creation of new +Fraktur and script alphabets required the assistance of someone with +experience in font design. + + +\subsection{2.1} Euler + +With Donald Knuth's assistance and encouragement, Hermann Zapf, one of the +premier font designers of this century, was commissioned to create designs +for Fraktur and script, and for a somewhat experimental, upright cursive +alphabet that would represent a mathematician's handwriting on a blackboard +and that could be used in place of italic. The designs that resulted were +named Euler, in honor of Leonhard Euler, a prominent mathematician of the +eighteenth century. Zapf's designs were rendered in \MF{} code by graduate +students at Stanford, working under Knuth's direction; the process by which +the \MF{} fonts were implemented is described in a report by David Siegel +[DRS85]. The Euler fonts were designed to be used as math symbols; they are +not intended for setting running text. + +The Fraktur face of the Euler family has been used in production by the +AMS since it became available. However, no extensive test or use had +been made of the script or cursive until Knuth decided that they should be +used in a textbook, {\sl Concrete Mathematics}, written by him and two +co-authors [GKP88]. During the course of preparing that book, a number of +errors, particularly in spacing parameters affecting the placement of sub- +and superscripts, were discovered. All these errors have been corrected in +the medium-weight versions of the Euler fonts (almost no boldface symbols +were used in {\sl Concrete Mathematics\/}). Knuth also noticed that the +style of some symbols in the Computer Modern extension font, in particular +the integral sign, was too slanted to be attractive with Euler, and +consequently he prepared a new (partial) extension font for use with Euler. +Knuth described his experience with the Euler fonts in a \TUB\/ article +[DEK89]. In the article he also identified the macros he used and where they +can be obtained. + +The Euler fonts are sparsely populated; only the alphabetic locations are +filled in most instances (see the font charts in \fontchartapp{} for +specifics). For this reason, when processing the file for this User's +Guide, and in particular the font charts, warnings about ``Missing +characters'' are not a cause for concern. + + +\subsection{2.2} Additional Computer Modern fonts for use in math + +Only the 10-point size of the Computer Modern bold math italic (which +includes Greek), symbol, and math extension fonts are included in standard +distributions of \TeX{}. Since these symbols are often needed in +mathematics, other sizes have been constructed, using the principles +demonstrated in Knuth's {\sl Computer Modern Typefaces\/} [DEK86E], and +included in the AMSFonts collection. + + +\subsection{2.3} Symbols + +Two fonts of ``extra'' symbols are included in the AMSFonts collection. +These are named \fontname{msam} and \fontname{msbm}, and have been +implemented in ``new'' \MF{} (\mf84); they replace earlier fonts (named +\fontname{msxm} and \fontname{msym}) that were defined in old \MF{} +(\mf79)\null. These fonts contain symbols needed in the publishing program +of the AMS, including the MathSci online database, and include the +uppercase letters of an alphabet known as Blackboard Bold +($\Bbb A, \dots, \Bbb Z$). + + +\subsection{2.4} Cyrillic + +Titles of books reviewed in \MR\/ are traditionally rendered in their +original language. For books published in Russian or other Slavic +languages, this frequently requires use of the cyrillic alphabet. +A cyrillic font was developed at AMS using \MF\/79 with the \fontname{am} +fonts as a model. This font was organized in a manner suitable for use with +the transliteration scheme adopted by {\sl MR\/} in 1980, and contained only +those letters which appear in current mathematical literature. +In particular, this meant that the letters dropped from the Russian +alphabet after the Revolution of 1917, and some letters used in non-Slavic +languages now rendered in cyrillic (such as Azerbaijani, from which no +mathematical literature is currently reviewed in {\sl MR\/}) were absent. + +In 1988, the Humanities and Arts Computing Center of the University of +Washington undertook a font development project for support of scholars +in Slavic languages. The fonts developed through this project include +several different font layouts. One layout is based on that of the +original AMS cyrillic augmented with `{\cyr \u\i}' (cyrillic short `i'), +`{\cyr\"e}' (umlauted `e'), and several pre-Revolutionary letters. +The fonts with the AMS layout are included in the AMSFonts collection +with the permission of the University of Washington developers. +%For information on cyrillic fonts with other layouts, see \furtherinfo. +``Virtual property list'' (\fn{.vpl}) files are also included in the +collection to support several other layouts; these can be found in the +\fn{cyr-alt} area, and are accomanied by a \fn{README} file with +further information. + +The cyrillic fonts are based on Computer Modern letter shapes. +Type styles include ordinary upright, bold (based on CM bold +extended), caps and small caps, italic, and upright sans serif. +The principal text fonts (upright, italic and boldface) are present in +sizes from 5 through 10 point; +sans serif is in sizes 8, 9 and 10 point; +caps and small caps are in 10 point only. +See also \typeiapp{} for information on a PostScript (Type~1) version +of the cyrillic fonts, in particular concerning the sizes provided in +that format. + + +\subsection{2.5} Caps/small caps + +The font \fontname{cmcsc10} is referenced in \filename{plain.tex} and +should be included in all standard \TeX{} distributions. However, Knuth +did not generate this font in any other sizes. The AMSFonts collection +includes 8 and 9-point sizes, generated according to the same principles as +other CM fonts of these sizes. + + +\subsection{2.6} Dummy font + +The dummy font contains no ligature or kerning information, and all +dimensions and parameter values are set to zero. This is a pseudo-font, +which has only general font metrics and no characters. No \filename{.pk} +or \filename{.gf} files are needed for this font; it is provided only in +\filename{.tfm} and \filename{.mf} form. + +The dummy font is used in \AmSTeX{} to implement ``syntax checking''. +(Syntax checking is activated by the |\printoptions| command as +described in \JoT{} [MDS86].) In this mode, the dummy font replaces all +the usual ``printing'' fonts, so that \TeX{} never accumulates any text +to be set, and never tries to write out a page, but in the process of +reading the input file, checks all control sequences for syntactic +correctness. In this mode, an input file will be processed perhaps 30 +percent faster than if it were actually being set. However, some errors +and conditions are not detected during a syntax check; in particular, +overfull boxes cannot be detected until setting actually occurs. + + +\subsection{2.6} PostScript (Type 1) implementation of AMSFonts + +The AMSFonts are available in Type~1 outline form as an alternative +to the bitmap images generated by \MF. The Type~1 files are not +part of the regular AMSFonts distribution, but can be obtained at +no charge from the AMS server. For details, see \typeiapp. