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authorNorbert Preining <norbert@preining.info>2017-07-13 10:42:53 +0900
committerNorbert Preining <norbert@preining.info>2017-07-13 10:42:53 +0900
commit7aee74c9077bc1745ff6e9e6279b7e2d3ba737a9 (patch)
tree4e3311305f33207d716b2ded83640cb48dbf0263 /texmf-dist/doc
parent0300e2ce502b6eef25f937744878ca26ebdedce4 (diff)
add lucidabr
Diffstat (limited to 'texmf-dist/doc')
-rw-r--r--texmf-dist/doc/latex/lucidabr/Makefile24
-rw-r--r--texmf-dist/doc/latex/lucidabr/README26
-rw-r--r--texmf-dist/doc/latex/lucidabr/README.TUG135
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucfont.tex91
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucida-amsmath.pdfbin0 -> 220287 bytes
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucida-amsmath.tex2334
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucida-oneline-samples.tex86
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucida-sample.pdfbin0 -> 393399 bytes
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucida-sample.tex303
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucidabr.dtx1323
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucidabr.fdd316
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucidabr.ins75
-rw-r--r--texmf-dist/doc/latex/lucidabr/lucidabr.pdfbin0 -> 161392 bytes
-rw-r--r--texmf-dist/doc/latex/lucidabr/manifest.txt16
14 files changed, 4729 insertions, 0 deletions
diff --git a/texmf-dist/doc/latex/lucidabr/Makefile b/texmf-dist/doc/latex/lucidabr/Makefile
new file mode 100644
index 00000000..b1fa8b7b
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/Makefile
@@ -0,0 +1,24 @@
+# Trivial Makefile to generate and move files to the appropriate directory.
+# Copyright 2005, 2006, 2007 TeX Users Group.
+# You may freely use, modify and/or distribute this file.
+
+styles = lucmtime.sty lucbmath.sty lucidabr.sty lucidbrb.sty \
+ lucidbry.sty lucmin.sty luctime.sty
+fd = lmrhlcm.fd omlhlcm.fd omlhlh.fd omshlcy.fd omshlh.fd omxhlcv.fd
+
+default: $(styles) $(fd)
+
+$(styles) $(fd): lucidabr.ins
+ latex '\nonstopmode\input $<'
+
+$(styles): lucidabr.dtx
+$(fd): lucidabr.fdd
+
+lucidabr.pdf: lucidabr.dtx
+ pdflatex '\nonstopmode\input $<'
+
+texmf = ../../..
+install: $(styles) $(fd)
+ mv -f $(styles) $(texmf)/tex/latex/lucidabr/
+ mv -f $(fd) $(texmf)/tex/latex/lucidabr/
+ rm -f lucfont.tex lucidabr.log lucidabr.aux
diff --git a/texmf-dist/doc/latex/lucidabr/README b/texmf-dist/doc/latex/lucidabr/README
new file mode 100644
index 00000000..06956ce4
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/README
@@ -0,0 +1,26 @@
+Copyright 2007 TeX Users Group.
+You may freely use, modify and/or distribute this file (README).
+
+This lucidabr package provides LaTeX support for the Lucida fonts.
+
+The related lucida package, at
+http://mirror.ctan.org/fonts/psfonts/bh/lucida, provides basic TeX
+support files, such as tfm and map files.
+
+The lucidabr and lucida packages on CTAN are free, but the Lucida fonts
+are not: you must order them from TUG or another source to actually
+typeset anything in Lucida. The TUG Lucida web pages explain the
+details -- see http://tug.org/lucida.
+
+For installation instructions, after ordering the fonts from TUG, see the
+README.TUG file. (You'll get the same info in email after ordering.)
+
+If you have questions or problems regarding installation or use, please
+email lucida@tug.org; this is an open list for Lucida discussion, and
+you can subscribe via http://tug.org/mailman/listinfo/lucida. Questions
+or problems related to ordering or licensing should go to
+lucida-admin@tug.org.
+
+The lucidabr package is looking for an active maintainer to improve the
+documentation, add some requested features, and generally maintain the
+distribution. If you are interested, please email.
diff --git a/texmf-dist/doc/latex/lucidabr/README.TUG b/texmf-dist/doc/latex/lucidabr/README.TUG
new file mode 100644
index 00000000..a536ad01
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/README.TUG
@@ -0,0 +1,135 @@
+To install the Lucida font distribution from TUG:
+
+1) download the zip file from TUG via the url given to you after ordering.
+
+2) change directories to a suitable texmf hierarchy; your "local texmf"
+ tree is the best choice. More info below(*).
+
+3) unzip the archive as retrieved. It unpacks into subdirectories
+ fonts/, tex/, and so on. These directories will probably already
+ exist if you already have a local texmf tree; that's ok. You must
+ use an unzip program or settings which does *not* create any
+ top-level directory of its own (such as "lucida-complete/"), but just
+ unpacks what is in the zip file.
+
+4) remake the so-called "filename database", unless you unpacked in a
+ personal directory, such as ~/Library/texmf on MacOSX.
+ Under Unix, this is generally done by running the command mktexlsr.
+ Under MiKTeX, it is generally done in the MiKTeX program:
+ Start > Programs > MiKTeX > MiKTeX Options > General
+ > Refresh Now (the file name database).
+ (or from a DOS command line, if you prefer: initexmf --update-fndb)
+
+5) enable the Lucida "map files", if necessary.
+ Under Unix, this is generally done by running the command
+updmap-sys --enable Map lucida.map
+ (on MacOSX, typically as root, so: sudo updmap-sys ...)
+ For MiKTeX, the procedure is more complicated; see below(**).
+
+ Some distributions already have the map file enabled. You can tell
+ by running the sample document mentioned below on your system. If it
+ starts calling programs like mktexpk, and fonts are unable to be
+ loaded, and you don't get any actual Lucida in the output, then you
+ need to enable the map file. If the output is fine, you're all set.
+
+6) remake the filename database again; this is not always necessary,
+ depending on your setup, but should never hurt.
+
+7) the document doc/fonts/lucidabr/lucida-sample.pdf explains the basic
+ usage of the fonts in LaTeX, and is itself typeset using Lucida. The
+ LaTeX source is also included (lucida-sample.tex) so that you can see
+ how it was produced. Running this file through LaTeX yourself is a
+ good test of the installation.(***) Some additional documentation and
+ samples are included in doc/fonts/lucidabr and doc/fonts/lucida.
+
+If you have questions or problems regarding installation or use, please
+email lucida@tug.org; this is an open and publicly archived list for
+Lucida discussion, and you can subscribe via
+http://tug.org/mailman/listinfo/lucida. Questions or problems related
+to ordering or licensing should go to lucida-admin@tug.org.
+
+The TUG Lucida home page is http://tug.org/lucida.
+Happy typesetting!
+
+--
+(*) Finding and/or creating your texmf-local tree:
+
+TeX systems have thousands of files, arranged in one or more
+"trees" of directories. Your system can quickly look through
+the trees that it knows about.
+
+When you install TeX, you may have noticed or set up a "local" tree,
+used for your own macros and other files. The advantage of a local tree
+is that if you install an new version of your TeX system then these
+local materials will not be overwritten. A local tree is the best place
+to install the Lucida fonts.
+
+Typical names for local trees are "C:\Local TeX Files" on Windows or
+"/usr/local/texlive/texmf-local" on Unix. They might be entirely empty.
+How to find any local trees that you have depends on your system:
+
+ MiKTeX
+ From inside MiKTeX click on "MiKTeX Settings" and go to the Roots
+ tab. Some paths shown there have a "Description" such as UserConfig
+ or UserData; these are not local paths. For your local path you can
+ use any path without a Description.
+
+ If you see only paths that have a description then you can create a new
+ local path by clicking on "Add" (for more info, see the MiKTeX page
+ http://docs.miktex.org/manual/localadditions.html).
+
+ TeX Live and MacTeX
+ From a system terminal (aka command prompt and shell window) enter the
+ command
+ kpsewhich --var-value TEXMFLOCAL
+ to see the directory name.
+
+
+(**) Enabling the Lucida map file under MiKTeX:
+
+1. Edit the map configuration file updmap.cfg. In a DOS Window/Command
+Prompt window, run:
+initexmf --edit-config-file updmap
+ You'll want to edit this in a text editor such as Notepad. If the
+ file or any of the leading directories do not exist, create them.
+
+2. Add this one line to updmap.cfg and save it.
+Map lucida.map
+
+3. Back at the DOS prompt, run
+initexmf --mkmaps
+ (Ignore any error messages.)
+
+Hopefully that is it. Resume above at step 5.
+
+
+(***) Potential problems:
+
+1. If when you run a Lucida document you get complaints about missing
+ fonts, mktexpk could not make bitmaps, etc., most likely you need to
+ enable the Lucida map file. See step 4 above.
+
+2. If you do try latex-ing lucida-sample.tex and get an error at the line:
+ \DeclareEncodingSubset{TS1}{hlh}{1} % including \oldstylenums
+Please check your version of the textcomp.sty style file against
+the current release, available at:
+ http://www.ctan.org/tex-archive/macros/latex/unpacked/textcomp.sty
+
+
+--
+Legal: the Lucida fonts are made available only under an end-user or
+site license, which you must have agreed to when you ordered the fonts.
+The license text is available in the distribution files
+doc/fonts/lucidabr/lucida-license-*.txt, or online at
+http://tug.org/store/lucida. (This README.TUG file itself may be freely
+used, modified and/or distributed.)
+
+The Lucida typeface family was designed by Charles Bigelow and Kris Holmes.
+(R) Lucida is a trademark of Bigelow & Holmes Inc.
+registered in the U.S. Patent & Trademark Office and other
+jurisdictions.
+
+TUG gratefully acknowledges Y&Y for the original Lucida TeX distribution,
+Walter Schmidt for creating and updating the TeX font support files,
+PCTeX for sponsoring him and allowing his work to be redistributed, and
+Morten Hoegholm for working on the samples and other TeXnical help.
diff --git a/texmf-dist/doc/latex/lucidabr/lucfont.tex b/texmf-dist/doc/latex/lucidabr/lucfont.tex
new file mode 100644
index 00000000..3b73399b
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucfont.tex
@@ -0,0 +1,91 @@
+%%
+%% This is file `lucfont.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% lucidabr.dtx (with options: `T1,lucfont')
+%%
+%% Copyright 1995, 1996 Sebastian Rahtz
+%% Copyright 1997, 1998 Sebastian Rahtz, David Carlisle
+%% Copyright 2005 TeX Users Group
+%%
+%% This file is part of the lucidabr package.
+%%
+%% 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 2003/12/01 or later.
+%%
+%% This work has the LPPL maintenance status "maintained".
+%%
+%% The Current Maintainer of this work is the TeX Users Group
+%% (http://tug.org/lucida).
+%%
+%% The list of all files belonging to the lucidabr package is
+%% given in the file `manifest.txt'.
+%%
+%% The list of derived (unpacked) files belonging to the distribution
+%% and covered by LPPL is defined by the unpacking scripts (with
+%% extension .ins) which are part of the distribution.
+%%
+\ProvidesFile{lucfont.tex}
+ [2005/11/29 v4.3 %
+ Lucida Bright text font test
+ (SPQR/DPC/TUG)]
+\documentclass{article}
+\usepackage[T1]{fontenc}
+\begin{document}
+\title{All the Lucida text fonts}
+\author{prepared by Sebastian Rahtz}
+\date{February 19th 1995}
+\maketitle
+\def\test#1#2#3#4#5{%
+ \item[#1/#2/#3]#4 (#5):
+ {\fontfamily{#1}\fontseries{#2}\fontshape{#3}\selectfont
+ Animadversion for a giraffe costs \pounds123. Wa\ss\ ist
+ das f\"ur ein Klopf?
+ We are often na{\"\i}ve vis-\`{a}-vis
+the d{\ae}monic ph{\oe}nix's official r\^{o}le in fluffy souffl\'{e}s}
+}
+
+\begin{description}
+\test{hlx}{b}{it}{hlxdi8t}{LucidaFax-DemiItalic}
+\test{hlx}{b}{n}{hlxd8t}{LucidaFax-Demi}
+\test{hlx}{m}{it}{hlxrir8t}{LucidaFax-Italic}
+\test{hlx}{m}{n}{hlxr8t}{LucidaFax}
+
+\test{hlh}{b}{it}{hlcdib8t}{LucidaBright-DemiItalic}
+\test{hlh}{b}{n}{hlcdb8t}{LucidaBright-Demi}
+\test{hlh}{m}{it}{hlcrib8t}{LucidaBright-Italic}
+\test{hlh}{m}{n}{hlcrb8t}{LucidaBright}
+
+\test{hlce}{m}{it}{hlcrie8t}{LucidaCalligraphy-Italic}
+
+\test{hlcf}{m}{n}{hlcrf8t}{LucidaBlackletter}
+
+\test{hlcn}{m}{it}{hlcrin8t}{LucidaCasual-Italic}
+\test{hlcn}{m}{n}{hlcrn8t}{LucidaCasual}
+
+\test{hlst}{b}{n}{hlsbt8t}{LucidaSans-TypewriterBold}
+\test{hlst}{b}{sl}{hlsbot8t}{LucidaSans-TypewriterBoldOblique}
+
+\test{hls}{ub}{it}{hlsbi8t}{LucidaSans-BoldItalic}
+\test{hls}{ub}{n}{hlsb8t}{LucidaSans-Bold}
+\test{hls}{b}{it}{hlsdi8t}{LucidaSans-DemiItalic}
+\test{hls}{b}{n}{hlsd8t}{LucidaSans-Demi}
+\test{hls}{m}{it}{hlsri8t}{LucidaSans-Italic}
+\test{hls}{m}{n}{hlsr8t}{LucidaSans}
+
+\test{hlct}{b}{n}{hlcbt8t}{LucidaTypewriterBold}
+\test{hlct}{b}{sl}{hlcbot8t}{LucidaTypewriterOblique}
+\test{hlcw}{m}{it}{hlcriw8t}{LucidaHandwriting-Italic}
+
+\end{description}
+\end{document}
+\endinput
+%%
+%% End of file `lucfont.tex'.
diff --git a/texmf-dist/doc/latex/lucidabr/lucida-amsmath.pdf b/texmf-dist/doc/latex/lucidabr/lucida-amsmath.pdf
new file mode 100644
index 00000000..3ed7cd1f
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucida-amsmath.pdf
Binary files differ
diff --git a/texmf-dist/doc/latex/lucidabr/lucida-amsmath.tex b/texmf-dist/doc/latex/lucidabr/lucida-amsmath.tex
new file mode 100644
index 00000000..48eb29d1
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucida-amsmath.tex
@@ -0,0 +1,2334 @@
+% lucida-amsmath.tex
+% Copyright 2005 TeX Users Group.
+%
+% This file is based on testmath.tex by the AMS. Unrestricted
+% permission is granted to copy, modify, and extract portions of this file.
+%
+% This is a documentation file for the lucidabr package, showing
+% advanced mathematical and AMS usage for the Lucida fonts.
+% http://tug.org/lucida
+
+\documentclass{article}
+\pagestyle{headings}
+
+\title{Sample Paper for the \pkg{amsmath} and \pkg{lucidabr} Packages\\
+File name: \fn{\jobname.tex}}
+\author{\TeX\ Users Group \& American Mathematical Society}
+\date{Version 2.1, 28 November 2005}
+
+\setlength\textwidth{375pt}
+
+\usepackage{amsmath,amsthm}
+\usepackage[T1]{fontenc}
+\usepackage{lucidabr}
+
+% Some definitions useful in producing this sort of documentation:
+\chardef\bslash=`\\ % p. 424, TeXbook
+% Normalized (nonbold, nonitalic) tt font, to avoid font
+% substitution warning messages if tt is used inside section
+% headings and other places where odd font combinations might
+% result.