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{3} How to use AMSFonts with \LaTeX{} + +\subsection{3.1} General + +These instructions are for current \LaTeX{} (version 2$\varepsilon$, dated +January 1995 or later). If you have version 2.09 of \LaTeX{}, dated 1993 or +earlier, you must upgrade to current \LaTeX{}. Earlier versions of \LaTeX{} +are no longer supported for AMSFonts; however, the \LaTeX{} compatibility +mode will usually allow documents prepared for version 2.09 to be processed +with the current version. + +To use the AMSFonts collection with \LaTeX{} you choose from an +assortment of \LaTeX{} ``packages'' that provide various kinds of access +to the fonts, calling the packages that you need in a given document +through standard \LaTeX{} \cn{usepackage} statements. For example, the +statement +\begintt +\usepackage{amsfonts} +\endtt +calls in the \pkg{amsfonts} package, which provides blackboard bold +and Fraktur letters and selective access to the math symbol fonts +\fn{msam} and \fn{msbm}. + +These packages are currently available: + +\begingroup +\raggedright +\parskip=0pt +\item{\bull} {\tt amsfonts} -- for blackboard bold letters, Fraktur letters, + and miscellaneous symbols +\item{\bull} {\tt amssymb} -- superset of the \pkg{amsfonts} package, defines + the full set of symbol names for the \fn{msam} and \fn{msbm} fonts +\item{\bull} {\tt eufrak} -- for Fraktur letters; redundant if \fn{amsfonts} + is used +\item{\bull} {\tt eucal} -- Makes \cn{mathcal} use Euler script instead of + the usual Computer Modern calligraphic alphabet +\item{\bull} {\tt euscript} -- old name of the \pkg{eucal} package, now + obsolete but included for convenience in printing pre-existing documents +%\item{\bull} {\tt eurom} -- for Euler cursive (roman) letters +\endgraf +\endgroup + +All of the above packages have a `\opt{psamsfonts}' option that should +be used if and only if your copy of the AMSFonts collection is the +Y\&Y/Blue Sky Research PostScript version. In that version, the font +files are not provided in all the sizes (5,6,7,8,9,10), but only in sizes +5,7,10, with sizes 6,8,9 produced by interpolation. In practice it's +easy to tell if you need to use the \opt{psamsfonts} option: you'll get +an error message about a missing \fn{.tfm} file: +\begingroup \parindent0pt +\begintt +! Font \U/AMSa/m/n/9=msam9 not loadable: Metric (TFM) file not found. +\endtt +\endgroup +where the mentioned font name is one of the AMS font names (\fn{msam}, +\fn{msbm}, \fn{eufm}, etc.), and the font size is 6, 8, or 9. +If this happens to you, look at your \cn{usepackage} statements and +change +$$\hbox{|\usepackage{amssymb}|\qquad to\qquad +|\usepackage[psamsfonts]{amssymb}|}$$ +or +$$\hbox{|\usepackage{eucal}|\qquad to\qquad +|\usepackage[psamsfonts]{eucal}|}$$ +and so forth. + +If you are using an AMS document class (\fn{amsart}, \fn{amsbook}, +\fn{amsproc}) or an AMS author package, apply the option \fn{[psamsfonts]} +to \cn{documentclass} as well. + +\Warn Adding the option \fn{[psamsfonts]} to an existing file may + result in changed line and page breaks, owing to the fact that sizes + 6, 8, and 9 are produced by interpolation. +\endx + +Use of the PostScript AMSFonts is explicitly marked in individual +documents because the interpolation process used produces character +metrics that are not identical with those of the noninterpolated font +files for the corresponding sizes. If these discrepancies were simply +ignored, {\it there would be no warning} of unexpected changes in line +or page breaks that might occur in documents exchanged between colleagues. +As it is, if you find it necessary to add or remove the \fn{psamsfonts} +option in order to print a colleague's document, you are free to go ahead +and do so, but the fact that you must make that change should be understood +as a reminder that a small possibility of changed line breaks or page +breaks does exist. + +A package \pkg{cmmib57} provides analogous font +definitions for the fonts \fn{cmmib} and \fn{cmbsy} (yes, both in the +same package, despite the name), for those users who have the Y\&Y/Blue +Sky Research PostScript versions of those fonts. Typical usage is: +\begintt +\documentclass{article} +\usepackage{cmmib57} +\endtt + + +\subsection{3.2} Computer Modern bold math italic and symbols + +The package \pkg{amsbsy} (part of the \AmS-\LaTeX{} distribution) defines +two commands to obtain bold symbols: + +\begingroup +\smallskip +\description +\item {\cn{boldsymbol}} -- for bold numbers and other nonalphabetic symbols, + as well as bold Greek letters, which cannot be made bold via the \cn{mathbf} + command, and bold math italic letters +\item {\cn{pmb}} -- ``poor man's bold'', which overlays multiple copies + of the same symbol with slight offsets, for cases where \cn{boldsymbol} + does not work, e.g., a bold font is not available +\enddescription +\endgroup + +\noindent +\cn{boldsymbol} can also be used to obtain bold letters from the Euler fonts. + +These commands are valid in math mode only. For example, +\begintt +$$\boldsymbol{\beta} \pmb{\boxdot} +\boldsymbol{\Omega} \boldsymbol+ \pmb{\mathbb{R}}$$ +\endtt +(Since this User's Guide is not prepared with \LaTeX{}, getting output +for this expression is left as an exercise to the user.) + + +\subsection{3.3} Blackboard bold letters (uppercase only) + +The \pkg{amsfonts} package defines a ``math alphabet'' command \cn{mathbb} +for printing letters of the blackboard bold alphabet that resides in the +\fn{msbm} font. This alphabet is restricted to uppercase only (no +lowercase, no numerals). The suggested method for defining a \cn{R} +command to print a blackboard bold R is as follows: +\begintt +\usepackage{amsfonts} +\newcommand{\R}{\mathbb{R}} +\endtt + + +\subsection{3.4} Extra math symbols + +The \pkg{amssymb} package defines math symbol commands for all the extra +math symbols in the \fn{msam} and \fn{msbm} fonts, as listed in the +table in Section 7. Thus if you want to use the \cn{blacktriangle} +$\blacktriangle$ and \cn{nsubseteq} $\nsubseteq$ symbols, the easiest +way is to put the statement +\begintt +\usepackage{amssymb} +\endtt +in the preamble of your document. + +If you want more selective access to the math symbols in those fonts +you can use the \pkg{amsfonts} package instead and define math symbol +commands individually using \LaTeX{}'s \cn{DeclareMathSymbol} +(cf.