+\DeclareRobustCommand*\ntt{\normalfont\ttfamily}
+% command name
+\newcommand{\cn}[1]{{\ntt\bslash#1}}
+% LaTeX package name
+\newcommand{\pkg}[1]{{\ntt#1}}
+% File name
+\newcommand{\fn}[1]{{\ntt#1}}
+% environment name
+\newcommand{\env}[1]{{\ntt#1}}
+
+% Theorem environments
+
+%% \theoremstyle{plain} %% This is the default
+\newtheorem{thm}{Theorem}[section]
+\newtheorem{cor}[thm]{Corollary}
+\newtheorem{lem}[thm]{Lemma}
+\newtheorem{prop}[thm]{Proposition}
+\newtheorem{ax}{Axiom}
+
+\theoremstyle{definition}
+\newtheorem{defn}{Definition}[section]
+
+\theoremstyle{remark}
+\newtheorem{rem}{Remark}[section]
+\newtheorem*{notation}{Notation}
+
+%\numberwithin{equation}{section}
+
+\newcommand{\thmref}[1]{Theorem~\ref{#1}}
+\newcommand{\secref}[1]{\S\ref{#1}}
+\newcommand{\lemref}[1]{Lemma~\ref{#1}}
+
+\newcommand{\bysame}{\mbox{\rule{3em}{.4pt}}\,}
+
+% Math definitions
+
+\newcommand{\A}{\mathcal{A}}
+\newcommand{\B}{\mathcal{B}}
+\newcommand{\st}{\sigma}
+\newcommand{\XcY}{{(X,Y)}}
+\newcommand{\SX}{{S_X}}
+\newcommand{\SY}{{S_Y}}
+\newcommand{\SXY}{{S_{X,Y}}}
+\newcommand{\SXgYy}{{S_{X|Y}(y)}}
+\newcommand{\Cw}[1]{{\hat C_#1(X|Y)}}
+\newcommand{\G}{{G(X|Y)}}
+\newcommand{\PY}{{P_{\mathcal{Y}}}}
+\newcommand{\X}{\mathcal{X}}
+\newcommand{\wt}{\widetilde}
+\newcommand{\wh}{\widehat}
+
+\DeclareMathOperator{\per}{per}
+\DeclareMathOperator{\cov}{cov}
+\DeclareMathOperator{\non}{non}
+\DeclareMathOperator{\cf}{cf}
+\DeclareMathOperator{\add}{add}
+\DeclareMathOperator{\Cham}{Cham}
+\DeclareMathOperator{\IM}{Im}
+\DeclareMathOperator{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\DeclareMathOperator{\seg}{seg}
+
+% \interval is used to provide better spacing after a [ that
+% is used as a closing delimiter.
+\newcommand{\interval}[1]{\mathinner{#1}}
+
+% Notation for an expression evaluated at a particular condition. The
+% optional argument can be used to override automatic sizing of the
+% right vert bar, e.g. \eval[\biggr]{...}_{...}
+\newcommand{\eval}[2][\right]{\relax
+ \ifx#1\right\relax \left.\fi#2#1\rvert}
+
+% Enclose the argument in vert-bar delimiters:
+\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
+\let\abs=\envert
+
+% Enclose the argument in double-vert-bar delimiters:
+\newcommand{\enVert}[1]{\left\lVert#1\right\rVert}
+\let\norm=\enVert
+
+\begin{document}
+\maketitle
+\markboth{Sample paper for the {\ntt\lowercase{amsmath}} and {\ntt\lowercase{lucidabr}} packages}
+{Sample paper for the {\ntt\lowercase{amsmath}} and {\ntt\lowercase{lucidabr}} packages}
+\renewcommand{\sectionmark}[1]{}
+
+\section{Introduction}
+
+{\def\thefootnote{}
+% article.cls uses 1.8em for the footnote indent.
+\footnotetext{\kern-1.8em \textregistered\ Lucida is a trademark of
+Bigelow \& Holmes Inc.\ registered in the U.S. Patent \& Trademark
+Office and other jurisdictions.}
+}
+
+This paper contains examples of various features from the widely used
+\pkg{amsmath} package used with the Lucida math fonts.
+
+When loading the packages, you must load \pkg{amsmath} before
+\pkg{lucidabr}. Work is planned for improving interaction between these
+packages.
+
+For more information about Lucida and \TeX, and an order form for the
+fonts, please see {\tt http://tug.org/store/lucida}.
+
+\section{Enumeration of Hamiltonian paths in a graph}
+
+Let $\mathbf{A}=(a_{ij})$ be the adjacency matrix of graph $G$. The
+corresponding Kirchhoff matrix $\mathbf{K}=(k_{ij})$ is obtained from
+$\mathbf{A}$ by replacing in $-\mathbf{A}$ each diagonal entry by the
+degree of its corresponding vertex; i.e., the $i$th diagonal entry is
+identified with the degree of the $i$th vertex. It is well known that
+\begin{equation}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\quad i=1,\dots,n
+\end{equation}
+where $\mathbf{K}(i|i)$ is the $i$th principal submatrix of
+$\mathbf{K}$.
+\begin{verbatim}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\end{verbatim}
+
+Let $C_{i(j)}$ be the set of graphs obtained from $G$ by attaching edge
+$(v_iv_j)$ to each spanning tree of $G$. Denote by $C_i=\bigcup_j
+C_{i(j)}$. It is obvious that the collection of Hamiltonian cycles is a
+subset of $C_i$. Note that the cardinality of $C_i$ is $k_{ii}\det
+\mathbf{K}(i|i)$. Let $\wh X=\{\hat x_1,\dots,\hat x_n\}$.
+\begin{verbatim}
+$\wh X=\{\hat x_1,\dots,\hat x_n\}$
+\end{verbatim}
+Define multiplication for the elements of $\wh X$ by
+\begin{equation}\label{multdef}
+\hat x_i\hat x_j=\hat x_j\hat x_i,\quad \hat x^2_i=0,\quad
+i,j=1,\dots,n.
+\end{equation}
+Let $\hat k_{ij}=k_{ij}\hat x_j$ and $\hat k_{ij}=-\sum_{j\not=i} \hat
+k_{ij}$. Then the number of Hamiltonian cycles $H_c$ is given by the
+relation \cite{liuchow:formalsum}
+\begin{equation}\label{H-cycles}
+\biggl(\prod^n_{\,j=1}\hat x_j\biggr)H_c=\frac{1}{2}\hat k_{ij}\det
+\wh{\mathbf{K}}(i|i),\qquad i=1,\dots,n.
+\end{equation}
+The task here is to express \eqref{H-cycles}
+in a form free of any $\hat x_i$,
+$i=1,\dots,n$. The result also leads to the resolution of enumeration of
+Hamiltonian paths in a graph.
+
+It is well known that the enumeration of Hamiltonian cycles and paths in
+a complete graph $K_n$ and in a complete bipartite graph $K_{n_1n_2}$
+can only be found from \textit{first combinatorial principles}
+\cite{hapa:graphenum}. One wonders if there exists a formula which can
+be used very efficiently to produce $K_n$ and $K_{n_1n_2}$. Recently,
+using Lagrangian methods, Goulden and Jackson have shown that $H_c$ can
+be expressed in terms of the determinant and permanent of the adjacency
+matrix \cite{gouja:lagrmeth}. However, the formula of Goulden and
+Jackson determines neither $K_n$ nor $K_{n_1n_2}$ effectively. In this
+paper, using an algebraic method, we parametrize the adjacency matrix.
+The resulting formula also involves the determinant and permanent, but
+it can easily be applied to $K_n$ and $K_{n_1n_2}$. In addition, we
+eliminate the permanent from $H_c$ and show that $H_c$ can be
+represented by a determinantal function of multivariables, each variable
+with domain $\{0,1\}$. Furthermore, we show that $H_c$ can be written by
+number of spanning trees of subgraphs. Finally, we apply the formulas to
+a complete multigraph $K_{n_1\dots n_p}$.
+
+The conditions $a_{ij}=a_{ji}$, $i,j=1,\dots,n$, are not required in
+this paper. All formulas can be extended to a digraph simply by
+multiplying $H_c$ by 2.
+
+\section{Main Theorem}
+\label{s:mt}
+
+\begin{notation} For $p,q\in P$ and $n\in\omega$ we write
+$(q,n)\le(p,n)$ if $q\le p$ and $A_{q,n}=A_{p,n}$.
+\begin{verbatim}
+\begin{notation} For $p,q\in P$ and $n\in\omega$
+...
+\end{notation}
+\end{verbatim}
+\end{notation}
+
+Let $\mathbf{B}=(b_{ij})$ be an $n\times n$ matrix. Let $\mathbf{n}=\{1,
+\dots,n\}$. Using the properties of \eqref{multdef}, it is readily seen
+that
+
+\begin{lem}\label{lem-per}
+\begin{equation}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat x_i\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)\per \mathbf{B}
+\end{equation}
+where $\per \mathbf{B}$ is the permanent of $\mathbf{B}$.
+\end{lem}
+
+Let $\wh Y=\{\hat y_1,\dots,\hat y_n\}$. Define multiplication
+for the elements of $\wh Y$ by
+\begin{equation}
+\hat y_i\hat y_j+\hat y_j\hat y_i=0,\quad i,j=1,\dots,n.
+\end{equation}
+Then, it follows that
+\begin{lem}\label{lem-det}
+\begin{equation}\label{detprod}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat y_j\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat y_i\biggr)\det\mathbf{B}.
+\end{equation}
+\end{lem}
+
+Note that all basic properties of determinants are direct consequences
+of Lemma ~\ref{lem-det}. Write
+\begin{equation}\label{sum-bij}
+\sum_{j\in\mathbf{n}}b_{ij}\hat y_j=\sum_{j\in\mathbf{n}}b^{(\lambda)}
+_{ij}\hat y_j+(b_{ii}-\lambda_i)\hat y_i\hat y
+\end{equation}
+where
+\begin{equation}
+b^{(\lambda)}_{ii}=\lambda_i,\quad b^{(\lambda)}_{ij}=b_{ij},
+\quad i\not=j.
+\end{equation}
+Let $\mathbf{B}^{(\lambda)}=(b^{(\lambda)}_{ij})$. By \eqref{detprod}
+and \eqref{sum-bij}, it is
+straightforward to show the following
+result:
+\begin{thm}\label{thm-main}
+\begin{equation}\label{detB}
+\det\mathbf{B}=
+\sum^n_{l =0}\sum_{I_l \subseteq n}
+\prod_{i\in I_l}(b_{ii}-\lambda_i)
+\det\mathbf{B}^{(\lambda)}(I_l |I_l ),
+\end{equation}
+where $I_l =\{i_1,\dots,i_l \}$ and $\mathbf{B}^{(\lambda)}(I_l |I_l )$
+is the principal submatrix obtained from $\mathbf{B}^{(\lambda)}$
+by deleting its $i_1,\dots,i_l $ rows and columns.
+\end{thm}
+
+\begin{rem}
+Let $\mathbf{M}$ be an $n\times n$ matrix. The convention
+$\mathbf{M}(\mathbf{n}|\mathbf{n})=1$ has been used in \eqref{detB} and
+hereafter.
+\end{rem}
+
+Before proceeding with our discussion, we pause to note that
+\thmref{thm-main} yields immediately a fundamental formula which can be
+used to compute the coefficients of a characteristic polynomial
+\cite{mami:matrixth}:
+\begin{cor}\label{BI}
+Write $\det(\mathbf{B}-x\mathbf{I})=\sum^n_{l =0}(-1)
+^l b_l x^l $. Then
+\begin{equation}\label{bl-sum}
+b_l =\sum_{I_l \subseteq\mathbf{n}}\det\mathbf{B}(I_l |I_l ).
+\end{equation}
+\end{cor}
+Let
+\begin{equation}
+\mathbf{K}(t,t_1,\dots,t_n)
+=\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix},
+\end{equation}
+\begin{verbatim}
+\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}
+\end{verbatim}
+where
+\begin{equation}
+D_i=\sum_{j\in\mathbf{n}}a_{ij}t_j,\quad i=1,\dots,n.
+\end{equation}
+
+Set
+\begin{equation*}
+D(t_1,\dots,t_n)=\frac{\delta}{\delta t}\eval{\det\mathbf{K}(t,t_1,\dots,t_n)
+}_{t=1}.
+\end{equation*}
+Then
+\begin{equation}\label{sum-Di}
+D(t_1,\dots,t_n)
+=\sum_{i\in\mathbf{n}}D_i\det\mathbf{K}(t=1,t_1,\dots,t_n; i|i),
+\end{equation}
+where $\mathbf{K}(t=1,t_1,\dots,t_n; i|i)$ is the $i$th principal
+submatrix of $\mathbf{K}(t=1,t_1,\dots,t_n)$.
+
+Theorem ~\ref{thm-main} leads to
+\begin{equation}\label{detK1}
+\det\mathbf{K}(t_1,t_1,\dots,t_n)
+=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}t^{n-\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda t)}(\overline{I}|\overline I).
+\end{equation}
+Note that
+\begin{equation}\label{detK2}
+\det\mathbf{K}(t=1,t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda)}(\overline{I}|\overline{I})=0.
+\end{equation}
+
+Let $t_i=\hat x_i,i=1,\dots,n$. Lemma ~\ref{lem-per} yields
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\begin{verbatim}
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\end{verbatim}
+
+By \eqref{H-cycles}, \eqref{detprod}, and \eqref{sum-bij}, we have
+\begin{prop}\label{prop:eg}
+\begin{equation}
+H_c=\frac1{2n}\sum^n_{l =0}(-1)^{l}
+D_{l},
+\end{equation}
+where
+\begin{equation}\label{delta-l}
+D_{l}=\eval[2]{\sum_{I_{l}\subseteq \mathbf{n}}
+D(t_1,\dots,t_n)}_{t_i=\left\{\begin{smallmatrix}
+0,& \text{if }i\in I_{l}\quad\\% \quad added for centering
+1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}.
+\end{equation}
+\end{prop}
+
+\section{Application}
+\label{lincomp}
+
+We consider here the applications of Theorems~\ref{th-info-ow-ow} and
+~\ref{th-weak-ske-owf} to a complete
+multipartite graph $K_{n_1\dots n_p}$. It can be shown that the
+number of spanning trees of $K_{n_1\dots n_p}$
+may be written
+\begin{equation}\label{e:st}
+T=n^{p-2}\prod^p_{i=1}
+(n-n_i)^{n_i-1}
+\end{equation}
+where
+\begin{equation}
+n=n_1+\dots+n_p.
+\end{equation}
+
+It follows from Theorems~\ref{th-info-ow-ow}
+and~\ref{th-weak-ske-owf} that
+\begin{equation}\label{e:barwq}
+\begin{split}
+H_c&=\frac1{2n}
+\sum^n_{{l}=0}(-1)^{l}(n-{l})^{p-2}
+\sum_{l _1+\dots+l _p=l}\prod^p_{i=1}
+\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
+\biggl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\biggr].\end{split}
+\end{equation}
+\begin{verbatim}
+... \binom{n_i}{l _i}\\
+\end{verbatim}
+and
+\begin{equation}\label{joe}
+\begin{split}
+H_c&=\frac12\sum^{n-1}_{l =0}
+(-1)^{l}(n-l )^{p-2}
+\sum_{l _1+\dots+l _p=l}
+\prod^p_{i=1}\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}
+\left(1-\frac{l _p}{n_p}\right)
+[(n-l )-(n_p-l _p)].
+\end{split}
+\end{equation}
+
+The enumeration of $H_c$ in a $K_{n_1\dotsm n_p}$ graph can also be
+carried out by Theorem ~\ref{thm-H-param} or ~\ref{thm-asym}
+together with the algebraic method of \eqref{multdef}.
+Some elegant representations may be obtained. For example, $H_c$ in
+a $K_{n_1n_2n_3}$ graph may be written
+\begin{equation}\label{j:mark}
+\begin{split}
+H_c=&
+\frac{n_1!\,n_2!\,n_3!}
+{n_1+n_2+n_3}\sum_i\left[\binom{n_1}{i}
+\binom{n_2}{n_3-n_1+i}\binom{n_3}{n_3-n_2+i}\right.\\
+&+\left.\binom{n_1-1}{i}
+\binom{n_2-1}{n_3-n_1+i}
+\binom{n_3-1}{n_3-n_2+i}\right].\end{split}
+\end{equation}
+
+\section{Secret Key Exchanges}
+\label{SKE}
+
+Modern cryptography is fundamentally concerned with the problem of
+secure private communication. A Secret Key Exchange is a protocol
+where Alice and Bob, having no secret information in common to start,
+are able to agree on a common secret key, conversing over a public
+channel. The notion of a Secret Key Exchange protocol was first
+introduced in the seminal paper of Diffie and Hellman
+\cite{dihe:newdir}. \cite{dihe:newdir} presented a concrete
+implementation of a Secret Key Exchange protocol, dependent on a
+specific assumption (a variant on the discrete log), specially
+tailored to yield Secret Key Exchange. Secret Key Exchange is of
+course trivial if trapdoor permutations exist. However, there is no
+known implementation based on a weaker general assumption.
+
+The concept of an informationally one-way function was introduced
+in \cite{imlelu:oneway}. We give only an informal definition here:
+
+\begin{defn} A polynomial time
+computable function $f = \{f_k\}$ is informationally
+one-way if there is no probabilistic polynomial time algorithm which
+(with probability of the form $1 - k^{-e}$ for some $e > 0$)
+returns on input $y \in \{0,1\}^{k}$ a random element of $f^{-1}(y)$.
+\end{defn}
+In the non-uniform setting \cite{imlelu:oneway} show that these are not
+weaker than one-way functions:
+\begin{thm}[\cite{imlelu:oneway} (non-uniform)]
+\label{th-info-ow-ow}
+The existence of informationally one-way functions
+implies the existence of one-way functions.
+\end{thm}
+We will stick to the convention introduced above of saying
+``non-uniform'' before the theorem statement when the theorem
+makes use of non-uniformity. It should be understood that
+if nothing is said then the result holds for both the uniform and
+the non-uniform models.
+
+It now follows from \thmref{th-info-ow-ow} that
+
+\begin{thm}[non-uniform]\label{th-weak-ske-owf} Weak SKE
+implies the existence of a one-way function.
+\end{thm}
+
+More recently, the polynomial-time, interior point algorithms for linear
+programming have been extended to the case of convex quadratic programs
+\cite{moad:quadpro,ye:intalg}, certain linear complementarity problems
+\cite{komiyo:lincomp,miyoki:lincomp}, and the nonlinear complementarity
+problem \cite{komiyo:unipfunc}. The connection between these algorithms
+and the classical Newton method for nonlinear equations is well
+explained in \cite{komiyo:lincomp}.
+
+\section{Review}
+\label{computation}
+
+We begin our discussion with the following definition:
+
+\begin{defn}
+
+A function $H\colon \Re^n \to \Re^n$ is said to be
+\emph{B-differentiable} at the point $z$ if (i)~$H$ is Lipschitz
+continuous in a neighborhood of $z$, and (ii)~ there exists a positive
+homogeneous function $BH(z)\colon \Re^n \to \Re^n$, called the
+\emph{B-derivative} of $H$ at $z$, such that
+\[ \lim_{v \to 0} \frac{H(z+v) - H(z) - BH(z)v}{\enVert{v}} = 0. \]
+The function $H$ is \textit{B-differentiable in set $S$} if it is
+B-differentiable at every point in $S$. The B-derivative $BH(z)$ is said
+to be \textit{strong} if
+\[ \lim_{(v,v') \to (0,0)} \frac{H(z+v) - H(z+v') - BH(z)(v
+ -v')}{\enVert{v - v'}} = 0. \]
+\end{defn}
+
+
+\begin{lem}\label{limbog} There exists a smooth function $\psi_0(z)$
+defined for $\abs{z}>1-2a$ satisfying the following properties\textup{:}
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item $\psi_0(z)$ is bounded above and below by positive constants
+$c_1\leq \psi_0(z)\leq c_2$.
+\item If $\abs{z}>1$, then $\psi_0(z)=1$.
+\item For all $z$ in the domain of $\psi_0$, $\Delta_0\ln \psi_0\geq 0$.
+\item If $1-2a<\abs{z}<1-a$, then $\Delta_0\ln \psi_0\geq
+c_3>0$.
+\end{enumerate}
+\end{lem}
+
+\begin{proof}
+We choose $\psi_0(z)$ to be a radial function depending only on $r=\abs{z}$.
+Let $h(r)\geq 0$ be a suitable smooth function satisfying $h(r)\geq c_3$
+for $1-2a<\abs{z}<1-a$, and $h(r)=0$ for $\abs{z}>1-\tfrac a2$. The radial
+Laplacian
+\[\Delta_0\ln\psi_0(r)=\left(\frac {d^2}{dr^2}+\frac
+1r\frac d{dr}\right)\ln\psi_0(r)\]
+has smooth coefficients for $r>1-2a$. Therefore, we may
+apply the existence and uniqueness theory for ordinary differential
+equations. Simply let $\ln \psi_0(r)$ be the solution of the differential
+equation
+\[\left(\frac{d^2}{dr^2}+\frac 1r\frac d{dr}\right)\ln \psi_0(r)=h(r)\]
+with initial conditions given by $\ln \psi_0(1)=0$ and
+$\ln\psi_0'(1)=0$.
+
+Next, let $D_\nu$ be a finite collection of pairwise disjoint disks,
+all of which are contained in the unit disk centered at the origin in
+$C$. We assume that $D_\nu=\{z\mid \abs{z-z_\nu}<\delta\}$. Suppose that
+$D_\nu(a)$ denotes the smaller concentric disk $D_\nu(a)=\{z\mid
+\abs{z-z_\nu}\leq (1-2a)\delta\}$. We define a smooth weight function
+$\Phi_0(z)$ for $z\in C-\bigcup_\nu D_\nu(a)$ by setting $\Phi_
+0(z)=1$ when $z\notin \bigcup_\nu D_\nu$ and $\Phi_
+0(z)=\psi_0((z-z_\nu)/\delta)$ when $z$ is an element of $D_\nu$. It
+follows from \lemref{limbog} that $\Phi_ 0$ satisfies the properties:
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item \label{boundab}$\Phi_ 0(z)$ is bounded above and below by
+positive constants $c_1\leq \Phi_ 0(z)\leq c_2$.
+\item \label{d:over}$\Delta_0\ln\Phi_ 0\geq 0$ for all
+$z\in C-\bigcup_\nu D_\nu(a)$,
+the domain where the function $\Phi_ 0$ is defined.
+\item \label{d:ad}$\Delta_0\ln\Phi_ 0\geq c_3\delta^{-2}$
+when $(1-2a)\delta<\abs{z-z_\nu}<(1-a)\delta$.
+\end{enumerate}
+Let $A_\nu$ denote the annulus $A_\nu=\{(1-2a)\delta<\abs{z-z_\nu}<(1-a)
+\delta \}$, and set $A=\bigcup_\nu A_\nu$. The
+properties (\ref{d:over}) and (\ref{d:ad}) of $\Phi_ 0$
+may be summarized as $\Delta_0\ln \Phi_ 0\geq c_3\delta^{-2}\chi_A$,
+where $\chi _A$ is the characteristic function of $A$.
+\end{proof}
+
+Suppose that $\alpha$ is a nonnegative real constant. We apply
+Proposition~\ref{prop:eg} with $\Phi(z)=\Phi_ 0(z) e^{\alpha\abs{z}^2}$. If
+$u\in C^\infty_0(R^2-\bigcup_\nu D_\nu(a))$, assume that $\mathcal{D}$
+is a bounded domain containing the support of $u$ and $A\subset
+\mathcal{D}\subset R^2-\bigcup_\nu D_\nu(a)$. A calculation gives
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2\Phi_ 0(z) e^{\alpha\abs{z}^2}
+\geq c_4\alpha\int_{\mathcal{D}}\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}
++c_5\delta^{-2}\int_ A\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}.\]
+
+The boundedness, property (\ref{boundab}) of $\Phi_ 0$, then yields
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2e^{\alpha\abs{z}^2}\geq c_6\alpha
+\int_{\mathcal{D}}\abs{u}^2e^{\alpha\abs{z}^2}
++c_7\delta^{-2}\int_ A\abs{u}^2e^{\alpha\abs{z}^2}.\]
+
+Let $B(X)$ be the set of blocks of $\Lambda_{X}$
+and let $b(X) = \abs{B(X)}$. If $\phi \in Q_{X}$ then
+$\phi$ is constant on the blocks of $\Lambda_{X}$.
+\begin{equation}\label{far-d}
+ P_{X} = \{ \phi \in M \mid \Lambda_{\phi} = \Lambda_{X} \},
+\qquad
+Q_{X} = \{\phi \in M \mid \Lambda_{\phi} \geq \Lambda_{X} \}.
+\end{equation}
+If $\Lambda_{\phi} \geq \Lambda_{X}$ then
+$\Lambda_{\phi} = \Lambda_{Y}$ for some $Y \geq X$ so that
+\[ Q_{X} = \bigcup_{Y \geq X} P_{Y}. \]
+Thus by M\"obius inversion
+\[ \abs{P_{Y}}= \sum_{X\geq Y} \mu (Y,X)\abs{Q_{X}}.\]
+Thus there is a bijection from $Q_{X}$ to $W^{B(X)}$.
+In particular $\abs{Q_{X}} = w^{b(X)}$.
+
+Next note that $b(X)=\dim X$. We see this by choosing a
+basis for $X$ consisting of vectors $v^{k}$ defined by
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\begin{verbatim}
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\end{verbatim}
+
+\begin{lem}\label{p0201}
+Let $\A$ be an arrangement. Then
+\[ \chi (\A,t) = \sum_{\B \subseteq \A}
+(-1)^{\abs{\B}} t^{\dim T(\B)}. \]
+\end{lem}
+
+In order to compute $R''$ recall the definition
+of $S(X,Y)$ from \lemref{lem-per}. Since $H \in \B$,
+$\A_{H} \subseteq \B$. Thus if $T(\B) = Y$ then
+$\B \in S(H,Y)$. Let $L'' = L(\A'')$. Then
+\begin{equation}\label{E_SXgYy}
+\begin{split}
+R''&= \sum_{H\in \B \subseteq \A} (-1)^{\abs{\B}}
+t^{\dim T(\B)}\\
+&= \sum_{Y \in L''} \sum_{\B \in S(H,Y)}
+(-1)^{\abs{\B}}t^{\dim Y} \\
+&= -\sum_{Y \in L''} \sum_{\B \in S(H,Y)} (-1)^
+{\abs{\B - \A_{H}}} t^{\dim Y} \\
+&= -\sum_{Y \in L''} \mu (H,Y)t^{\dim Y} \\
+&= -\chi (\A '',t).
+\end{split}
+\end{equation}
+
+\begin{cor}\label{tripleA}
+Let $(\A,\A',\A'')$ be a triple of arrangements. Then
+\[ \pi (\A,t) = \pi (\A',t) + t \pi (\A'',t). \]
+\end{cor}
+
+\begin{defn}
+Let $(\A,\A',\A'')$ be a triple with respect to
+the hyperplane $H \in \A$. Call $H$ a \textit{separator}
+if $T(\A) \not\in L(\A')$.
+\end{defn}
+
+\begin{cor}\label{nsep}
+Let $(\A,\A',\A'')$ be a triple with respect to $H \in \A$.
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item
+If $H$ is a separator then
+\[ \mu (\A) = - \mu (\A'') \]
+and hence
+\[ \abs{\mu (\A)} = \abs{ \mu (\A'')}. \]
+
+\item If $H$ is not a separator then
+\[\mu (\A) = \mu (\A') - \mu (\A'') \]
+and
+\[ \abs{\mu (\A)} = \abs{\mu (\A')} + \abs{\mu (\A'')}. \]
+\end{enumerate}
+\end{cor}
+
+\begin{proof}
+It follows from \thmref{th-info-ow-ow} that $\pi(\A,t)$
+has leading term
+\[(-1)^{r(\A)}\mu (\A)t^{r(\A)}.\]
+The conclusion
+follows by comparing coefficients of the leading
+terms on both sides of the equation in
+Corollary~\ref{tripleA}. If $H$ is a separator then
+$r(\A') < r(\A)$ and there is no contribution
+from $\pi (\A',t)$.
+\end{proof}
+
+The Poincar\'e polynomial of an arrangement
+will appear repeatedly
+in these notes. It will be shown to equal the
+Poincar\'e polynomial
+of the graded algebras which we are going to
+associate with $\A$. It is also the Poincar\'e
+polynomial of the complement $M(\A)$ for a
+complex arrangement. Here we prove
+that the Poincar\'e polynomial is the chamber
+counting function for a real arrangement. The
+complement $M(\A)$ is a disjoint union of chambers
+\[M(\A) = \bigcup_{C \in \Cham(\A)} C.\]
+The number
+of chambers is determined by the Poincar\'e
+polynomial as follows.
+
+\begin{thm}\label{th-realarr}
+Let $\A_{\mathbf{R}}$ be a real arrangement. Then
+\[ \abs{\Cham(\A_{\mathbf{R}})} = \pi (\A_{\mathbf{R}},1). \]
+\end{thm}
+
+\begin{proof}
+We check the properties required in Corollary~\ref{nsep}:
+(i) follows from $\pi (\Phi_{ l},t) = 1$, and (ii) is a
+consequence of Corollary~\ref{BI}.
+\end{proof}
+
+\begin{figure}
+\vspace{5cm}
+(figure intentionally left blank)
+\caption[]{$Q(\A_{1}) = xyz(x-z)(x+z)(y-z)(y+z)$}
+\end{figure}
+
+\begin{figure}
+\vspace{5cm}
+(figure intentionally left blank)
+\caption[]{$Q(\A_{2})= xyz(x+y+z)(x+y-z)(x-y+z)(x-y-z)$}
+\end{figure}
+
+
+\begin{thm}
+\label{T_first_the_int}
+Let $\phi$ be a protocol for a random pair $\XcY$.
+If one of $\st_\phi(x',y)$ and $\st_\phi(x,y')$ is a prefix of the other
+and $(x,y)\in\SXY$, then
+\[
+\langle \st_j(x',y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y')\rangle_{j=1}^\infty .
+\]
+\end{thm}
+\begin{proof}
+We show by induction on $i$ that
+\[
+\langle \st_j(x',y)\rangle_{j=1}^i
+=\langle \st_j(x,y)\rangle_{j=1}^i
+=\langle \st_j(x,y')\rangle_{j=1}^i.
+\]
+The induction hypothesis holds vacuously for $i=0$. Assume it holds for
+$i-1$, in particular
+$[\st_j(x',y)]_{j=1}^{i-1}=[\st_j(x,y')]_{j=1}^{i-1}$. Then one of
+$[\st_j(x',y)]_{j=i}^{\infty}$ and $[\st_j(x,y')]_{j=i}^{\infty}$ is a
+prefix of the other which implies that one of $\st_i(x',y)$ and
+$\st_i(x,y')$ is a prefix of the other. If the $i$th message is
+transmitted by $P_\X$ then, by the separate-transmissions property and
+the induction hypothesis, $\st_i(x,y)=\st_i(x,y')$, hence one of
+$\st_i(x,y)$ and $\st_i(x',y)$ is a prefix of the other. By the
+implicit-termination property, neither $\st_i(x,y)$ nor $\st_i(x',y)$
+can be a proper prefix of the other, hence they must be the same and
+$\st_i(x',y)=\st_i(x,y)=\st_i(x,y')$. If the $i$th message is
+transmitted by $\PY$ then, symmetrically, $\st_i(x,y)=\st_i(x',y)$ by
+the induction hypothesis and the separate-transmissions property, and,
+then, $\st_i(x,y)=\st_i(x,y')$ by the implicit-termination property,
+proving the induction step.
+\end{proof}
+
+If $\phi$ is a protocol for $(X,Y)$, and $(x,y)$, $(x',y)$ are distinct
+inputs in $\SXY$, then, by the correct-decision property,
+$\langle\st_j(x,y)\rangle_{j=1}^\infty\ne\langle
+\st_j(x',y)\rangle_{j=1}^\infty$.
+
+Equation~(\ref{E_SXgYy}) defined $\PY$'s ambiguity set $\SXgYy$
+to be the set of possible $X$ values when $Y=y$.
+The last corollary implies that for all $y\in\SY$,
+the multiset%
+\footnote{A multiset allows multiplicity of elements.
+Hence, $\{0,01,01\}$ is prefix free as a set, but not as a multiset.}
+of codewords $\{\st_\phi(x,y):x\in\SXgYy\}$ is prefix free.
+
+\section{One-Way Complexity}
+\label{S_Cp1}
+
+$\Cw1$, the one-way complexity of a random pair $\XcY$,
+is the number of bits $P_\X$ must transmit in the worst case
+when $\PY$ is not permitted to transmit any feedback messages.
+Starting with $\SXY$, the support set of $\XcY$, we define $\G$,
+the \textit{characteristic hypergraph} of $\XcY$, and show that
+\[
+\Cw1=\lceil\,\log\chi(\G)\rceil\ .
+\]
+
+Let $\XcY$ be a random pair. For each $y$ in $\SY$, the support set of
+$Y$, Equation~(\ref{E_SXgYy}) defined $\SXgYy$ to be the set of possible
+$x$ values when $Y=y$. The \textit{characteristic hypergraph} $\G$ of
+$\XcY$ has $\SX$ as its vertex set and the hyperedge $\SXgYy$ for each
+$y\in\SY$.
+
+
+We can now prove a continuity theorem.
+\begin{thm}\label{t:conl}
+Let $\Omega \subset\mathbf{R}^n$ be an open set, let
+$u\in BV(\Omega ;\mathbf{R}^m)$, and let
+\begin{equation}\label{quts}
+T^u_x=\left\{y\in\mathbf{R}^m:
+ y=\tilde u(x)+\left\langle \frac{Du}{\abs{Du}}(x),z
+\right\rangle \text{ for some }z\in\mathbf{R}^n\right\}
+\end{equation}
+for every $x\in\Omega \backslash S_u$. Let $f\colon \mathbf{R}^m\to
+\mathbf{R}^k$ be a Lipschitz continuous function such that $f(0)=0$, and
+let $v=f(u)\colon \Omega \to \mathbf{R}^k$. Then $v\in BV(\Omega
+;\mathbf{R}^k)$ and
+\begin{equation}
+Jv=\eval{(f(u^+)-f(u^-))\otimes \nu_u\cdot\,
+\mathcal{H}_{n-1}}_{S_u}.