\ [LFG] or [GMS94]): +\begintt +\usepackage{amsfonts} +\DeclareMathSymbol{\blacktriangle}{\mathord}{AMSa}{"4E} +\DeclareMathSymbol{\nsubseteq}{\mathrel}{AMSb}{"2A} +\endtt +This alternative might be useful to you if adding the \pkg{amssymb} +package to your document leads to an error message of the form +\begintt +! TeX capacity exceeded, sorry (hash size=3000) +\endtt +This could happen if you have an older version of \TeX{} with a +relatively low limit on the number of commands that can be defined in a +single document. (But in that case, note that there may be configuration +options for increasing that limit; check the documentation for your +\TeX{} system.) + +Since \cn{DeclareMathSymbol} is used in the \pkg{amssymb} package, the +definitions for particular symbols can be borrowed from there (file +\fn{amssymb.sty}). Alternatively, the values can be obtained from the +tables in Section 7.2, as follows: + +\begingroup +\raggedright +\item{\bull} First digit identifies font: +\itemitem{1} AMSa +\itemitem{2} AMSb +\item{\bull} Second digit identifies class: +\itemitem{0} \cn{mathord} +\itemitem{2} \cn{mathbin} +\itemitem{3} \cn{mathrel} +\item{\bull} Third and fourth digits identify (hex) location in font. +\endgraf +\endgroup + + +\subsection{3.5} Euler Fraktur letters + +A math alphabet command \cn{mathfrak} for using Fraktur letters such as +$\mathfrak{A}\;\mathfrak{m}\;\mathfrak{g}\;\mathfrak{H}$ in math can be +obtained by using any of the packages \pkg{amssymb}, \pkg{amsfonts}, or +\pkg{eufrak}. + + +\subsection{3.6} Euler script letters (uppercase only) + +The main purpose of the \pkg{eucal} package is to change \LaTeX{}'s +\cn{mathcal} command so that it produces Euler script instead of +Computer Modern calligraphic letters: +\ctab{\hfil#\tabskip1em& + #ABCDEFGHIJKLMNOPQRSTUVWXYZ\hfil} +CM calligraphic:& \tensy\\ +Euler script:& \teneusm +\endctab +There is also an option \opt{mathscr} for the \pkg{eucal} package that +causes Euler script to be associated to a \cn{mathscr} command, leaving +the \cn{mathcal} command unaffected. This imitates the behavior of the +predecessor package \pkg{euscript}. + + +%\subsection{3.7} Euler cursive (roman) letters +% +%Math alphabet commands \cn{matheurm} and \cn{matheurb} are defined by +%the package \pkg{eurom} for medium weight and bold forms of the Euler +%cursive letters respectively, for example, \matheurm{A}, \matheurb{A}, +%\matheurm{B}, \matheurb{B}. + + +\subsection{3.7} University of Washington Cyrillic fonts + +There is no AMS package for \LaTeX{} at the present time to support the +use of Cyrillic languages in \LaTeX{} documents with the \fn{wncy*} +fonts. Producing a proper Cyrillic package involves rather difficult +questions of input and output encodings, for which it would be useful to +rely on general mechanisms provided by \LaTeX{}. + +If you require these fonts, you can consult the \LaTeX{} documentation +[LFG], [L94] and use directly the commands described there, such as +\cn{DeclareFontFamily}, \cn{DeclareFontShape}, and \cn{symbol}. A scheme +for accessing letters that don't correspond to the 26-letter Latin alphabet +will be needed; the file \fn{cyracc.def} can be used as a starting point. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{4} How to use AMSFonts with \AmSTeX{} + +In \JoT{}, Michael Spivak describes various fonts that are used in +mathematics in addition to the fonts provided with the standard +distributions of \TeX. Two references in particular are of interest with +respect to AMSFonts: the section {\bf Fonts in math mode} in Chapter 19, +and Appendix G, {\bf Further fonts}. The first describes the use of +letters from alphabets, including Fraktur, and the second, mostly +nonalphabetic symbols. + +Instructions for using the fonts of the AMSFonts collection with \AmSTeX{} +are also given in the {\sl User's Guide to \AmSTeX{} Version~2.2\/} [AMS01] +and in Appendix~G of editions of \JoT{} [MDS90] dated 1990 or later. + +Additional fonts to be used with \AmSTeX{} should be specified at the top +of the document input file, in what is known as the ``preamble''. The +arrangement of commands at the top of an input file is the following: +\begintt +\input amstex +\documentstyle{...} +|<preamble commands> +\endtt + +\AmSTeX{} provides a simple method for accessing most of the fonts in the +AMSFonts collection. The two extra symbol fonts and Euler Fraktur are +loaded automatically by the preprint style (\filename{amsppt.sty}). +If you are using \AmSTeX{}, but not the preprint style, the method used to +load these fonts and define the associated symbol names depends on how many +symbols will be needed. If a lot of the symbols will be needed, or +you aren't worried about memory space and just want to do what is easiest, +all three fonts will be loaded and the symbol names defined if you type the +command |\UseAMSsymbols| in the preamble. This will load the file +\filename{amssym.tex}, in which all the symbol names (more than 200 of them) +are defined. If only a few symbols from these fonts are needed, the +commands |\loadmsam|, |\loadmsbm|, and |\loadeufm| will load the +medium-weight versions of the two extra symbol fonts and Euler Fraktur +respectively. The command |\newsymbol| can then be used to define just +those symbols that are needed; its use is described in Section 7, +{\bf Using the extra symbols}.% +\footnote{*}{Additional fonts from the AMSFonts collection can be accessed + easily in \AmSTeX{}. + However, users should be aware that \TeX{} limits the number of + math mode font families to 16, of which 11 are predefined in \AmSTeX{}. + Only those additional families should be activated that will actually + be used in a document, to avoid exceeding the limit.