+\end{equation}
+In addition, for $\abs{\wt{D}u}$-almost every $x\in\Omega $ the
+restriction of the function $f$ to $T^u_x$ is differentiable at $\tilde
+u(x)$ and
+\begin{equation}
+\wt{D}v=\nabla (\eval{f}_{T^u_x})(\tilde u)
+\frac{\wt{D}u}{\abs{\wt{D}u}}\cdot\abs{\wt{D}u}.\end{equation}
+\end{thm}
+
+Before proving the theorem, we state without proof three elementary
+remarks which will be useful in the sequel.
+\begin{rem}\label{r:omb}
+Let $\omega\colon \left]0,+\infty\right[\to \left]0,+\infty\right[$
+be a continuous function such that $\omega (t)\to 0$ as $t\to
+0$. Then
+\[\lim_{h\to 0^+}g(\omega(h))=L\Leftrightarrow\lim_{h\to
+0^+}g(h)=L\]
+for any function $g\colon \left]0,+\infty\right[\to \mathbf{R}$.
+\end{rem}
+\begin{rem}\label{r:dif}
+Let $g \colon \mathbf{R}^n\to \mathbf{R}$ be a Lipschitz
+continuous function and assume that
+\[L(z)=\lim_{h\to 0^+}\frac{g(hz)-g(0)}h\]
+exists for every $z\in\mathbf{Q}^n$ and that $L$ is a linear function of
+$z$. Then $g$ is differentiable at 0.
+\end{rem}
+\begin{rem}\label{r:dif0}
+Let $A \colon \mathbf{R}^n\to \mathbf{R}^m$ be a linear function, and
+let $f \colon \mathbf{R}^m\to \mathbf{R}$ be a function. Then the
+restriction of $f$ to the range of $A$ is differentiable at 0 if and
+only if $f(A)\colon \mathbf{R}^n\to \mathbf{R}$ is differentiable at 0
+and
+\[\nabla(\eval{f}_{\IM(A)})(0)A=\nabla (f(A))(0).\]
+\end{rem}
+
+\begin{proof}
+ We begin by showing that $v\in BV(\Omega;\mathbf{R}^k)$ and
+\begin{equation}\label{e:bomb}
+\abs{Dv}(B)\le K\abs{Du}(B)\qquad\forall B\in\mathbf{B}(\Omega ),
+\end{equation}
+where $K>0$ is the Lipschitz constant of $f$. By \eqref{sum-Di} and by
+the approximation result quoted in \secref{s:mt}, it is possible to find
+a sequence $(u_h)\subset C^1(\Omega ;\mathbf{R}^m)$ converging to $u$ in
+$L^1(\Omega ;\mathbf{R}^m)$ and such that
+\[\lim_{h\to +\infty}\int_\Omega \abs{\nabla u_h}\,dx=\abs{Du}(\Omega ).\]
+The functions $v_h=f(u_h)$ are locally Lipschitz continuous in $\Omega
+$, and the definition of differential implies that $\abs{\nabla v_h}\le
+K\abs{\nabla u_h}$ almost everywhere in $\Omega $. The lower semicontinuity
+of the total variation and \eqref{sum-Di} yield
+\begin{equation}
+\begin{split}
+\abs{Dv}(\Omega )\le\liminf_{h\to +\infty}\abs{Dv_h}(\Omega) &
+=\liminf_{h\to +\infty}\int_\Omega \abs{\nabla v_h}\,dx\\
+&\le K\liminf_{h\to +\infty}\int_\Omega
+\abs{\nabla u_h}\,dx=K\abs{Du}(\Omega).
+\end{split}\end{equation}
+Since $f(0)=0$, we have also
+\[\int_\Omega \abs{v}\,dx\le K\int_\Omega \abs{u}\,dx;\]
+therefore $u\in BV(\Omega ;\mathbf{R}^k)$. Repeating the same argument
+for every open set $A\subset\Omega $, we get \eqref{e:bomb} for every
+$B\in\mathbf{B}(\Omega)$, because $\abs{Dv}$, $\abs{Du}$ are Radon measures. To
+prove \lemref{limbog}, first we observe that
+\begin{equation}\label{e:SS}
+S_v\subset S_u,\qquad\tilde v(x)=f(\tilde u(x))\qquad \forall x\in\Omega
+\backslash S_u.\end{equation}
+In fact, for every $\varepsilon >0$ we have
+\[\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>\varepsilon \}\subset \{y\in
+B_\rho(x): \abs{u(y)-\tilde u(x)}>\varepsilon /K\},\]
+hence
+\[\lim_{\rho\to 0^+}\frac{\abs{\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>
+\varepsilon \}}}{\rho^n}=0\]
+whenever $x\in\Omega \backslash S_u$. By a similar argument, if $x\in
+S_u$ is a point such that there exists a triplet $(u^+,u^-,\nu_u)$
+satisfying \eqref{detK1}, \eqref{detK2}, then
+\[
+(v^+(x)-v^-(x))\otimes \nu_v=(f(u^+(x))-f(u^-(x)))\otimes\nu_u\quad
+\text{if }x\in S_v
+\]
+and $f(u^-(x))=f(u^+(x))$ if $x\in S_u\backslash S_v$. Hence, by (1.8)
+we get
+\begin{equation*}\begin{split}
+Jv(B)=\int_{B\cap S_v}(v^+-v^-)\otimes \nu_v\,d\mathcal{H}_{n-1}&=
+\int_{B\cap S_v}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}\\
+&=\int_{B\cap S_u}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}
+\end{split}\end{equation*}
+and \lemref{limbog} is proved.
+\end{proof}
+
+To prove \eqref{e:SS}, it is not restrictive to assume that $k=1$.
+Moreover, to simplify our notation, from now on we shall assume that
+$\Omega = \mathbf{R}^n$. The proof of \eqref{e:SS} is divided into two
+steps. In the first step we prove the statement in the one-dimensional
+case $(n=1)$, using \thmref{th-weak-ske-owf}. In the second step we
+achieve the general result using \thmref{t:conl}.
+
+\subsection*{Step 1}
+Assume that $n=1$. Since $S_u$ is at most countable, \eqref{sum-bij}
+yields that $\abs{\wt{D}v}(S_u\backslash S_v)=0$, so that
+\eqref{e:st} and \eqref{e:barwq} imply that $Dv=\wt{D}v+Jv$ is
+the Radon-Nikod\'ym decomposition of $Dv$ in absolutely continuous and
+singular part with respect to $\abs{\wt{D} u}$. By
+\thmref{th-weak-ske-owf}, we have
+\begin{equation*}
+\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Dv(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})},\qquad
+\frac{\wt{D}u}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Du(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{equation*}
+$\abs{\wt{D}u}$-almost everywhere in $\mathbf{R}$. It is well known
+(see, for instance, \cite[2.5.16]{ste:sint}) that every one-dimensional
+function of bounded variation $w$ has a unique left continuous
+representative, i.e., a function $\hat w$ such that $\hat w=w$ almost
+everywhere and $\lim_{s\to t^-}\hat w(s)=\hat w(t)$ for every $t\in
+\mathbf{R}$. These conditions imply
+\begin{equation}
+\hat u(t)=Du(\interval{\left]-\infty,t\right[}),
+\qquad \hat v(t)=Dv(\interval{\left]-\infty,t\right[})\qquad
+\forall t\in\mathbf{R}
+\end{equation}
+and
+\begin{equation}\label{alimo}
+\hat v(t)=f(\hat u(t))\qquad\forall t\in\mathbf{R}.\end{equation}
+Let $t\in\mathbf{R}$ be such that
+$\abs{\wt{D}u}(\interval{\left[t,s\right[})>0$ for every $s>t$ and
+assume that the limits in \eqref{joe} exist. By \eqref{j:mark} and
+\eqref{far-d} we get
+\begin{equation*}\begin{split}
+\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}&=\frac {f(\hat
+u(s))-f(\hat u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&=\frac{f(\hat u(s))-f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}u
+}(\interval{\left[t,s\right[}))}%
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&+\frac
+{f(\hat u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}
+u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{split}\end{equation*}
+for every $s>t$. Using the Lipschitz condition on $f$ we find
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}
+\left\lvert\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} -\frac{f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)
+\abs{\wt{D}u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\right\rvert\\
+\le K\left\lvert
+\frac{\hat u(s)-\hat u(t)}
+ {\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+-\frac{\wt{D}u}{\abs{
+\wt{D}u}}(t)\right\rvert.\end{multline*}
+}% end of group with \multlinegap=0pt
+By \eqref{e:bomb}, the function $s\to
+\abs{\wt{D}u}(\interval{\left[t,s\right[})$ is continuous and
+converges to 0 as $s\downarrow t$. Therefore Remark~\ref{r:omb} and the
+previous inequality imply
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0^+}
+\frac{f(\hat u(t)+h\dfrac{\wt{D}u}{\abs{\wt{D}u}}
+(t))-f(\hat u(t))}h\quad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}.\]
+By \eqref{joe}, $\hat u(x)=\tilde u(x)$ for every
+$x\in\mathbf{R}\backslash S_u$; moreover, applying the same argument to
+the functions $u'(t)=u(-t)$, $v'(t)=f(u'(t))=v(-t)$, we get
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0}
+\frac{f(\tilde u(t)
++h\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t))-f(\tilde u(t))}{h}
+\qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}\]
+and our statement is proved.
+
+\subsection*{Step 2}
+
+Let us consider now the general case $n>1$. Let $\nu\in \mathbf{R}^n$ be
+such that $\abs{\nu}=1$, and let $\pi_\nu=\{y\in\mathbf{R}^n: \langle
+y,\nu\rangle =0\}$. In the following, we shall identify $\mathbf{R}^n$
+with $\pi_\nu\times\mathbf{R}$, and we shall denote by $y$ the variable
+ranging in $\pi_\nu$ and by $t$ the variable ranging in $\mathbf{R}$. By
+the just proven one-dimensional result, and by \thmref{thm-main}, we get
+\[\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\wt{D}u_y}{\abs{
+\wt{D}u_y}}(t))-f(\tilde u(y+t\nu))}h=\frac{\wt{D}v_y}{\abs{
+\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}\]
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. We claim that
+\begin{equation}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}u_y}
+{\abs{\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}
+\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$. In fact, by
+\eqref{sum-ali} and \eqref{delta-l} we get
+\begin{multline*}
+\int_{\pi_\nu}\frac{\wt{D}u_y}{\abs{\wt{D}u_y}}\cdot\abs{\wt{D}u_y
+}\,d\mathcal{H}_{n-1}(y)=\int_{\pi_\nu}\wt{D}u_y\,d\mathcal{H}_{n-1}(y)\\
+=\langle \wt{D}u,\nu\rangle =\frac
+{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}\cdot
+\abs{\langle \wt{D}u,\nu\rangle }=\int_{\pi_\nu}\frac{
+\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}
+(y+\cdot \nu)\cdot\abs{\wt{D}u_y}\,d\mathcal{H}_{n-1}(y)
+\end{multline*}
+and \eqref{far-d} follows from \eqref{sum-Di}. By the same argument it
+is possible to prove that
+\begin{equation}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}v_y}{\abs{\wt{D}u_y}}(t)\qquad\abs{
+\wt{D}u_y}\text{-a.e. in }\mathbf{R}\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. By \eqref{far-d}
+and \eqref{E_SXgYy} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(y+t\nu))-f(\tilde
+u(y+t\nu))}{h}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(y+t\nu)\]
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$, and using again
+\eqref{detK1}, \eqref{detK2} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\langle
+\wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde
+u(x))}{h}=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu
+\rangle }}(x)
+\]
+$\abs{\langle \wt{D}u,\nu\rangle}$-a.e. in $\mathbf{R}^n$.
+
+Since the function $\abs{\langle \wt{D}u,\nu\rangle }/\abs{\wt{D}u}$
+is strictly positive $\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere,
+we obtain also
+\begin{multline*}
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\abs{\langle
+\wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde u(x))}{h}\\
+=\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\frac
+{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(x)
+\end{multline*}
+$\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere in $\mathbf{R}^n$.
+
+Finally, since
+\begin{align*}
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}u,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}u}{\abs{\wt{D}u}},\nu\right\rangle
+ \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n\\
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}},\nu\right\rangle
+ \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n
+\end{align*}
+and since both sides of \eqref{alimo}
+are zero $\abs{\wt{D}u}$-almost everywhere
+on $\abs{\langle \wt{D}u,\nu\rangle }$-negligible sets, we conclude that
+\[
+\lim_{h\to 0}\frac{f\left(
+\tilde u(x)+h\left\langle \dfrac{\wt{D}
+u}{\abs{\wt{D}u}}(x),\nu\right\rangle \right)-f(\tilde u(x))}h
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}}(x),\nu\right\rangle,
+\]
+$\abs{\wt{D}u}$-a.e. in $\mathbf{R}^n$.
+Since $\nu$ is arbitrary, by Remarks \ref{r:dif} and~\ref{r:dif0}
+the restriction of $f$ to
+the affine space $T^u_x$ is differentiable at $\tilde u(x)$ for $\abs{\wt{D}
+u}$-almost every $x\in \mathbf{R}^n$ and \eqref{quts} holds.\qed
+
+It follows from \eqref{sum-Di}, \eqref{detK1}, and \eqref{detK2} that
+\begin{equation}\label{Dt}
+D(t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I|\overline I).
+\end{equation}
+Let $t_i=\hat x_i$, $i=1,\dots,n$. Lemma 1 leads to
+\begin{equation}\label{Dx}
+D(\hat x_1,\dots,\hat x_n)=\prod_{i\in\mathbf{n}}\hat x_i
+\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}\per \mathbf{A}
+^{(\lambda)}(I|I)\det\mathbf{A}^{(\lambda)}(\overline I|\overline I).
+\end{equation}
+By \eqref{H-cycles}, \eqref{sum-Di}, and \eqref{Dx},
+we have the following result:
+\begin{thm}\label{thm-H-param}
+\begin{equation}\label{H-param}
+H_c=\frac{1}{2n}\sum^n_{l =1}l (-1)^{l -1}A_{l}
+^{(\lambda)},
+\end{equation}
+where
+\begin{equation}\label{A-l-lambda}
+A^{(\lambda)}_l =\sum_{I_l \subseteq\mathbf{n}}\per \mathbf{A}
+^{(\lambda)}(I_l |I_l )\det\mathbf{A}^{(\lambda)}
+(\overline I_{l}|\overline I_l ),\abs{I_{l}}=l .
+\end{equation}
+\end{thm}
+
+It is worth noting that $A_l ^{(\lambda)}$ of \eqref{A-l-lambda} is
+similar to the coefficients $b_l $ of the characteristic polynomial of
+\eqref{bl-sum}. It is well known in graph theory that the coefficients
+$b_l $ can be expressed as a sum over certain subgraphs. It is
+interesting to see whether $A_l $, $\lambda=0$, structural properties
+of a graph.
+
+We may call \eqref{H-param} a parametric representation of $H_c$. In
+computation, the parameter $\lambda_i$ plays very important roles. The
+choice of the parameter usually depends on the properties of the given
+graph. For a complete graph $K_n$, let $\lambda_i=1$, $i=1,\dots,n$.
+It follows from \eqref{A-l-lambda} that
+\begin{equation}\label{compl-gr}
+A^{(1)}_l =\begin{cases} n!,&\text{if }l =1\\
+0,&\text{otherwise}.\end{cases}
+\end{equation}
+By \eqref{H-param}
+\begin{equation}
+H_c=\frac 12(n-1)!.
+\end{equation}
+For a complete bipartite graph $K_{n_1n_2}$, let $\lambda_i=0$, $i=1,\dots,n$.
+By \eqref{A-l-lambda},
+\begin{equation}
+A_l =
+\begin{cases} -n_1!n_2!\delta_{n_1n_2},&\text{if }l =2\\
+0,&\text{otherwise }.\end{cases}
+\label{compl-bip-gr}
+\end{equation}
+Theorem ~\ref{thm-H-param}
+leads to
+\begin{equation}
+H_c=\frac1{n_1+n_2}n_1!n_2!\delta_{n_1n_2}.
+\end{equation}
+
+Now, we consider an asymmetrical approach. Theorem \ref{thm-main} leads to
+\begin{multline}
+\det\mathbf{K}(t=1,t_1,\dots,t_n;l |l )\\
+=\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\prod_{i\in I}t_i\prod_{j\in I}
+(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\end{multline}
+
+By \eqref{H-cycles} and \eqref{sum-ali} we have the following asymmetrical
+result:
+\begin{thm}\label{thm-asym}
+\begin{equation}
+H_c=\frac12\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\per\mathbf{A}^{(\lambda)}(I|I)\det
+\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \})
+\end{equation}
+which reduces to Goulden--Jackson's formula when $\lambda_i=0,i=1,\dots,n$
+\cite{mami:matrixth}.