} + +Two sizes of fonts, suitable for body text and for passages requiring smaller +type (e.g.\ abstracts and footnotes), are incorporated in the preprint style +\filename{amsppt.sty}. These are accessed through the control sequences +|\tenpoint| and |\eightpoint|, which are ordinarily referred to only by +higher-level commands that identify the kind of text being input (e.g.\ +|\title|, |\abstract|, |\footnote|). Most fonts in the AMSFonts collection +have |\load...|\ instructions defined in \AmSTeX{} and will be accessed +properly for use with the preprint style when the |\load| instructions are +included in the preamble of the document input. If you are not using the +preprint style, you can use the font definitions in \filename{amsppt.sty} as a +model. + +If you are using the PostScript version of the AMSFonts developed by +Y\&Y/Blue Sky Research, only selected sizes (5, 7 and 10) are provided, and +the other sizes are produced by interpolation. With the \AmSTeX{} preprint +style, use the command \cn{PSAMSFonts}, placed after the \cn{documentstyle} +line and before \cn{topmatter} and \cn{document}, to access these fonts +correctly. Papers and monographs submitted to the AMS for publication are +required to use this command. + +\Warn Adding the command \cn{PSAMSFonts} to an existing file may result + in changed line and page breaks, owing to the fact that sizes + 6, 8, and 9 are produced by interpolation. +\endx + +\subsection{4.1} Euler + +The Euler fonts are defined only in math mode, in sizes appropriate for +text and two orders of sub- and superscripts. They can be activated by +invoking the proper |\load| instructions before the |\documentstyle| +command, in the preamble of a paper in which the fonts are to be used. +(The medium-weight Fraktur font is activated automatically by the preprint +style.) The Euler fonts can be activated by the following commands: + +\begingroup +\smallskip +\parskip=0pt +\def\1 #1 {\item{}{\tt\bs#1}\qquad\ignorespaces} +\1 loadeufm Euler Fraktur medium (automatic with the preprint style) +\1 loadeufb Euler Fraktur bold +\1 loadeurm Euler cursive medium +\1 loadeurb Euler cursive bold +\1 loadeusm Euler script medium +\1 loadeusb Euler script bold +\endgraf +\endgroup + +After the \fontname{eufm} font has been loaded, the medium-weight Fraktur +letters can be produced by typing |\frak| followed by the desired letter. +For example, |$\frak g \frak A$| yields $\frak g \frak A$. \AmSTeX{} 2.1 also +defines |\eufm|, |\eufb|, |\eurm|, |\eurb|, |\eusm| and |\eusb|. + + +\subsection{4.2} Computer Modern bold math italic and symbols + +The Computer Modern bold math italic (\fontname{cmmib}) and bold math +symbol (\fontname{cmbsy}) fonts can both be loaded in \AmSTeX{} by the +command |\loadbold|; there are no predefined commands to load them separately. +|\loadbold| must be invoked in the preamble of the document input file. + +A rather elaborate mechanism has been defined in \AmSTeX{} to simplify +access to bold letters and symbols, in math mode only. Three control +sequences are available, each of which affects a particular class of +characters: + +\begingroup +\smallskip +\parskip=0pt +\setbox0=\hbox{\tt xboldsymbol} +\def\1 #1 {\item{}\hbox to\wd0{\tt\bs#1\hfil}\qquad\ignorespaces} +\1 bold for a single letter or numeral +\1 boldkey for other symbols that appear on the keyboard +\1 boldsymbol for a symbol specified by a single control sequence +\endgraf +\endgroup +\noindent +These facilities are described in more detail in the {\sl User's Guide to +\AmSTeX{} Version~2.2\/} [AMS01] and editions of \Joy\/ published in 1990 +or later [MDS90]. + + +\subsection{4.3} Computer Modern math extension font + +Smaller sizes of the math extension font are appropriate for use in text +smaller than ten-point and in sub- and superscripts. They are provided +automatically for these environments in the preprint style. If you are +not using the preprint style, you can use the font definitions in either +\filename{amsppt.sty} or Appendix~E of \TB\/ [DEK86A] as a model. + + +\subsection{4.4} Extra symbols + +The medium-weight versions of the two extra symbol fonts are available +automatically, including all the symbol names, if you are using the preprint +style or if you have specified |\input amssym|. If you wish to load these +fonts separately, use the appropriate control sequence |\loadmsam| or +|\loadmsbm| in the preamble of your document. If you load the fonts +separately, a few symbols will be defined when one of the fonts is loaded, +but most must be defined using the |\newsymbol| command before they can be +used. See Section 7, {\bf Using the extra symbols}, for +information on both the symbol names and on using |\newsymbol| to define them. + + +\subsection{4.5} Cyrillic + +Cyrillic is not referred to in the \AmSTeX{} files as distributed. +The cyrillic fonts included in AMSFonts are intended for use mainly in text, +not as symbols in math. Detailed instructions for loading and using cyrillic +appear below in Section 6, {\bf Using cyrillic}. + + +\subsection{4.6} Caps/small caps + +Caps/small caps are loaded automatically by the \AmSTeX{} preprint style +for use in ten-point and eight-point text. If you are not using the preprint +style, you can use the font definitions in either \filename{amsppt.sty} +or Appendix~E of \TB\/ [DEK86A] as a model. + + +\subsection{4.7} Dummy font + +No special action is needed to use the dummy font with \AmSTeX{}. +It is already built into the syntax checking procedure. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{5} How to use AMSFonts with plain \TeX{} or other macro packages + +If you are not using \LaTeX{} or \AmSTeX{} then there are too many +variables for us to provide much specific guidance. It will be necessary +to assume that you either have some experience with \TeX{} macros or +have a \TeX nician available to help you. However, some general +guidelines may be helpful. + +Two models for defining fonts should be accessible to most users: +\item{\bull} Appendix E of \TB\/ contains size-specific font definitions + for \hbox{|\tenpoint|}, \hbox{|\ninepoint|} and |\eightpoint| that permit + size-switching, including support of mathematics. +\item{\bull} \filename{amsppt.sty}, the file of macros supporting the + \AmSTeX{} preprint style, contains similar font definitions, |\tenpoint| + and |\eightpoint|. + +The font-size-switching facilities of \LaTeX{} are not recommended as a +model because they include many features (such as loading fonts on demand) +that make them too complex to be copied easily for uses outside of +\LaTeX{} except by someone with substantial \TeX{} expertise. + +Before attempting to load all available fonts into every \TeX{} job, +determine (if you can) how many fonts can be accommodated by the +implementation of \TeX{} you are using. It is generally a good idea to +load seldom-used fonts selectively. + + +\subsection{5.1} Euler + +The following commands will load the medium-weight Euler Fraktur font, and +can be used as a model for accessing the other Euler fonts. +\begintt +\font\teneufm=eufm10 +\font\seveneufm=eufm7 +\font\fiveeufm=eufm5 +\newfam\eufmfam +\textfont\eufmfam=\teneufm +\scriptfont\eufmfam=\seveneufm +\scriptscriptfont\eufmfam=\fiveeufm +\def\eufm#1{{\fam\eufmfam\relax#1}} +\endtt + +Individual letters in the Euler fonts are accessible by the ordinary +letters on your keyboard, once the font has been loaded and named by +a control sequence equivalent to |\eufm|. + +The medium-weight Fraktur font, \fontname{eufm}, can also be loaded by +|\input amssym.def|; this loads the two extra symbol fonts as well. + + +\subsection{5.2} Computer Modern bold math italic and symbols + +The \fontname{cmmib} and \fontname{cmbsy} fonts can be loaded and made +accessible to math in ten-point environments by the following code: +\begintt +\font\tencmmib=cmmib10 \skewchar\tencmmib='177 +\font\sevencmmib=cmmib7 \skewchar\sevencmmib='177 +\font\fivecmmib=cmmib5 \skewchar\fivecmmib='177 +\newfam\cmmibfam +\textfont\cmmibfam=\tencmmib \scriptfont\cmmibfam=\sevencmmib + \scriptscriptfont\cmmibfam=\fivecmmib + +\font\tencmbsy=cmbsy10 \skewchar\tencmbsy='60 +\font\sevencmbsy=cmbsy7 \skewchar\sevencmbsy='60 +\font\fivecmbsy=cmbsy5 \skewchar\fivecmbsy='60 +\newfam\cmbsyfam +\textfont\cmbsyfam=\tencmbsy \scriptfont\cmbsyfam=\sevencmbsy + \scriptscriptfont\cmbsyfam=\fivecmbsy +\endtt +The \TeX{} primitive |\mathchar| must be used to access individual characters +from a font in math mode. +|\mathchar|, like the |\char| primitive, requires that you know the position in +the font of the character you are accessing. However, |\mathchar| also +requires that you specify the ``class'' and the family of the math character +being accessed. See Chapter 17 of \TB{} for more details on the use of +|\mathchar|, as well as |\mathchardef|, which will allow you to define your own +macro names for individual characters in these fonts. + +\Note The file \filename{amssym.def} contains a convenient macro, +|\hexnumber@|, to determine the family number of the font being accessed +through |\mathchar|. For example, the |\mathchar| statement to properly access +the bold alpha in the \fn{cmmib} font would be: +\begintt +\mathchar"0\hexnumber@\cmmibfam0B +\endtt +\endx + + +\subsection{5.3} Computer Modern math extension font + +The 10-point \fontname{cmex} font is loaded by \filename{plain.tex}. +To install the 7-point size appropriate for sub- and superscripts in +a ten-point math environment, include the following code in your file: +\begintt +\font\sevenex=cmex7 +\scriptfont3=\sevenex \scriptscriptfont3=\sevenex +\endtt +To use other sizes implies the use of switchable-size fonts, +which may be implemented according to the models cited +at the beginning of this section. + + +\subsection{5.4} Extra symbols + +Detailed instructions for accessing the \fontname{msam} and \fontname{msbm} +fonts are given in Section 7, {\bf Using the extra symbols}. + + +\subsection{5.5} Cyrillic + +See Section 6, {\bf Using cyrillic}, for instructions. + + +\subsection{5.6} Caps/small caps + +The 10-point \fontname{cmcsc} font is loaded by \filename{plain.tex}. +To use the smaller versions implies the use of switchable-size fonts, +which may be implemented according to the models cited at the beginning +of this section. + + +\subsection{5.7} Dummy font + +The dummy font was designed to be used for syntax checking. The general +technique is described in Appendix~D of \TB, p.~401. This has been +implemented in the file \filename{amstex.tex}, which can be used as a model. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{6} Using cyrillic + +\def\2#1{${}\mapsto{}${\cyr#1}} + +\newcount\cyrtablefigno \cyrtablefigno=1 +\def\cyrtablefig{Figure~\number\cyrtablefigno} + +The cyrillic fonts in the AMSFonts collection have been designed so that +input using the transliteration conventions of {\sl Mathematical +Reviews\/} will be converted directly to cyrillic text. Other +transliteration schemes exist, as well as methods for keying directly +from the keyboard to access cyrillic characters. We have included two +sets of virtual fonts in this distribution, which provide access to the +characters of the cyrillic fonts through the KOI-8 or Alternativnyj +Variant (AV) encodings. At the present time macro support is provided +only for the {\sl Mathematical Reviews\/} transliteration scheme; to use +one of the other encodings, you must seek support from other sources. +Also, the instructions in this section are unsuitable for \LaTeX{}; they +apply only to \AmSTeX{}, plain \TeX{}, and other macro packages that use +plain \TeX{} font loading methods. + +The following cyrillic fonts are included: + +\item{} \fontname{wncyr} (upright), in sizes 5, 6, 7, 8, 9, and 10 point +\item{} \fontname{wncyb} (bold), in the same range of sizes as \fontname{wncyr} +\item{} \fontname{wncyi} (italic), in the same range of sizes as + \fontname{wncyr} +\item{} \fontname{wncysc} (caps and small caps), in size 10 point +\item{} \fontname{wncyss} (upright sans serif), in sizes 8, 9, and 10 point + +\noindent +(The Y\&Y/Blue Sky PostScript collection contains only 10-point outlines. +Other sizes must be obtained by scaling.) + +The file \filename{cyracc.def}, which is included in the AMSFonts collection, +must be input to any document using the cyrillic fonts as defined with the +AMS layout. Since the cyrillic alphabet contains more letters than the +roman alphabet, some cyrillic letters are accessed by combinations of roman +letters, accented letters, or control sequences. \filename{cyracc.def} +contains the definitions of these accents and control sequences. +If this file is not input, some cyrillic letters will be inaccessible. + + +\subsection{6.1} Making cyrillic available to a document + +If you are using plain \TeX{}, include the following instructions near the +top of the document input file to make the 10-point cyrillic font available +for use in text (see below for cyrillic in