+\end{thm}
+
+\section{Various font features of the \pkg{amsmath} package}
+\label{s:font}
+\subsection{Bold versions of special symbols}
+
+In the \pkg{amsmath} package \cn{boldsymbol} is used for getting
+individual bold math symbols and bold Greek letters---everything in
+math except for letters of the Latin alphabet,
+where you'd use \cn{mathbf}. For example,
+\begin{verbatim}
+A_\infty + \pi A_0 \sim
+\mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
+\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
+\end{verbatim}
+looks like this:
+\[A_\infty + \pi A_0 \sim \mathbf{A}_{\boldsymbol{\infty}}
+\boldsymbol{+} \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}\]
+
+\subsection{``Poor man's bold''}
+If a bold version of a particular symbol doesn't exist in the
+available fonts,
+then \cn{boldsymbol} can't be used to make that symbol bold.
+At the present time, this means that
+\cn{boldsymbol} can't be used with symbols from
+the \fn{msam} and \fn{msbm} fonts, among others.
+In some cases, poor man's bold (\cn{pmb}) can be used instead
+of \cn{boldsymbol}:
+% Can't show example from msam or msbm because this document is
+% supposed to be TeXable even if the user doesn't have
+% AMSFonts. MJD 5-JUL-1990
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\begin{verbatim}
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\end{verbatim}
+So-called ``large operator'' symbols such as $\sum$ and $\prod$
+require an additional command, \cn{mathop},
+to produce proper spacing and limits when \cn{pmb} is used.
+For further details see \textit{The \TeX book}.
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\begin{verbatim}
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\end{verbatim}
+
+\section{Compound symbols and other features}
+\label{s:comp}
+\subsection{Multiple integral signs}
+
+\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral signs
+with the spacing between them nicely adjusted, in both text and
+display style. \cn{idotsint} gives two integral signs with dots
+between them.
+\begin{gather}
+\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A
+f(x,y,z)\,dx\,dy\,dz\\
+\iiiint\limits_A
+f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k)
+\end{gather}
+
+\subsection{Over and under arrows}
+
+Some extra over and under arrow operations are provided in
+the \pkg{amsmath} package. (Basic \LaTeX\ provides
+\cn{overrightarrow} and \cn{overleftarrow}).
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\begin{verbatim}
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\end{verbatim}
+These all scale properly in subscript sizes:
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\begin{verbatim}
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\end{verbatim}
+
+\subsection{Dots}
+
+Normally you need only type \cn{dots} for ellipsis dots in a
+math formula. The main exception is when the dots
+fall at the end of the formula; then you need to
+specify one of \cn{dotsc} (series dots, after a comma),
+\cn{dotsb} (binary dots, for binary relations or operators),
+\cn{dotsm} (multiplication dots), or \cn{dotsi} (dots after
+an integral). For example, the input
+\begin{verbatim}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\].
+\end{verbatim}
+produces
+\begin{quotation}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\]
+\end{quotation}
+
+\subsection{Accents in math}
+
+Double accents:
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\begin{verbatim}
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\end{verbatim}
+This double accent operation is complicated
+and tends to slow down the processing of a \LaTeX\ file.
+
+
+\subsection{Dot accents}
+\cn{dddot} and \cn{ddddot} are available to
+produce triple and quadruple dot accents
+in addition to the \cn{dot} and \cn{ddot} accents already available
+in \LaTeX:
+\[\dddot{Q}\qquad\ddddot{R}\]
+\begin{verbatim}
+\[\dddot{Q}\qquad\ddddot{R}\]
+\end{verbatim}
+
+\subsection{Roots}
+
+In the \pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust
+the position of the root index of a radical:
+\begin{verbatim}
+\sqrt[\leftroot{-2}\uproot{2}\beta]{k}
+\end{verbatim}
+gives good positioning of the $\beta$:
+\[\sqrt[\leftroot{-2}\uproot{2}\beta]{k}\]
+
+\subsection{Boxed formulas} The command \cn{boxed} puts a box around its
+argument, like \cn{fbox} except that the contents are in math mode:
+\begin{verbatim}
+\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}
+\end{verbatim}
+\[\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}.\]
+
+\subsection{Extensible arrows}
+\cn{xleftarrow} and \cn{xrightarrow} produce
+arrows that extend automatically to accommodate unusually wide
+subscripts or superscripts. The text of the subscript or superscript
+are given as an optional resp.\@ mandatory argument:
+Example:
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+ \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\begin{verbatim}
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+ \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\end{verbatim}
+
+\subsection{\cn{overset}, \cn{underset}, and \cn{sideset}}
+Examples:
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\begin{verbatim}
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\end{verbatim}
+
+The command \cn{sideset} is for a rather special
+purpose: putting symbols at the subscript and superscript
+corners of a large operator symbol such as $\sum$ or $\prod$,
+without affecting the placement of limits.
+Examples:
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\begin{verbatim}
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\end{verbatim}
+
+\subsection{The \cn{text} command}
+The main use of the command \cn{text} is for words or phrases in a
+display:
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\begin{verbatim}
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\end{verbatim}
+
+\subsection{Operator names}
+The more common math functions such as $\log$, $\sin$, and $\lim$
+have predefined control sequences: \verb=\log=, \verb=\sin=,
+\verb=\lim=.
+The \pkg{amsmath} package provides \cn{DeclareMathOperator} and
+\cn{DeclareMathOperator*}
+for producing new function names that will have the
+same typographical treatment.
+Examples:
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\begin{verbatim}
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\end{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\begin{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\end{verbatim}
+\cn{esssup} and \cn{meas} would be defined in the document preamble as
+\begin{verbatim}
+\DeclareMathOperator*{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\end{verbatim}
+
+The following special operator names are predefined in the \pkg{amsmath}
+package: \cn{varlimsup}, \cn{varliminf}, \cn{varinjlim}, and
+\cn{varprojlim}. Here's what they look like in use:
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+ \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+ \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\begin{verbatim}
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+ \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+ \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\end{verbatim}
+
+\subsection{\cn{mod} and its relatives}
+The commands \cn{mod} and \cn{pod} are variants of
+\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses,
+whereas \cn{pod} omits the `mod' and retains the parentheses.
+Examples:
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\begin{verbatim}
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\end{verbatim}
+
+\subsection{Fractions and related constructions}
+\label{fracs}
+
+The usual notation for binomials is similar to the fraction concept,
+so it has a similar command \cn{binom} with two arguments. Example:
+\begin{equation}
+\begin{split}
+\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\begin{verbatim}
+\begin{equation}
+\begin{split}
+[\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\end{verbatim}
+There are also abbreviations
+\begin{verbatim}
+\dfrac \dbinom
+\tfrac \tbinom
+\end{verbatim}
+for the commonly needed constructions
+\begin{verbatim}
+{\displaystyle\frac ... } {\displaystyle\binom ... }
+{\textstyle\frac ... } {\textstyle\binom ... }
+\end{verbatim}
+
+The generalized fraction command \cn{genfrac} provides full access to
+the six \TeX{} fraction primitives:
+\begin{align}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+ \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+ \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+ \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{align}
+\begin{verbatim}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+ \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+ \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+ \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{verbatim}
+
+\subsection{Continued fractions}
+The continued fraction
+\begin{equation}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{equation}
+can be obtained by typing
+\begin{verbatim}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{verbatim}
+Left or right placement of any of the numerators is accomplished by using
+\cn{cfrac[l]} or \cn{cfrac[r]} instead of \cn{cfrac}.
+
+\subsection{Smash}
+
+In \pkg{amsmath} there are optional arguments \verb"t" and \verb"b" for
+the plain \TeX\ command \cn{smash}, because sometimes it is advantageous
+to be able to `smash' only the top or only the bottom of something while
+retaining the natural depth or height. In the formula
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$ \cn{smash}\verb=[b]= has been
+used to limit the size of the radical symbol.
+\begin{verbatim}
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$
+\end{verbatim}
+Without the use of \cn{smash}\verb=[b]= the formula would have appeared
+thus: $X_j=(1/\sqrt{\lambda_j})X_j'$, with the radical extending to
+encompass the depth of the subscript $j$.
+
+\subsection{The `cases' environment}
+`Cases' constructions like the following can be produced using
+the \env{cases} environment.
+\begin{equation}
+P_{r-j}=
+ \begin{cases}
+ 0& \text{if $r-j$ is odd},\\
+ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
+ \end{cases}
+\end{equation}
+\begin{verbatim}
+\begin{equation} P_{r-j}=
+ \begin{cases}
+ 0& \text{if $r-j$ is odd},\\
+ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
+ \end{cases}
+\end{equation}
+\end{verbatim}
+Notice the use of \cn{text} and the embedded math.
+
+\subsection{Matrix}
+
+Here are samples of the matrix environments,
+\cn{matrix}, \cn{pmatrix}, \cn{bmatrix}, \cn{Bmatrix}, \cn{vmatrix}
+and \cn{Vmatrix}:
+\begin{equation}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{equation}
+%
+\begin{verbatim}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{verbatim}
+
+To produce a small matrix suitable for use in text, use the
+\env{smallmatrix} environment.
+\begin{verbatim}
+\begin{math}
+ \bigl( \begin{smallmatrix}
+ a&b\\ c&d
+ \end{smallmatrix} \bigr)
+\end{math}
+\end{verbatim}
+To show
+the effect of the matrix on the surrounding lines of
+a paragraph, we put it here: \begin{math}
+ \bigl( \begin{smallmatrix}
+ a&b\\ c&d
+ \end{smallmatrix} \bigr)
+\end{math}
+and follow it with enough text to ensure that there will
+be at least one full line below the matrix.
+
+\cn{hdotsfor}\verb"{"\textit{number}\verb"}" produces a row of dots in a matrix
+spanning the given number of columns:
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\begin{verbatim}
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\end{verbatim}
+The spacing of the dots can be varied through use of a square-bracket
+option, for example, \verb"\hdotsfor[1.5]{3}". The number in square brackets
+will be used as a multiplier; the normal value is 1.
+
+\subsection{The \cn{substack} command}
+
+The \cn{substack} command can be used to produce a multiline
+subscript or superscript:
+for example
+\begin{verbatim}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{verbatim}
+produces a two-line subscript underneath the sum:
+\begin{equation}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{equation}
+A slightly more generalized form is the \env{subarray} environment which
+allows you to specify that each line should be left-aligned instead of
+centered, as here:
+\begin{equation}
+\sum_{\begin{subarray}{l}
+ 0\le i\le m\\ 0<j<n
+ \end{subarray}}
+ P(i,j)
+\end{equation}
+\begin{verbatim}
+\sum_{\begin{subarray}{l}
+ 0\le i\le m\\ 0<j<n
+ \end{subarray}}
+ P(i,j)
+\end{verbatim}
+
+
+\subsection{Big-g-g delimiters}
+Here are some big delimiters, first in \cn{normalsize}:
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]
+\begin{verbatim}
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]
+\end{verbatim}
+and now in \cn{Large} size:
+{\Large
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]}
+\begin{verbatim}
+{\Large
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]}
+\end{verbatim}
+
+\newpage
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\makeatletter
+
+%% This turns on vertical rules at the right and left margins, to
+%% better illustrate the spacing for certain multiple-line equation
+%% structures.
+\def\@makecol{\ifvoid\footins \setbox\@outputbox\box\@cclv
+ \else\setbox\@outputbox
+ \vbox{\boxmaxdepth \maxdepth
+ \unvbox\@cclv\vskip\skip\footins\footnoterule\unvbox\footins}\fi
+ \xdef\@freelist{\@freelist\@midlist}\gdef\@midlist{}\@combinefloats
+ \setbox\@outputbox\hbox{\vrule width\marginrulewidth
+ \vbox to\@colht{\boxmaxdepth\maxdepth
+ \@texttop\dimen128=\dp\@outputbox\unvbox\@outputbox
+ \vskip-\dimen128\@textbottom}%
+ \vrule width\marginrulewidth}%
+ \global\maxdepth\@maxdepth}
+\newdimen\marginrulewidth
+\setlength{\marginrulewidth}{.1pt}
+\makeatother
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\appendix
+\section{Examples of multiple-line equation structures}
+\label{s:eq}
+
+\textbf{\large Note: Starting on this page, vertical rules are
+added at the margins so that the positioning of various display elements
+with respect to the margins can be seen more clearly.}
+
+\subsection{Split}
+The \env{split} environment is not an independent environment
+but should be used inside something else such as \env{equation}
+or \env{align}.
+
+If there is not enough room for it, the equation number for a
+\env{split} will be shifted to the previous line, when equation numbers are
+on the left; the number shifts down to the next line when numbers are on
+the right.
+\begin{equation}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+ \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+ \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+ L_{x,y_\varepsilon(\varepsilon s)}
+ \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{equation}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+ \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+ \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+ L_{x,y_\varepsilon(\varepsilon s)}
+ \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+Unnumbered version:
+\begin{equation*}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+ \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+ \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+ L_{x,y_\varepsilon(\varepsilon s)}
+ \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{equation*}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+ \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+ \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+ L_{x,y_\varepsilon(\varepsilon s)}
+ \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+If the option \env{centertags} is included in the options
+list of the \pkg{amsmath} package,
+the equation numbers for \env{split} environments will be
+centered vertically on the height
+of the \env{split}:
+{\makeatletter\ctagsplit@true
+\begin{equation}
+\begin{split}
+ \abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)-\int_{\gamma(t)}^a
+ \frac{d\theta}{k(\theta,t)}
+ \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega\left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}
+\end{equation}}%
+Some text after to test the below-display spacing.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+Use of \env{split} within \env{align}:
+{\delimiterfactor750
+\begin{align}
+\begin{split}\abs{I_1}
+ &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+&\le C_3\left[\int_\Omega\left(\int_{a}^x
+ g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+ \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+ c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\label{eq:A}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+ -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+ \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+ \left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}
+\end{align}}%
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align}
+\begin{split}\abs{I_1}
+ &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+&\le C_3\left[\int_\Omega\left(\int_{a}^x
+ g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+ \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+ c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\label{eq:A}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+ -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+ \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+ \left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}
+\end{align}
+\end{verbatim}
+
+%%%%%%%%%%%%%%%%%%
+
+\newpage
+Unnumbered \env{align}, with a number on the second \env{split}:
+\begin{align*}
+\begin{split}
+ \abs{I_1}&=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+ &\le C_3\left[\int_\Omega\left(\int_{a}^x
+ g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\phantom{=}\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+ \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+ c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+ -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+ \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+ \left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\tag{\theequation$'$}
+\end{align*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align*}
+\begin{split}
+ \abs{I_1}&=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+ &\le C_3\left[\int_\Omega\left(\int_{a}^x
+ g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\phantom{=}\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+ \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+ c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\\
+\begin{split}
+ \abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+ -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+ \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+ \left\lvert \wt{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+ \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\tag{\theequation$'$}
+\end{align*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Multline}
+Numbered version:
+\begin{multline}\label{eq:E}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline}
+To test the use of \verb=\label= and
+\verb=\ref=, we refer to the number of this
+equation here: (\ref{eq:E}).
+
+\begin{verbatim}
+\begin{multline}\label{eq:E}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version:
+\begin{multline*}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{multline*}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\iffalse % bugfix needed, error message "Multiple \tag"
+ % [mjd,24-Jan-1995]
+\newpage
+And now an ``unnumbered'' version numbered with a literal tag:
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+\end{verbatim}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+The same display with \verb=\multlinegap= set to zero.
+Notice that the space on the left in
+the first line does not change, because of the equation number, while
+the second line is pushed over to the right margin.
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}}%
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+ \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\fi % matches \iffalse above [mjd,24-Jan-1995]
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Gather}
+Numbered version with \verb;\notag; on the second line:
+\begin{gather}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg(a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\notag\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+\colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather}
+\begin{verbatim}
+\begin{gather}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg(a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\notag\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+\colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version.
+\begin{gather*}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg (a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+ \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather*}
+Some text after to test the below-display spacing.
+\begin{verbatim}
+\begin{gather*}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg (a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+ \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Align}
+Numbered version:
+\begin{align}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+ -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+ -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version:
+\begin{align*}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+ -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align*}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+ -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+A variation:
+\begin{align}
+x& =y && \text {by (\ref{eq:C})}\\
+x'& = y' && \text {by (\ref{eq:D})}\\
+x+x' & = y+y' && \text {by Axiom 1.}
+\end{align}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align}
+x& =y && \text {by (\ref{eq:C})}\\
+x'& = y' && \text {by (\ref{eq:D})}\\
+x+x' & = y+y' && \text {by Axiom 1.}
+\end{align}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Align and split within gather}
+When using the \env{align} environment within the \env{gather}
+environment, one or the other, or both, should be unnumbered (using the
+\verb"*" form); numbering both the outer and inner environment would
+cause a conflict.
+
+Automatically numbered \env{gather} with \env{split} and \env{align*}:
+\begin{gather}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align*}
+\zeta^0 &=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align*}
+\end{gather}
+Here the \env{split} environment gets a number from the outer
+\env{gather} environment; numbers for individual lines of the
+\env{align*} are suppressed because of the star.