math): +\begintt +\input cyracc.def +\font\tencyr=wncyr10 +\def\cyr{\tencyr\cyracc} +\endtt +If you require cyrillic text in more than one size, you must take a +different approach in defining |\cyr|. An appropriate model appears in +Appendix~E of \TB\/ [DEK86A], pages 414--15. The definition of |\cyr| +should be incorporated into size-specific macros such as |\tenpoint| and +|\eightpoint| similarly to what is done there for |\bf|. Don't forget to +include the command |\cyracc| in the definition. + +If you are using \AmSTeX{} and the preprint style, include the following +instructions in the preamble of your document input file to make +cyrillic available in 10-point and 8-point text: +\begintt +\input cyracc.def +\catcode`\@=11 +\font@\tencyr=wncyr10 +\font@\eightcyr=wncyr8 +\catcode`\@=13 +\addto\tenpoint{\def\cyr{\tencyr\cyracc}} +\addto\eightpoint{\def\cyr{\eightcyr\cyracc}} +\endtt +(The |\font@| command not only loads the fonts, but also makes them behave +properly during syntax checking.) +If you are not using the preprint style, you can use the font definitions +in either \filename{amsppt.sty} or \TB\/ Appendix~E as a model. + +The macro definitions in \filename{cyracc.def} govern the behavior of +cyrillic-specific control sequences, including accents, in cyrillic and +noncyrillic text. Definitions governing noncyrillic text are activated +as soon as \filename{cyracc.def} is |\input|. This will permit text input +according to the scheme shown in \cyrtablefig{} to be typeset in +transliterated form, according to the {\sl MR\/} conventions. To produce +actual cyrillic text, enclose the cyrillic input in a group that begins with +the instruction |\cyr| {\sl inside\/} the group, as +\begintt +... {\cyr ...} ... +\endtt +Enclosing in braces both the |\cyr| and the text to be set in cyrillic type +(in the same way that an italic phrase would be indicated in a roman text) +is particularly important for two reasons. First, like |\it|, |\cyr| must +be explicitly terminated to return to roman text. And second, unlike |\it|, +the special cyrillic control sequences invoked by |\cyracc| are interpreted +differently by \TeX{} depending on whether they are in a cyrillic or a +noncyrillic environment. The ``cyrillic'' interpretation is not turned +off simply by invoking |\rm|. Failure to follow this practice will yield +gibberish. + + +\subsection{6.2} Cyrillic input + +The table in \cyrtablefig{} follows the alphabetical order of the table +published in the 1983 MR author index. The three paired columns +contain: (1)~Cyrillic; (2)~Input; (3)~Transliteration. + +The letters in the Cyrillic columns will appear in the +typeset output when the corresponding codes from the Input columns +are used in the |{\cyr ...}| context described above. The roman +letters in the Transliteration columns will appear in the output when +the corresponding codes from the Input columns are used in a noncyrillic +environment, i.e., have not been preceded by |\cyr|. + +\penalty0 +\topinsert +\begingroup +\input amsfndoc.cyr +\endgroup +\endinsert + +\penalty0 +\indent +Several points should be noted here. + +\nobreak +\item{\bull} Input codes for uppercase cyrillic which consist of more than + one letter, e.g. |Zh|\2{Zh}, can also be input in all caps, e.g. |ZH|\2{ZH}, + if the context is entirely in caps. + +\item{\bull} Particular care is necessary when the letter t\2{t} is followed + by s\2{s}. The control sequence |\cydot| (``cyrillic dot'') + is provided as a separator to keep those letters distinct: + |t\cydot s|~(t\cydot s)\2{t\cydot s}. + Otherwise, they will be combined as ts\2{ts}. + +\item{} The t\cydot s pair appears, for example, in the word + |sovet\cydot ski\u\i| + (sovet\cydot ski\u\i)\2{sovet\cydot ski\u\i} + and is not uncommon in the suffix of reflexive verbs, e.g. + \hbox{|nakhodyat\cydot sya|} + (nakhodyat\cydot sya)\2{nakhodyat\cydot sya}. + +\item{\bull} Because there is not a one-to-one correspondence between + cyrillic and roman letters, some cyrillic letters have been placed + in locations where a roman letter does not have a cyrillic + counterpart. A user who is aware of this fact may be able to + detect input keying that does not conform to the recommendations + shown in \cyrtablefig, and correct it more easily than otherwise. + The following nonstandard assignments have been made:\newline +\indent |c|\2{c}; |h|\2{h}; |q|\2{q}; |w|\2{w}; |x|\2{x}. + +\item{\bull} Some very strange effects can occur in cyrillic text + hyphenated by the default English hyphenation rules; in particular, + a cyrillic letter input as a group of letters can be decomposed. + (Most multiple-letter input groups are converted to a single cyrillic + letter by way of \TeX's ligaturing mechanism.) For example, + |shch|\2{shch} might, in especially unlucky circumstances, be + decomposed as {\cyr s-hch}, {\cyr sh-ch} or {\cyr shc-h}. + In other words, if there is any chance that cyrillic text might fall + into a position where hyphenation could occur, the results should be + checked very carefully, and discretionary hyphens used as appropriate. + +\item{\bull} Hyphenation patterns do not exist for the AMS cyrillic font + when the input conventions shown here are used. Furthermore, it is + probably impracticable to attempt to develop such rules, since the + rules to recognize control sequences and complicated ligatures, both + used extensively by the AMS cyrillic input conventions, are not easily + specified to \TeX's hyphenation mechanism. Another approach to + hyphenation, requiring some changes to the cyrillic \filename{.tfm} + files, has been described by Dimitri Vulis in a \TUB\/ article [DLV89]. + + +\subsection{6.3} Cyrillic in math + +Although the cyrillic fonts are intended for use as text, individual +letters are sometimes requested in math; for example, {\cyr SH} may be +used to represent the Shafarevich group. When cyrillic is needed in +math mode, replace the definition of |\cyr| shown previously (which +will work only for text) by the following instructions (which will +support the use of cyrillic in both text and math): +\begintt +\newfam\cyrfam +\font\tencyr=wncyr10 +\font\sevencyr=wncyr7 +\font\fivecyr=wncyr5 +\def\cyr{\fam\cyrfam\tencyr\cyracc} +\textfont\cyrfam=\tencyr \scriptfont\cyrfam=\sevencyr + \scriptscriptfont\cyrfam=\fivecyr +\endtt +If only the 10-point cyrillic font has been accessed, the references +to |\sevencyr| and |\fivecyr| can be changed to |\tencyr| to save memory. +When using \AmSTeX{} and the preprint style, use |\font@| instead of |\font|, +remembering to change the |\catcode| of the |@| appropriately, and embed the +font family specifications in |\addto\tenpoint|, as shown above. + +If other base text sizes are used besides ten point, the suggestions given +above in Section 6.1, {\bf Making cyrillic available}, apply here as well. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\makeatletter + +% Define macros for presentation of tables of symbols. +\def\BBB#1{\par\bigbreak + \leavevmode\llap{$\bullet$\enspace}{\bf#1}} +\def\ttcs#1{\leavevmode\hbox{\tt\bs\ignorespaces#1\unskip}} +\newdimen\biggest +\setbox0\hbox{$\dashrightarrow$}\biggest=\wd0 +\def\1#1{\hbox to\biggest{\hfil$\csname#1\endcsname$\hfil}\ \ % + \ttcs{#1}} + +\def\getID@#1{\edef\next@{\expandafter\meaning\csname#1\endcsname}% + \expandafter\getID@@\next@0\getID@@} +\def\getID@@#1"#2#3#4#5#6\getID@@{\def\next@{#6}% + \ifx\next@\empty + \def\next@{#2}% + \ifx\next@\msafam@ + \def\ID@{10#3#4}% + \else + \def\ID@{20#3#4}% + \fi + \else + \def\next@{#3}% + \ifx\next@\msafam@ + \def\ID@{1#2#4#5}% + \else + \def\ID@{2#2#4#5}% + \fi + \fi} +\def\2#1{\hbox to.5\hsize + {\hbox to\biggest{\hfill$\csname#1\endcsname$\hfill}\ \ % + \getID@{#1}{\tt\ID@}\ \ \ttcs{#1}\hfill}} +\def\3#1#2{\hbox to.5\hsize + {\hbox to\biggest{\hfil$\csname#1\endcsname$\hfil}\ \ % + \getID@{#1}{\tt\ID@}\ \ \ttcs{#1}, \ttcs{#2}\hss}} +\def\4#1{\hbox to.5\hsize + {\hbox to\biggest{\hfill$\csname#1\endcsname$\hfill}\ \ % + \getID@{#1}{\tt\ID@}\ \ \ttcs{#1}\ \ {\eightpoint(U)}\hfill}} + +\makeatother + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{7} Using the extra symbols + +Most users of the extra symbol fonts will probably want to make them +accessible to their \TeX{} jobs with the least possible fuss. For \AmSTeX{} +users, these fonts are available automatically with the preprint style, and +other methods of loading them for use with \AmSTeX{} are described above. +To load these fonts with \LaTeX{} or \AmS-\LaTeX{}, see Section 3.4, +{\bf Extra math symbols}. + +If you are not using \AmSTeX{} or \LaTeX{}, the easiest method of loading +these fonts and defining the control sequences for accessing the symbols is +to place the command +\begintt +\input amssym.tex +\endtt +at the top of your input file. This will load the fonts \fontname{msam}, +\fontname{msbm}, and \fontname{eufm} in sizes 10, 7, and 5 point, suitable +for use in ordinary ten-point math environments, and define the names of +all the symbols in these fonts. However, this assigns more than 200 +control sequence names, so if you are limited for space, an alternative +method may be preferred. + +If you type just |\input amssym.def| (or |\usepackage{amsfonts}| for +\LaTeX), the fonts will be loaded, but only the +names of the few special symbols listed below will be defined. + +First there are four symbols that are normally used outside of math mode: +$$\vcenter{\halign to\hsize{\1{#}\hfil\tabskip\centering& + \hbox to.5\hsize{\1{#}\hfil}\tabskip0pt\cr +checkmark&circledR\cr +maltese¥\cr}} +$$ +These symbols, like \P, \S, \dag, and \ddag, can also be used in math mode; +they will change sizes correctly in subscripts and superscripts. + +Next are four symbols that are ``delimiters'' (although there are +no larger versions obtainable with \ttcs{left} and \ttcs{right}), so they +must be used in math mode: +$$\vcenter{\halign to\hsize{\1{#}\hfil\tabskip\centering& + \hbox to.5\hsize{\1{#}\hfil}\tabskip0pt\cr + ulcorner&urcorner\cr + llcorner&lrcorner\cr}}$$ + +Finally, two dashed arrows are constructed from symbols in this family +(note that one of them has two names; it can be accessed by either one): +$$\vcenter{\halign to\hsize{\1{#}\hfil\tabskip\centering& + \hbox to.5\hsize{\1{#}\hfil}\tabskip0pt\cr + \omit\hbox to.5\hsize{\hbox to\biggest{\hfil$\dashrightarrow$\hfil}\ \ % + \ttcs{dashrightarrow}, \ttcs{dasharrow}\hss}&dashleftarrow\cr}}$$ + +The Blackboard Bold letters $\Bbb A,\dots,\Bbb Z$ can be accessed by typing +(in math mode) |\Bbb A|$,\dots,$|\Bbb Z| in plain \TeX{} or \AmSTeX, or +|\mathbb{A}|$,\dots,$|\mathbb{Z}| in \LaTeX. + +Wider versions of the \filename{plain.tex} |\widehat| and |\widetilde| +are now available. + +Letters in the \fontname{eufm} font can be accessed (in math mode) by typing, +for example, |\frak A \frak g| to get $\frak A \frak g$ +(|\mathfrak{Ag}| in \LaTeX). For the other Euler +fonts, see the various ``Euler'' subsections under the sections for +different macro packages (\LaTeX{}, \AmSTeX{}, plain \TeX{}). + +\subsection{7.1} The {\tt\bs newsymbol} command (\AmSTeX{} or plain \TeX{}) + +All other symbols of the \fontname{msam} and \fontname{msbm} fonts must be +named by control sequences so that they can be used (in math mode only) when +the fonts are loaded. If you are very short on space for control sequence +names, and need only a few of these symbols, you can omit the loading of +\filename{amssym.tex} and instead assign only the names you will need by +using the command |\newsymbol| for each symbol you need, to create a +control sequence that will properly produce that symbol. The control +sequence can be either the ``standard'' name, as listed below, or one +of your own choosing. + +The list of symbols below shows for each symbol the symbol itself, a +four-character~``ID'', and the ``standard'' name of the symbol. +(The first character of the ID identifies the font family in which a +symbol resides. Symbols from the \fontname{msam} family have {\tt1} as the +first character; symbols from the \fontname{msbm} family have {\tt2} as the +first character.) +For example, the symbol $\nleqslant$ appears as +\medskip +\noindent\kern\parindent\2{nleqslant} +\medskip +\noindent +To produce a control sequence with this name, the instruction +\begintt +\newsymbol\nleqslant 230A +\endtt +appears in the file \filename{amssym.tex}. This same instruction can +be typed by a user who is not using the \AmSTeX{} preprint style and has +chosen not to load all the symbols, and thereafter the control sequence +|\nleqslant| will produce the symbol $\nleqslant$ (in math mode), and will +act properly as a ``binary relation''. + +A few symbols in these fonts replace symbols defined in \filename{plain.tex} +by combinations of symbols available in the Computer Modern fonts. These +are |\angle|~($\angle$) and |\hbar|~($\hbar$) from the group +``Miscellaneous symbols'', and |\rightleftharpoons|~($\rightleftharpoons$) +from the group ``Arrows'' below. The new symbols will +change sizes correctly in subscripts and superscripts, provided that you +are using appropriate redefinitions. In order to use |\newsymbol| to +replace an existing definition, the name must first be ``undefined''. +Here are the lines you must put in your file if you are not using the +\AmSTeX{} preprint style or |\input amssym| (which perform the redefinition +automatically): +\begintt +\undefine\angle +\newsymbol\angle 105C +\undefine\hbar +\newsymbol\hbar 207E +\undefine\rightleftharpoons +\newsymbol\rightleftharpoons 130A +\endtt +\noindent +These symbols are flagged in the tables below with a ``{\eightpoint(U)}'', +as a reminder that they must be undefined. + +\subsection{7.2} The extra symbols + +Note in the tables that some symbols are shown with two names; in such a +case, either one can be used to access the symbol. + +\BBB{Lowercase Greek letters} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +digamma&varkappa\cr}$$ + +\BBB{Hebrew letters} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +beth&gimel\cr +daleth\cr +}$$ + +\BBB{Miscellaneous symbols} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +\omit\4{hbar}&backprime\cr +hslash&varnothing\cr +vartriangle&blacktriangle\cr +triangledown&blacktriangledown\cr +square&blacksquare\cr +lozenge&blacklozenge\cr +circledS&bigstar\cr +\omit\4{angle}&sphericalangle\cr +measuredangle&\omit\cr +nexists&complement\cr +mhoð\cr +Finv&diagup\cr +Game&diagdown\cr +Bbbk&\omit\cr +}$$ + +\BBB{Binary operators} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +dotplus<imes\cr +smallsetminus&rtimes\cr +\omit\3{Cap}{doublecap}&leftthreetimes\cr +\omit\3{Cup}{doublecup}&rightthreetimes\cr +barwedge&curlywedge\cr +veebar&curlyvee\cr +% %%%%%%%%%% +%\noalign{\newpage} +% %%%%%%%%%% +doublebarwedge\cr +boxminus&circleddash\cr +boxtimes&circledast\cr +boxdot&circledcirc\cr +boxplus¢erdot\cr +divideontimes&intercal\cr} +$$ + +\BBB{Binary relations} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +leqq&geqq\cr +leqslant&geqslant\cr +eqslantless&eqslantgtr\cr +lesssim>rsim\cr +lessapprox>rapprox\cr +approxeq&eqsim\cr +lessdot>rdot\cr +\omit\3{lll}{llless}&\omit\3{ggg}{gggtr}\cr +lessgtr>rless\cr +lesseqgtr>reqless\cr +lesseqqgtr>reqqless\cr +\omit\3{doteqdot}{Doteq}&eqcirc\cr +risingdotseq&circeq\cr +fallingdotseq&triangleq\cr +backsim&thicksim\cr +backsimeq&thickapprox\cr +subseteqq&supseteqq\cr +Subset&Supset\cr +sqsubset&sqsupset\cr +preccurlyeq&succcurlyeq\cr +curlyeqprec&curlyeqsucc\cr +precsim&succsim\cr +precapprox&succapprox\cr +vartriangleleft&vartriangleright\cr +trianglelefteq&trianglerighteq\cr +vDash&Vdash\cr +Vvdash\cr +smallsmile&shortmid\cr +smallfrown&shortparallel\cr +bumpeq&between\cr +Bumpeq&pitchfork\cr +varpropto&backepsilon\cr +blacktriangleleft&blacktriangleright\cr +therefore&because\cr}$$ +\bigbreak +\BBB{Negated relations} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +nless&ngtr\cr +nleq&ngeq\cr +nleqslant&ngeqslant\cr +nleqq&ngeqq\cr +lneq&gneq\cr +lneqq&gneqq\cr +lvertneqq&gvertneqq\cr +lnsim&gnsim\cr +lnapprox&gnapprox\cr +% %%%%%%%%%% +%\noalign{\newpage} +% %%%%%%%%%% +nprec&nsucc\cr +npreceq&nsucceq\cr +precneqq&succneqq\cr +precnsim&succnsim\cr +precnapprox&succnapprox\cr +nsim&ncong\cr +nshortmid&nshortparallel\cr +nmid&nparallel\cr +nvdash&nvDash\cr +nVdash&nVDash\cr +ntriangleleft&ntriangleright\cr +ntrianglelefteq&ntrianglerighteq\cr +nsubseteq&nsupseteq\cr +nsubseteqq&nsupseteqq\cr +subsetneq&supsetneq\cr +varsubsetneq&varsupsetneq\cr +subsetneqq&supsetneqq\cr +varsubsetneqq&varsupsetneqq\cr}$$ + +\overfullrule=0pt + +\BBB{Arrows} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +leftleftarrows&rightrightarrows\cr +leftrightarrows&rightleftarrows\cr +Lleftarrow&Rrightarrow\cr +twoheadleftarrow&twoheadrightarrow\cr +leftarrowtail&rightarrowtail\cr +looparrowleft&looparrowright\cr +leftrightharpoons&\omit\4{rightleftharpoons}\cr +curvearrowleft&curvearrowright\cr +circlearrowleft&circlearrowright\cr +Lsh&Rsh\cr +upuparrows&downdownarrows\cr +upharpoonleft&\omit\3{upharpoonright}{restriction}\cr +downharpoonleft&downharpoonright\cr +multimap&rightsquigarrow\cr +leftrightsquigarrow\cr}$$ + +\BBB{Negated arrows} +$$\halign{\hbox to.5\hsize{\2{#}}&\2{#}\cr +nleftarrow&nrightarrow\cr +nLeftarrow&nRightarrow\cr +nleftrightarrow&nLeftrightarrow\cr}$$ + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\References{DEK86A} + +\bibitem [AMS01] {\sl User's Guide to \AmSTeX{} Version~2.2, August 2001}, + \AMS, Providence, RI, 2001; distributed with \AmSTeX{} Version~2.2. + +\bibitem [AMSPS] {\sl AMSFonts in Type 1 (PostScript) form}, AMS web + server, URL: |http://www.ams.org/tex/type1-fonts.html|. + +\bibitem [DEK86A] Donald E. Knuth, {\sl The \TeX book}, + Volume~A of \CandT, \AW{} Publishing Co., + Reading, MA, 1986. + +\bibitem [DEK86E] \bysame {\sl Computer Modern Typefaces}, + Volume~E of \CandT, \AW{} Publishing Co., + Reading, MA, 1986. + +\bibitem [DEK89] \bysame ``Typesetting Concrete Mathematics'', + {\sl \TUB\/} {\bf10} (1989), no.~1, 31--36; erratum, + {\sl \TUB\/} {\bf10} (1989), no.~3, 342. + +\bibitem [DLV89] Dimitri Vulis, ``Notes on Russian \TeX'', + {\sl \TUB\/} {\bf10} (1989), no.~3, 332--36. + +\bibitem [DRS86] David R Siegel, {\sl The Euler Project at Stanford}, + Computer Science Department, Stanford University, 1985. + +\bibitem [GKP88] Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, + {\sl Concrete Mathematics}, \AW{} Publishing Co., + Reading, MA, 1988. + +\bibitem[GMS94] {\sl The \LaTeX{} companion}, Michel Goossens, Frank + Mittelbach, and Alexander Samarin, \AW{} Publishing Company, + Reading, MA, 1994. Chapter~8 describing AMS-\LaTeX{} is obsolete; + a replacement chapter is available in PDF form from + |http://www.ctan.org/tex-archive/info/companion-rev/ch8.pdf|. + +\bibitem[L94] {\sl \LaTeX: A document preparation system}, Second edition, + Leslie Lamport, \AW{} Publishing Company, Reading, MA, 1994. + +\bibitem[LFG] ``\LaTeX{}2e font selection'', \fn{fntguide.tex} in the + \LaTeX{} distribution. + +\bibitem [MDS86] M. D. Spivak, \JoT, \AMS, Providence, RI, 1986. + +\bibitem [MDS90] \bysame \JoT, $2^{\rm nd}$ (revised) edition, + \AMS, Providence, RI, 1990. + +\endReferences + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begingroup \def\bye{\par\endinput} +\input amsfndoc.ins +\endgroup + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\appendix{D}{Font charts} +\begingroup \def\bye{\par\endinput} +\input amsfndoc.fnt +\endgroup + +\bye |