+
+\begin{verbatim}
+\begin{gather}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align*}
+\zeta^0 &=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align*}
+\end{gather}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+The \verb"*"-ed form of \env{gather} with the non-\verb"*"-ed form of
+\env{align}.
+\begin{gather*}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align} \zeta^0&=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align}
+\end{gather*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{gather*}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align} \zeta^0&=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align}
+\end{gather*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Alignat}
+Numbered version:
+\begin{alignat}{3}
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;}\label{eq:B}\\
+V_j & = v_j, & \qquad X_j & = x_j,
+ & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{alignat}{3}
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;}\label{eq:B}\\
+V_j & = v_j, & \qquad X_j & = x_j,
+ & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version:
+\begin{alignat*}3
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;} \\
+V_j & = v_j, & \qquad X_j & = x_j,
+ & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{alignat*}3
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;} \\
+V_j & = v_j, & \qquad X_j & = x_j,
+ & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+The most common use for \env{alignat} is for things like
+\begin{alignat}{2}
+x& =y && \qquad \text {by (\ref{eq:A})}\label{eq:C}\\
+x'& = y' && \qquad \text {by (\ref{eq:B})}\label{eq:D}\\
+x+x' & = y+y' && \qquad \text {by Axiom 1.}
+\end{alignat}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{alignat}{2}
+x& =y && \qquad \text {by (\ref{eq:A})}\label{eq:C}\\
+x'& = y' && \qquad \text {by (\ref{eq:B})}\label{eq:D}\\
+x+x' & = y+y' && \qquad \text {by Axiom 1.}
+\end{alignat}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\setlength{\marginrulewidth}{0pt}
+
+\begin{thebibliography}{10}
+
+\bibitem{dihe:newdir}
+W.~Diffie and E.~Hellman, \emph{New directions in cryptography}, IEEE
+Transactions on Information Theory \textbf{22} (1976), no.~5, 644--654.
+
+\bibitem{fre:cichon}
+D.~H. Fremlin, \emph{Cichon's diagram}, 1983/1984, presented at the
+S{\'e}minaire Initiation {\`a} l'Analyse, G. Choquet, M. Rogalski, J.
+Saint Raymond, at the Universit{\'e} Pierre et Marie Curie, Paris, 23e
+ann{\'e}e.
+
+\bibitem{gouja:lagrmeth}
+I.~P. Goulden and D.~M. Jackson, \emph{The enumeration of directed
+closed {E}uler trails and directed {H}amiltonian circuits by
+{L}angrangian methods}, European J. Combin. \textbf{2} (1981), 131--212.
+
+\bibitem{hapa:graphenum}
+F.~Harary and E.~M. Palmer, \emph{Graphical enumeration}, Academic
+Press, 1973.
+
+\bibitem{imlelu:oneway}
+R.~Impagliazzo, L.~Levin, and M.~Luby, \emph{Pseudo-random generation
+from one-way functions}, Proc. 21st STOC (1989), ACM, New York,
+pp.~12--24.
+
+\bibitem{komiyo:unipfunc}
+M.~Kojima, S.~Mizuno, and A.~Yoshise, \emph{A new continuation method
+for complementarity problems with uniform p-functions}, Tech. Report
+B-194, Tokyo Inst. of Technology, Tokyo, 1987, Dept. of Information
+Sciences.
+
+\bibitem{komiyo:lincomp}
+\bysame, \emph{A polynomial-time algorithm for a class of linear
+complementarity problems}, Tech. Report B-193, Tokyo Inst. of
+Technology, Tokyo, 1987, Dept. of Information Sciences.
+
+\bibitem{liuchow:formalsum}
+C.~J. Liu and Yutze Chow, \emph{On operator and formal sum methods for
+graph enumeration problems}, SIAM J. Algorithms Discrete Methods
+\textbf{5} (1984), 384--438.
+
+\bibitem{mami:matrixth}
+M.~Marcus and H.~Minc, \emph{A survey of matrix theory and matrix
+inequalities}, Complementary Series in Math. \textbf{14} (1964), 21--48.
+
+\bibitem{miyoki:lincomp}
+S.~Mizuno, A.~Yoshise, and T.~Kikuchi, \emph{Practical polynomial time
+algorithms for linear complementarity problems}, Tech. Report~13, Tokyo
+Inst. of Technology, Tokyo, April 1988, Dept. of Industrial Engineering
+and Management.
+
+\bibitem{moad:quadpro}
+R.~D. Monteiro and I.~Adler, \emph{Interior path following primal-dual
+algorithms, part {II}: Quadratic programming}, August 1987, Working
+paper, Dept. of Industrial Engineering and Operations Research.
+
+\bibitem{ste:sint}
+E.~M. Stein, \emph{Singular integrals and differentiability properties
+of functions}, Princeton Univ. Press, Princeton, N.J., 1970.
+
+\bibitem{ye:intalg}
+Y.~Ye, \emph{Interior algorithms for linear, quadratic and linearly
+constrained convex programming}, Ph.D. thesis, Stanford Univ., Palo
+Alto, Calif., July 1987, Dept. of Engineering--Economic Systems,
+unpublished.
+
+\end{thebibliography}
+
+\end{document}
+\endinput
diff --git a/texmf-dist/doc/latex/lucidabr/lucida-oneline-samples.tex b/texmf-dist/doc/latex/lucidabr/lucida-oneline-samples.tex
new file mode 100644
index 00000000..6dcb682a
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucida-oneline-samples.tex
@@ -0,0 +1,86 @@
+% lucida-oneline-samples.tex v1.0, 28 November 2005.
+% Copyright 2005 TeX Users Group.
+%
+% Unrestricted permission is granted to copy, modify, and/or extract
+% portions of this file.
+%
+% This is a documentation file for the lucidabr package, which creates
+% one-line samples of each font for use on the TUG Lucida web pages,
+% http://tug.org/lucida.
+%
+% (R) Lucida is a trademark of Bigelow \& Holmes Inc.\ registered in the
+% U.S. Patent \& Trademark Office and other jurisdictions.
+
+\documentclass{article}
+\usepackage{lucidabr}
+\usepackage[T1]{fontenc}
+\pagestyle{empty}
+\setlength\parindent{0pt}
+\newcommand*\smalldemo[3]{% #1=shortname, #2=font name, #3=font decl.
+ \par
+ {\fontsize{18}{21.5}#3%
+ \hbox{\hbox to 8pc{\hfil ABC\kern.5em xyz}\kern1.25em #2}%
+ \par
+ }%
+}
+\begin{document}
+
+\smalldemo{lbr}{LucidaBright}{\rmfamily}
+\smalldemo{lbi}{LucidaBright-Italic}{\itshape}
+\smalldemo{lbsl}{LucidaBright-Oblique}{\slshape}
+\smalldemo{lbd}{LucidaBright-Demi}{\bfseries}
+\smalldemo{lbdi}{LucidaBright-DemiItalic}{\bfseries\itshape}
+
+\vspace{\baselineskip}
+
+\smalldemo{lbrsc}{LucidaBrightSmallcaps}{\scshape}
+\smalldemo{lbdsc}{LucidaBrightSmallcaps-Demi}{\scshape\bfseries}
+
+\vspace{\baselineskip}
+
+\smalldemo{lstr}{LucidaSans-Typewriter}{\ttfamily}
+\smalldemo{lsto}{LucidaSans-TypewriterOblique}{\ttfamily\slshape}
+\smalldemo{lstb}{LucidaSans-TypewriterBold}{\ttfamily\bfseries}
+\smalldemo{lstbo}{LucidaSans-TypewriterBoldOblique}{\ttfamily\bfseries\slshape}
+
+
+\newpage
+
+\smalldemo{lsr}{LucidaSans}{\sffamily}
+\smalldemo{lsi}{LucidaSans-Italic}{\sffamily\itshape}
+\smalldemo{lsd}{LucidaSans-Demi}{\sffamily\bfseries}
+\smalldemo{lsdi}{LucidaSans-DemiItalic}{\sffamily\bfseries\itshape}
+\smalldemo{lsb}{LucidaSans-Bold}{\sffamily\fontseries{ub}\selectfont}
+\smalldemo{lsbi}{LucidaSans-BoldItalic}{\sffamily\itshape\fontseries{ub}\selectfont}
+
+\vspace{\baselineskip}
+
+\smalldemo{lbtr}{LucidaTypewriter}{\fontfamily{hlct}\selectfont}
+\smalldemo{lbto}{LucidaTypewriterOblique}{\fontfamily{hlct}\selectfont\slshape}
+\smalldemo{lbtb}{LucidaTypewriterBold}{\fontfamily{hlct}\selectfont\bfseries}
+\smalldemo{lbtbo}{LucidaTypewriterBoldOblique}{\fontfamily{hlct}\selectfont\bfseries\slshape}
+
+\vspace{\baselineskip}
+
+\smalldemo{lfr}{LucidaFax}{\fontfamily{hlx}\selectfont}
+\smalldemo{lfi}{LucidaFax-Italic}{\fontfamily{hlx}\selectfont\itshape}
+\smalldemo{lfd}{LucidaFax-Demi}{\fontfamily{hlx}\selectfont\bfseries}
+\smalldemo{lfdi}{LucidaFax-DemiItalic}{\fontfamily{hlx}\selectfont\bfseries\itshape}
+
+\vspace{\baselineskip}
+
+\smalldemo{lbl}{LucidaBlackletter}{\fontfamily{hlcf}\selectfont}
+\smalldemo{lbc}{LucidaCalligraphy-Italic}{\fontfamily{hlce}\selectfont}
+\smalldemo{lbh}{LucidaHandwriting-Italic}{\fontfamily{hlcw}\selectfont}
+
+\vspace{\baselineskip}
+
+\smalldemo{lbkr}{LucidaCasual}{\fontfamily{hlcn}\selectfont}
+\smalldemo{lbki}{LucidaCasual-Italic}{\fontfamily{hlcn}\selectfont\itshape}
+
+
+\newpage
+
+{\fontsize{44}{44}\fontseries{bf}\sffamily Lucida and \TeX}
+
+\end{document}
diff --git a/texmf-dist/doc/latex/lucidabr/lucida-sample.pdf b/texmf-dist/doc/latex/lucidabr/lucida-sample.pdf
new file mode 100644
index 00000000..afed7e1c
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucida-sample.pdf
Binary files differ
diff --git a/texmf-dist/doc/latex/lucidabr/lucida-sample.tex b/texmf-dist/doc/latex/lucidabr/lucida-sample.tex
new file mode 100644
index 00000000..ec6911ad
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucida-sample.tex
@@ -0,0 +1,303 @@
+% Copyright 2005, 2006 TeX Users Group.
+%
+% Copying and distribution of this file, with or without modification,
+% are permitted in any medium, without royalty.
+
+\documentclass[11pt]{article}
+
+% we have to change the font encoding for Lucida.
+\usepackage[T1]{fontenc}
+\usepackage{textcomp} % to get the right copyright, etc.
+
+% use Lucida fonts for both text and math.
+\usepackage[altbullet]{lucidabr} % get larger bullet
+\DeclareEncodingSubset{TS1}{hlh}{1} % including \oldstylenums
+
+% other features we'll use.
+\usepackage{framed}
+\reversemarginpar
+\addtolength\marginparwidth{20pt}
+
+% live url's if pdf.
+\usepackage{ifpdf}
+\ifpdf
+ \usepackage[breaklinks,colorlinks,linkcolor=black,citecolor=black,
+ pagecolor=black,urlcolor=black]{hyperref}
+\else
+ \usepackage{url}
+\fi
+
+\newcommand*\pkg[1]{\textsf{#1}}
+\newcommand*\opt[1]{\texttt{#1}}
+\newcommand*\cs[1]{\texttt{\char`\\#1}}
+
+\pagestyle{headings}
+
+\newcommand\demotext{%
+ For \textsterling 45, almost anything can
+ be found floating in fields.
+% !`THE DAZED BROWN FOX QUICKLY GAVE 12345--67890 JUMPS!
+ --- ?`But aren't Kafka's Schlo\ss{} and
+ \AE sop's \OE uvres often na\"\i ve vis-\`a-vis the d\ae monic
+ ph\oe nix's official r\^ole in fluffy souffl\'es?}
+
+\newcommand*\demotextsc{\textsc{Sphinx of black quartz, judge my vow}.}
+
+\newcommand*\demotextosf{\oldstylenums{0123456789}.}
+
+\newcommand*\raggedmarginpar[1]{\marginpar{\raggedright\hspace{0pt}#1}}
+
+\newcommand*\demo[2]{%
+ \par\leavevmode\raggedmarginpar{#1}%
+ \begin{minipage}[t]{\linewidth}%
+ \normalfont#2\demotext
+ \end{minipage}%
+}
+
+\newcommand*\demosc[2]{%
+ \par\leavevmode\raggedmarginpar{#1}{\normalfont#2\demotext
+ \newline\demotextsc\par}%
+}
+\newcommand*\demoscosf[2]{%
+ \par\leavevmode\raggedmarginpar{#1}{\normalfont#2\demotext
+ \newline\demotextsc\space\demotextosf\par}%
+}
+\newcommand*\demoosf[2]{%
+ \par\leavevmode\raggedmarginpar{#1}{\normalfont#2\demotext
+ \newline\space\demotextosf\par}%
+}
+
+
+\title{Using the Lucida fonts with \LaTeX}
+\author{\TeX\ Users Group\\[2pt]\url{http://tug.org/lucida}}
+\begin{document}
+\maketitle
+
+
+\section{Introduction}
+
+{\def\thefootnote{}
+% article.cls uses 1.8em for the footnote indent.
+\footnotetext{\kern-1.8em \textregistered\ Lucida is a trademark of
+Bigelow \& Holmes Inc.\ registered in the U.S. Patent \& Trademark
+Office and other jurisdictions.}
+}
+
+This document contains examples of the Lucida fonts available through
+TUG. They are divided into two sets, \textit{basic} and
+\textit{complete}, as displayed in the following sections.
+
+For more information about Lucida and \TeX, and an order form for the
+fonts, please see \url{http://tug.org/lucida}.
+
+
+\section{\LaTeX\ macro support for Lucida}
+
+The Lucida support primarily consists of two packages: \pkg{lucidabr}
+and \pkg{lucbmath}. The former changes both running text and math to use
+Lucida, whereas the latter only changes the math font setup in case you
+want to use a different text font with the Lucida math fonts.
+
+You may already have the macro packages installed as they are part of
+most \TeX{} distributions---try running the example below.
+
+If it complains that \texttt{lucidabr.sty} is not found, you must
+install the package; it's available on CTAN in
+\url{http://www.ctan.org/tex-archive/macros/latex/contrib/psnfssx/lucidabr},
+and (of course) also included in the TUG distribution when you order the
+fonts.
+
+\subsection{Basic example}
+
+The packages do \emph{not} support \LaTeX's (and \TeX's) default
+encoding (OT1). Supported encodings are T1, LY1, and TS1 (partial).
+What this means is that you have to use the \pkg{fontenc} package to
+switch the default.
+
+Here's a small example:
+
+\begin{verbatim}
+\documentclass{article}
+\usepackage[T1]{fontenc}
+\usepackage{textcomp}
+\usepackage{lucidabr}
+\begin{document}
+Here's some text. And here's some math:
+\[
+ \phi(x)=\int_{-\infty}^{x} e^{-x^{2}/2}
+\]
+Euro and copyright symbols are available:
+\texteuro \textcopyright \textbullet.
+\end{document}
+\end{verbatim}
+This results in the following output:
+\begin{framed}
+Here's some text. And here's some math:
+\[
+ \phi(x)=\int_{-\infty}^{x} e^{-x^{2}/2}
+\]
+Euro, copyright, and bullet symbols are available:
+\texteuro \textcopyright \textbullet.
+\end{framed}
+
+\subsection{More details}
+
+If the example runs ok, but produces no output, try refreshing the
+``filename database'' (e.g., run \texttt{mktexlsr}). Also, of course,
+you must actually purchase the fonts! (All the metrics and support
+files are on CTAN, but not the \texttt{.pfb} files containing the actual
+outlines.)
+
+It's best to load the \pkg{textcomp} package with \pkg{lucidabr}, or
+some symbols, notably \cs{textcopyright}, will be synthesized instead of
+coming from the fonts. We don't load \pkg{textcomp} automatically,
+since loading such fundamental packages behind the scenes can cause
+hard-to-debug trouble.
+
+Furthermore, the default \cs{textbullet} is quite small; the more normal
+one above is generated by specifying the \opt{altbullet} option when
+loading \pkg{lucidabr}.
+
+By default, oldstyle figures from the \pkg{textcomp} package, accessed
+with the \verb|\oldstylenums| command, are disabled for the Lucida fonts
+since they do not exist in all shapes. In order for \verb|\oldstylenums|
+to work, you must add the line
+\begin{verbatim}
+\DeclareEncodingSubset{TS1}{hlh}{1}
+\end{verbatim}
+to your preamble \emph{after} loading the \pkg{textcomp} package. The
+font family \texttt{hlhj} provides the oldstyle figures by default but
+there exists no bold italic version of these figures and the italic
+versions are only available if you buy the complete font set.
+
+Now, let's take a more systematic look at the fonts.
+
+
+\section{The \textsf{basic} font set}
+
+The basic set of fonts contains all the math fonts (shown in the
+accompanying \texttt{lucida-amsmath} document), a set of text fonts with
+accompanying small caps, and a monospaced font for code examples. The
+idea is that this is sufficient for mathematical papers and typical text
+usage.
+
+The roman text font is Lucida Bright. It comes with small caps and
+oldstyle figures only in the upright shapes:
+
+\begin{quote}
+\demoscosf{LucidaBright}{}
+
+\demo{LucidaBright-Italic}{\itshape}
+
+\demo{LucidaBright-Oblique}{\slshape}
+
+\demoscosf{LucidaBright-Demi}{\bfseries}
+
+\demo{LucidaBright-DemiItalic}{\bfseries\itshape}
+\end{quote}
+
+\noindent The basic set also contains Lucida Sans Typewriter in various
+shapes and series:
+\begin{quote}
+\demo{LucidaSans-Typewriter}{\ttfamily\raggedright}
+
+\demo{LucidaSans-Typewriter Oblique}{\ttfamily\slshape\raggedright}
+
+\demo{LucidaSans-Typewriter Bold}{\ttfamily\bfseries\raggedright}
+
+\demo{LucidaSans-Typewriter BoldOblique}
+ {\ttfamily\bfseries\slshape\raggedright}
+\end{quote}
+
+\section{The \textsf{complete} font set}
+
+The complete font set includes (naturally) all the basic fonts, and
+assorted other text font variations, starting with the full sans serif
+variant, Lucida Sans:
+\begin{quote}
+\demo{LucidaSans}{\sffamily}
+
+\demo{LucidaSans-Italic}{\sffamily\itshape}
+
+\demo{LucidaSans-Demi}{\sffamily\bfseries}
+
+\demo{LucidaSans-DemiItalic}
+ {\sffamily\bfseries\itshape}
+\end{quote}
+
+LucidaSans also exists in an ultra bold version, which you have to select
+manually with \verb|\fontseries{ub}\selectfont|.
+\begin{quote}
+\demo{LucidaSans-Bold}{\sffamily\fontseries{ub}\selectfont}
+
+\demo{LucidaSans-BoldItalic}
+ {\sffamily\itshape\fontseries{ub}\selectfont}
+\end{quote}
+
+
+A second, seriffed, typewriter font is included as well. By default the
+\pkg{lucidabr} package chooses Lucida Sans Typewriter for typewriter but
+you can change that by giving the option \opt{seriftt}, as in:\\
+\verb|\usepackage[seriftt]{lucidabr}|
+
+\begin{quote}
+\demo{Lucida Typewriter}{\fontfamily{hlct}\selectfont\raggedright}
+
+\demo{Lucida Typewriter Oblique}
+ {\fontfamily{hlct}\selectfont\slshape\raggedright}
+
+\demo{Lucida Typewriter Bold}{\fontfamily{hlct}\selectfont\bfseries\raggedright}
+
+\demo{Lucida Typewriter BoldOblique}
+ {\fontfamily{hlct}\selectfont\slshape\bfseries\raggedright}
+\end{quote}
+
+Lucida Fax is a complete text font. By giving the option \opt{fax} to
+\pkg{lucidabr} this becomes the default roman font. There are no small
+caps or oldstyle figures for this font.
+\begin{quote}
+\demo{LucidaFax}{\fontfamily{hlx}\selectfont}
+
+\demo{LucidaFax-Italic}
+ {\fontfamily{hlx}\selectfont\itshape}
+
+\demo{LucidaFax-Bold}{\fontfamily{hlx}\selectfont\bfseries}
+
+\demo{LucidaFax-BoldItalic}
+ {\fontfamily{hlx}\selectfont\itshape\bfseries}
+\end{quote}
+
+Lucida Casual exists in two versions only: medium upright and
+medium italic. You can still make it the default text font by giving the
+option \opt{casual} to \pkg{lucidabr}.
+\begin{quote}
+\demo{LucidaCasual}{\fontfamily{hlcn}\selectfont}
+
+\demo{LucidaCasual-Italic}
+ {\fontfamily{hlcn}\selectfont\itshape}
+\end{quote}
+
+
+Finally, three more esoteric fonts are included. Lucida Calligraphy
+contains italic oldstyle figures, which are used if available when
+selecting \verb|\oldstylenums| for Lucida Bright. If you choose the
+option \opt{calligraphic} for \pkg{lucidabr}, Lucida Calligraphy will be
+the default roman font. A similar option \opt{handwriting} makes Lucida
+Handwriting the default roman font.
+
+\begin{quote}
+\demo{LucidaCalligraphy-Italic}
+ {\fontfamily{hlce}\selectfont}
+
+\demo{LucidaHandwriting-Italic}
+ {\fontfamily{hlcw}\selectfont}
+
+\demo{Lucida Blackletter}
+ {\fontfamily{hlcf}\selectfont}
+\end{quote}
+
+This is all the Lucida fonts available with \TeX\ support. For more
+information about Lucida and \TeX, and an order form for the fonts,
+please see \url{http://tug.org/lucida}, and thanks.
+
+\end{document}
diff --git a/texmf-dist/doc/latex/lucidabr/lucidabr.dtx b/texmf-dist/doc/latex/lucidabr/lucidabr.dtx
new file mode 100644
index 00000000..c74ab27a
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucidabr.dtx
@@ -0,0 +1,1323 @@
+% \iffalse
+% lucidabr.dtx - principal LaTeX support for the Lucida typeface family.
+%% Copyright 1995, 1996 Sebastian Rahtz
+%% Copyright 1997, 1998 Sebastian Rahtz, David Carlisle
+%% Copyright 2005 TeX Users Group
+%%
+%% This file is part of the lucidabr package.
+%%
+%% 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 2003/12/01 or later.
+%%
+%% This work has the LPPL maintenance status "maintained".
+%%
+%% The Current Maintainer of this work is the TeX Users Group
+%% (http://tug.org/lucida).
+%%
+%% The list of all files belonging to the lucidabr package is
+%% given in the file `manifest.txt'.
+%%
+%% The list of derived (unpacked) files belonging to the distribution
+%% and covered by LPPL is defined by the unpacking scripts (with
+%% extension .ins) which are part of the distribution.
+%%
+%<*dtx>
+ \ProvidesFile{lucidabr.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<lucidabright>\ProvidesPackage{lucidabr}
+%<lucidbrb>\ProvidesPackage{lucidbrb}
+%<lucidbry>\ProvidesPackage{lucidbry}
+%<lucbmath&!lucidabright&!luctim>\ProvidesPackage{lucbmath}
+%<lucmtime>\ProvidesPackage{lucmtime}
+%<luctime>\ProvidesPackage{luctime}
+%<lucmin>\ProvidesPackage{lucmin}
+%<lucid>\ProvidesPackage{lucid}
+%<lucfont>\ProvidesFile{lucfont.tex}
+%<driver>\ProvidesFile{lucida.drv}
+% \fi
+% \ProvidesFile{lucidabr.dtx}
+ [2005/11/29 v4.3 %
+%<lucidabright> Lucida Bright +
+%<lucidbrb> Lucida Bright (Compatibility, KB Names)
+%<lucidbry> Lucida Bright (Compatibility, Y&Y Names)
+%<lucbmath> Lucida New Math + Lucida Expert
+%<luctime> + Adobe Times
+%<lucmtime> + Monotype Times
+%<lucmin> + Minion
+%<lucfont> Lucida Bright text font test
+ (SPQR/DPC/TUG)]
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage[set]{longtable}% `set' in case an old copy of the package
+\begin{document}
+\DocInput{lucidabr.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{2079}
+%
+% \GetFileInfo{lucidabr.dtx}
+%
+% \title{The \textsf{lucidabr} package\thanks{This file
+% has version number \fileversion, last
+% revised \filedate.\newline
+% \textregistered\ Lucida is a trademark of Bigelow \& Holmes Inc.\
+% registered in the U.S. Patent \& Trademark Office and other jurisdictions.}}
+% \author{Sebastian Rahtz, David Carlisle,
+% \\\TeX\ Users Group (\texttt{lucida@tug.org})}
+% \date{\filedate}
+%
+% \changes{v4.06}{1997/09/01}
+% {Remove use of double quote hex convention}
+% \changes{v4.10}{1998/01/19}
+% {(Lutz Haseloff) missing brace in provides package for lucbmath}
+% \changes{v4.11}{2005/11/25}
+% {(Karl Berry) documentation update for TUG distribution}
+%
+% \maketitle
+%
+% \section{Introduction}
+% This file contains \LaTeXe\ package files needed to use
+% Lucida Bright fonts, and \texttt{.fd} files for the fonts as named
+% with the Berry naming scheme. It is accompanied on CTAN by the metric
+% and other support files. The actual outline fonts need to be
+% purchased from the \TeX\ Users Group (\texttt{http://tug.org/lucida})
+% or another source.
+%
+% TUG is now the maintainer of this \texttt{lucidabr} \LaTeX\ support
+% package (many thanks to Morten H\o gholm), which is separate from the
+% \texttt{lucida} package containing the basic font metric files (many
+% thanks to Walter Schmidt).
+%
+% The \texttt{lucida-sample.tex} file in the distribution describes
+% basic usage of the fonts and this package, and gives examples of all
+% the fonts.
+%
+% The Lucida Bright font families:
+%
+% Note that the `demi bold' Lucida fonts are classed as `b' (bold)
+% in \LaTeX. The only `bold' font in the Lucida collection is
+% the bold sans serif font, which is classed as `ub' (ultra bold).
+%
+% \begin{longtable}{llll}
+% \multicolumn{2}{c}{Font File Name}&
+% \multicolumn{1}{c}{Font Name}
+% &\multicolumn{1}{c}{\LaTeX}\\
+% Standard & Original & & \\
+% \hline\hline
+% \endhead
+% hlxb8a & lfd & LucidaFax-Demi & hlx/b/n\\
+% hlxbi8a & lfdi & LucidaFax-DemiItalic & hlx/b/it\\
+% hlxr8a & lfr & LucidaFax & hlx/m/n\\
+% hlxri8a & lfi & LucidaFax-Italic & hlx/m/it\\[5pt]
+%
+% hlhb8a & lbd & LucidaBright-Demi & hlh/b/n\\
+% hlhbi8a & lbdi & LucidaBright-DemiItalic & hlh/b/it\\
+% hlhr8a & lbr & LucidaBright & hlh/m/n\\
+% hlhri8a & lbi & LucidaBright-Italic & hlh/m/it\\
+% hlhro8a & lbsl & LucidaBrightSlanted & hlh/m/sl\\
+% hlhrc8a & lbrsc & LucidaBrightSmallcaps & hlh/m/sc\\
+% hlhbc8a & lbdsc & LucidaBrightSmallcaps-Demi & hlh/b/sc\\[5pt]
+%
+% hlsbi8a & lsdi & LucidaSans-DemiItalic & hls/b/it\\
+% hlsb8a & lsd & LucidaSans-Demi & hls/b/n\\
+% hlsri8a & lsi & LucidaSans-Italic & hls/m/it\\
+% hlsr8a & lsr & LucidaSans & hls/m/n\\
+% hlsu8a & lsb & LucidaSans-Bold & hls/ub/n\\
+% hlsui8a & lsbi & LucidaSans-BoldItalic & hls/ub/it\\[5pt]
+%
+% hlcrf8a & lbl & LucidaBlackletter & hlcf/m/n\\[5pt]
+%
+% hlcriw8a & lbh & LucidaHandwriting-Italic & hlcw/m/n\\[5pt]
+%
+% hlcrie8a & lbc & LucidaCalligraphy-Italic & hlce/m/it\\[5pt]
+%
+% hlcrn8a & lbkr & LucidaCasual & hlcn/m/n\\*
+% hlcrin8a & lbki & LucidaCasual-Italic & hlcn/m/it\\[5pt]
+%
+% hlsrt8a & lstr & LucidaSans-Typewriter & hlst/m/n\\
+% hlsrot8a & lsto & LucidaSans-TypewriterOblique & hlst/m/sl\\
+% hlsbot8a & lstbo & LucidaSans-TypewriterBoldOblique & hlst/b/sl\\
+% hlsbt8a & lstb & LucidaSans-TypewriterBold & hlst/b/n\\[5pt]
+%
+% hlcrt8a & lbtr & LucidaTypewriter & hlct/m/n\\
+% hlcbt8a & lbtb & LucidaTypewriterBold & hlct/b/n\\
+% hlcrot8a & lbto & LucidaTypewriterOblique & hlct/m/sl\\
+% hlcbot8a & lbtbo & LucidaTypewriterBoldOblique & hlct/b/sl\\[5pt]
+%
+% hlcra & lbma & LucidaNewMath-Arrows & hlcm/m/n\\
+% hlcba & lbmad & LucidaNewMath-Arrows-Demi & hlcm/b/n\\
+% hlcrv & lbme & LucidaNewMath-Extension & hlcv/m/n\\
+% hlcry & lbms & LucidaNewMath-Symbol & hlcy/m/n\\
+% hlcdy & lbmsd & LucidaNewMath-Symbol-Demi & hlcy/b/n\\
+% hlcrim & lbmi & LucidaNewMath-Italic & hlcm/m/itx\\
+% hlcrima & lbmo & LucidaNewMath-AltItalic & hlcm/m/it\\
+% hlcdim & lbmdi & LucidaNewMath-DemiItalic & hlcm/b/itx\\
+% hlcdima & lbmdo & LucidaNewMath-AltDemiItalic & hlcm/b/it\\
+% hlcrm & lbmr & LucidaNewMath-Roman & hlcm/m/n\\
+% hlcdm & lbmd & LucidaNewMath-Demibold & hlcm/b/n\\
+% \hline
+% \end{longtable}
+%
+% \StopEventually{}
+%
+% \section{Packages}
+%
+%
+% \subsection{Lucmtime Package}
+% Adobe Times with Lucida Math.
+% \begin{macrocode}
+%<*luctime>
+\def\rmdefault{ptm}
+\def\sfdefault{cmss}
+\def\ttdefault{cmtt}
+\def\Mathdefault{ptmluc}
+\DeclareSymbolFont{letters}{OML}{ptmluc}{m}{it}
+\DeclareSymbolFont{operators}{OT1}{ptm}{m}{n}
+\SetSymbolFont{letters}{normal}{OML}{ptmluc}{m}{it}
+\SetSymbolFont{letters}{bold}{OML}{ptmluc}{b}{it}
+\SetSymbolFont{operators}{bold}{OT1}{ptm}{b}{n}
+\SetSymbolFont{operators}{normal}{OT1}{ptm}{m}{n}
+%</luctime>
+% \end{macrocode}
+% Monotype Times with Lucida Math.
+% \begin{macrocode}
+%<*lucmtime>
+\def\rmdefault{mntx}
+\def\sfdefault{cmss}
+\def\ttdefault{cmtt}
+\def\Mathdefault{mntluc}
+\DeclareSymbolFont{letters}{OML}{mntluc}{m}{it}
+\DeclareSymbolFont{operators}{OT1}{mntx}{m}{n}
+\SetSymbolFont{letters}{normal}{OML}{mntluc}{m}{it}
+\SetSymbolFont{letters}{bold}{OML}{mntluc}{b}{it}
+\SetSymbolFont{operators}{bold}{OT1}{mntx}{b}{n}
+\SetSymbolFont{operators}{normal}{OT1}{mntx}{m}{n}
+%</lucmtime>
+% \end{macrocode}
+%
+% \subsection{Lucmin Package}
+% Adobe Minion with Lucida Math.
+% \begin{macrocode}
+%<*lucmin>
+\def\rmdefault{zmn}
+\def\sfdefault{zmy}
+\def\ttdefault{hlct}
+\renewcommand{\bfdefault}{b}
+\def\Mathdefault{zmnluc}
+\DeclareSymbolFont{letters}{OML}{zmnluc}{m}{it}
+\DeclareSymbolFont{operators}{OT1}{zmn}{m}{n}
+\SetSymbolFont{letters}{normal}{OML}{zmnluc}{m}{it}
+\SetSymbolFont{letters}{bold}{OML}{zmnluc}{b}{it}
+\SetSymbolFont{operators}{bold}{OT1}{zmn}{b}{n}
+\SetSymbolFont{operators}{normal}{OT1}{zmn}{m}{n}
+%</lucmin>
+% \end{macrocode}
+%
+% \subsection{Lucidbrb and lucidbry Packages}
+% Compatibility with earlier releases.
+% \changes{v4.10}{1998/01/19}
+% {(Berthold Horn) add option handling to compatibility packages}
+% \begin{macrocode}
+%<*lucidbrb>
+\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{lucidabr}}
+\ProcessOptions
+\RequirePackage[expert,vargreek]{lucidabr}
+%</lucidbrb>
+%<*lucidbry>
+\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{lucidabr}}
+\ProcessOptions
+\RequirePackage[LY1]{fontenc}
+\RequirePackage[expert,vargreek]{lucidabr}
+%</lucidbry>
+% \end{macrocode}
+%
+% \subsection{Lucidbr and lucbmath Packages}
+% Set text and math with Lucida Bright fonts.
+% (Lucbmath package only sets the math fonts.)
+% \begin{macrocode}
+%<*lucidabright|lucbmath>
+\newif\iflucida@expert
+\DeclareOption{expert}{\lucida@experttrue}
+\DeclareOption{noexpert}{\lucida@expertfalse}
+% \end{macrocode}
+% Set up the variant text and math sizes which Y\&Y
+% suggest for Lucida. The figures for these two
+% options actually come from Frank Mittelbach (oh great one).
+%
+% The default is to scale, but two options allow you to
+% revert to normal behaviour, or get even smaller.
+% \begin{macrocode}
+\DeclareOption{nolucidascale}{%
+ \def\DeclareLucidaFontShape#1#2#3#4#5#6{%
+ \DeclareFontShape{#1}{#2}{#3}{#4}{<->#5}{#6}}}
+\DeclareOption{lucidascale}{%
+ \def\DeclareLucidaFontShape#1#2#3#4#5#6{%
+ \DeclareFontShape{#1}{#2}{#3}{#4}{%
+ <-5.5>s*[1.04]#5%
+ <5.5-6.5>s*[1.02]#5%
+ <6.5-7.5>s*[.99]#5%
+ <7.5-8.5>s*[.97]#5%
+ <8.5-9.5>s*[.96]#5%
+ <9.5-10.5>s*[.95]#5%
+ <10.5-11.5>s*[.94]#5%
+ <11.5-13>s*[.93]#5%
+ <13-15.5>s*[.92]#5%
+ <15.5-18.5>s*[.91]#5%
+ <18.5-22.5>s*[.9]#5%
+ <22.5->s*[.89]#5%
+ }{#6}}}
+\DeclareOption{lucidasmallscale}{%
+ \def\DeclareLucidaFontShape#1#2#3#4#5#6{%
+ \DeclareFontShape{#1}{#2}{#3}{#4}{%
+ <-5.5>s*[.98]#5%
+ <5.5-6.5>s*[.96]#5%
+ <6.5-7.5>s*[.94]#5%
+ <7.5-8.5>s*[.92]#5%
+ <8.5-9.5>s*[.91]#5%
+ <9.5-10.5>s*[.9]#5%
+ <10.5-11.5>s*[.89]#5%
+ <11.5-13>s*[.88]#5%
+ <13-15.5>s*[.87]#5%
+ <15.5-18.5>s*[.86]#5%
+ <18.5-22.5>s*[.85]#5%
+ <22.5->s*[.84]#5%
+ }{#6}}}
+% \end{macrocode}
+%
+% Choose style of letters. Italic3 is not really italic at all,
+% more a roman font with math spacing. Italic2 is not really
+% slanted but a different style of italic, so use an `itx' shape.
+% \begin{macrocode}
+\DeclareOption{mathitalic1}{\def\letters@shape{it}}
+\DeclareOption{mathitalic2}{\def\letters@shape{itx}}
+\DeclareOption{mathitalic3}{\def\letters@shape{n}}
+% \end{macrocode}
+%
+% Choose between slanted and upright lowercase Greek.
+% \begin{macrocode}
+\DeclareOption{slantedgreek}{\def\lcgreek@alphabet{letters}}
+\DeclareOption{uprightgreek}{\def\lcgreek@alphabet{mathupright}}
+% \end{macrocode}
+%
+% Enable use of |\upalpha| and |\varGamma|.
+% \begin{macrocode}
+\DeclareOption{vargreek}{\let\upalpha\relax\let\varGamma\relax}
+% \end{macrocode}
+%
+% Stop the AMS symbol names being declared.
+% \begin{macrocode}
+\DeclareOption{noamssymbols}{\let\blacksquare\endinput}
+% \end{macrocode}
+%
+% Set up the text encoding used in the operators font.
+% \changes{v4.05}{1997/04/17}
+% {use \cs{edef} not \cs{let} to get rid of \cs{long}. psnfss/2441}
+% \begin{macrocode}
+\edef\operator@encoding{\encodingdefault}
+\DeclareOption{OT1}{\def\operator@encoding{OT1}}
+\DeclareOption{T1}{\def\operator@encoding{T1}}
+\DeclareOption{LY1}{\def\operator@encoding{LY1}}
+% \end{macrocode}
+%
+% Set up the text encodings (not in the \textsf{lucmath} package).
+% \begin{macrocode}
+%<*lucidabright>
+\renewcommand{\rmdefault}{hlh}
+\renewcommand{\sfdefault}{hls}
+\renewcommand{\ttdefault}{hlst}
+\renewcommand{\bfdefault}{b}
+\DeclareOption{seriftt}{\def\ttdefault{hlct}}
+\DeclareOption{fax}{\def\rmdefault{hlx}}
+\DeclareOption{casual}{\def\rmdefault{hlcn}}
+\DeclareOption{calligraphic}{%
+ \normalfont
+ \DeclareFontShape\encodingdefault\rmdefault{m}{it}%
+ {<->ssub*hlce/m/it}{}}
+\DeclareOption{handwriting}{%
+ \normalfont
+ \DeclareFontShape\encodingdefault\rmdefault{m}{it}%
+ {<->ssub*hlcw/m/it}{}%
+ \DeclareFontShape\encodingdefault\rmdefault{b}{it}%
+ {<->ssub*hlcw/m/it}{}}
+% \end{macrocode}
+% The bullet in the lucida text fonts is rather small.
+% Some people may prefer this option, to use a larger one
+% from the math fonts.
+% \changes{v4.10}{1998/01/19}
+% {(Berthold Horn) add altbullet option for larger bullet}
+% \begin{macrocode}
+\DeclareOption{altbullet}{%
+ \normalfont
+ \DeclareTextCommand
+ \textbullet\encodingdefault{\UseTextSymbol{OMS}\textbullet}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+%</lucidabright>
+% \end{macrocode}
+%
+% \changes{v4.04}{1997/03/12}
+% {Add font tracing options copied from mathtime}
+%
+% This package makes a lot of redefinitions. The warnings can be rather
+% annoying so some package options control whether the information
+% is printed to the terminal or log file. More control can be obtained
+% by loading the \textsf{tracefnt} package.
+%
+% Just show font errors; Warning and info to the log file.
+% The default for this package.
+% \begin{macrocode}
+\DeclareOption{errorshow}{%
+ \def\@font@info#1{%
+ \GenericInfo{(Font)\@spaces\@spaces\@spaces\space\space}%
+ {LaTeX Font Info: \space\space\space#1}}%
+ \def\@font@warning#1{%
+ \GenericInfo{(Font)\@spaces\@spaces\@spaces\space\space}%
+ {LaTeX Font Warning: #1}}}
+% \end{macrocode}
+%
+% The normal \LaTeX\ default, Font Info to the log file and Font
+% Warning to the terminal.
+% \begin{macrocode}
+\DeclareOption{warningshow}{%
+ \def\@font@info#1{%
+ \GenericInfo{(Font)\@spaces\@spaces\@spaces\space\space}%
+ {LaTeX Font Info: \space\space\space#1}}%
+ \def\@font@warning#1{%
+ \GenericWarning{(Font)\@spaces\@spaces\@spaces\space\space}%
+ {LaTeX Font Warning: #1}}}
+% \end{macrocode}
+%
+% On some machines writing all the log info may slow things down
+% so extra option not to log font changes at all.
+% \begin{macrocode}
+\DeclareOption{nofontinfo}{%
+ \let\@font@info\@gobble
+ \let\@font@warning\@gobble}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\ExecuteOptions{noexpert,lucidascale,slantedgreek,mathitalic1,errorshow}
+\ProcessOptions
+% \end{macrocode}
+%
+% \begin{macrocode}
+%</lucidabright|lucbmath>
+% \end{macrocode}
+%
+% \begin{macrocode}
+%<*lucbmath>
+% \end{macrocode}
+% New encoding scheme for Math Arrows font
+% \begin{macrocode}
+ \DeclareFontEncoding{LMR}{}{}
+ \DeclareFontSubstitution{LMR}{hlcm}{m}{n}
+%<!luctim> \DeclareSymbolFont{letters}{OML}{hlcm}{m}{\letters@shape}
+\iflucida@expert
+ \DeclareSymbolFont{mathupright}{OML}{hlcm}{m}{n}
+\fi
+ \DeclareSymbolFont{symbols}{OMS}{hlcy}{m}{n}
+ \DeclareSymbolFont{largesymbols}{OMX}{hlcv}{m}{n}
+% \end{macrocode}
+% The new Expert set for bold math
+% \begin{macrocode}
+\iflucida@expert
+%<!luctim> \SetSymbolFont{letters}{bold}{OML}{hlcm}{b}{\letters@shape}
+ \SetSymbolFont{mathupright}{bold}{OML}{hlcm}{b}{n}
+ \SetSymbolFont{symbols}{bold}{OMS}{hlcy}{b}{n}
+\fi
+% \end{macrocode}
+%
+% \begin{macrocode}
+% \DeclareSymbolFont{italics}{\encodingdefault}{\rmdefault}{m}{it}
+ \DeclareSymbolFont{arrows}{LMR}{hlcm}{m}{n}
+\iflucida@expert
+% \DeclareSymbolFont{boldarrows}{LMR}{hlcm}{b}{n}
+ \SetSymbolFont{arrows}{bold}{LMR}{hlcm}{b}{n}
+\fi
+%</lucbmath>
+%<*lucbmath>
+%<*!luctim>
+\DeclareSymbolFont{operators}{\operator@encoding}{\rmdefault}{m}{n}
+\SetSymbolFont{operators}{bold}{\operator@encoding}{\rmdefault}{b}{n}
+\SetSymbolFont{operators}{normal}{\operator@encoding}{\rmdefault}{m}{n}
+% \end{macrocode}
+%
+% Explicitly redeclare all the alphabets just in case, but differentiate
+% between pure Lucida, and the Times mixture, since those have genuine
+% OT1 mimics.
+% \begin{macrocode}
+\DeclareMathAlphabet\mathbf \operator@encoding{\rmdefault}{b}{n}
+\DeclareMathAlphabet\mathrm \operator@encoding{\rmdefault}{m}{n}
+\DeclareMathAlphabet\mathsf \operator@encoding{\sfdefault}{m}{n}
+\DeclareMathAlphabet\mathit \operator@encoding{\rmdefault}{m}{it}
+\DeclareMathAlphabet\mathtt \operator@encoding{\ttdefault}{m}{n}
+\DeclareMathAlphabet\mathfrak\operator@encoding{hlcf}{m}{n}
+\SetMathAlphabet{\mathbf}{bold}{\operator@encoding}{\rmdefault}{b}{n}
+\SetMathAlphabet{\mathsf}{bold}{\operator@encoding}{\sfdefault}{b}{n}
+\SetMathAlphabet{\mathrm}{bold}{\operator@encoding}{\rmdefault}{b}{n}
+\SetMathAlphabet{\mathit}{bold}{\operator@encoding}{\rmdefault}{b}{it}
+\SetMathAlphabet{\mathtt}{bold}{\operator@encoding}{\ttdefault}{b}{n}
+%</!luctim>
+%<*luctim>
+\DeclareMathAlphabet {\mathbf}{OT1}{\Mathdefault}{b}{n}
+\DeclareMathAlphabet {\mathrm}{OT1}{\Mathdefault}{m}{n}
+\DeclareMathAlphabet {\mathsf}{OT1}{\sfdefault}{m}{n}
+\DeclareMathAlphabet {\mathit}{OT1}{\Mathdefault}{m}{it}
+\DeclareMathAlphabet {\mathtt}{OT1}{\ttdefault}{m}{n}
+\SetMathAlphabet{\mathbf}{bold}{OT1}{\Mathdefault}{b}{n}
+\SetMathAlphabet{\mathsf}{bold}{OT1}{\sfdefault}{b}{n}
+\SetMathAlphabet{\mathrm}{bold}{OT1}{\Mathdefault}{b}{n}
+\SetMathAlphabet{\mathit}{bold}{OT1}{\Mathdefault}{b}{it}
+\SetMathAlphabet{\mathtt}{bold}{OT1}{\ttdefault}{b}{n}
+%</luctim>
+\DeclareSymbolFontAlphabet{\mathbb}{arrows}
+\DeclareSymbolFontAlphabet{\mathscr}{symbols}
+\iflucida@expert
+ \DeclareSymbolFontAlphabet{\mathup}{mathupright}
+\fi
+ \DeclareMathAccent\vec {\mathord}{letters}{126}
+% \end{macrocode}
+%
+% Symbols taken from the operators font. Need to be careful
+% here as different encodings may have been used.
+%
+% First check that the AMS have not been redefining |\colon|.
+% If it does not have this original plain \TeX\ definition,
+% don't redefine it below.
+% \changes{v4.07}{1997/10/11}
+% {Clear \cs{@tempb}}
+% \begin{macrocode}
+\let\@tempb\@undefined
+\DeclareMathSymbol{\@tempb}{\mathpunct}{operators}{58}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\@tempa{T1}
+\ifx\operator@encoding\@tempa
+ \DeclareMathSymbol{!}{\mathclose}{operators}{33}
+ \DeclareMathSymbol{:}{\mathrel}{operators}{58}
+ \DeclareMathSymbol{;}{\mathpunct}{operators}{59}
+ \DeclareMathSymbol{?}{\mathclose}{operators}{63}
+ \ifx\colon\@tempb
+ \DeclareMathSymbol{\colon}{\mathpunct}{operators}{58}
+ \fi
+ \DeclareMathAccent{\acute}{\mathalpha}{operators}{1}
+ \DeclareMathAccent{\grave}{\mathalpha}{operators}{0}
+ \DeclareMathAccent{\ddot}{\mathalpha}{operators}{4}
+ \DeclareMathAccent{\tilde}{\mathalpha}{operators}{3}
+ \DeclareMathAccent{\bar}{\mathalpha}{operators}{9}
+ \DeclareMathAccent{\breve}{\mathalpha}{operators}{8}
+ \DeclareMathAccent{\check}{\mathalpha}{operators}{7}
+ \DeclareMathAccent{\hat}{\mathalpha}{operators}{2}
+ \DeclareMathAccent{\dot}{\mathalpha}{operators}{10}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\else
+\def\@tempa{OT1}
+\ifx\operator@encoding\@tempa
+ \DeclareMathSymbol{!}{\mathclose}{operators}{33}
+ \DeclareMathSymbol{:}{\mathrel}{operators}{58}
+ \DeclareMathSymbol{;}{\mathpunct}{operators}{59}
+ \DeclareMathSymbol{?}{\mathclose}{operators}{63}
+ \ifx\colon\@tempb
+ \DeclareMathSymbol{\colon}{\mathpunct}{operators}{58}
+ \fi
+ \DeclareMathAccent{\acute}{\mathalpha}{operators}{19}
+ \DeclareMathAccent{\grave}{\mathalpha}{operators}{18}
+ \DeclareMathAccent{\ddot}{\mathalpha}{operators}{127}
+ \DeclareMathAccent{\tilde}{\mathalpha}{operators}{126}
+ \DeclareMathAccent{\bar}{\mathalpha}{operators}{22}
+ \DeclareMathAccent{\breve}{\mathalpha}{operators}{21}
+ \DeclareMathAccent{\check}{\mathalpha}{operators}{20}
+ \DeclareMathAccent{\hat}{\mathalpha}{operators}{94}
+ \DeclareMathAccent{\dot}{\mathalpha}{operators}{95}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\else
+\def\@tempa{LY1}
+\ifx\operator@encoding\@tempa
+ \DeclareMathSymbol{!}{\mathclose}{operators}{33}
+ \DeclareMathSymbol{:}{\mathrel}{operators}{58}
+ \DeclareMathSymbol{;}{\mathpunct}{operators}{59}
+ \DeclareMathSymbol{?}{\mathclose}{operators}{63}
+ \ifx\colon\@tempb
+ \DeclareMathSymbol{\colon}{\mathpunct}{operators}{58}
+ \fi
+ \DeclareMathAccent{\acute}{\mathalpha}{operators}{19}
+ \DeclareMathAccent{\grave}{\mathalpha}{operators}{18}
+ \DeclareMathAccent{\ddot}{\mathalpha}{operators}{127}
+ \DeclareMathAccent{\tilde}{\mathalpha}{operators}{126}
+ \DeclareMathAccent{\bar}{\mathalpha}{operators}{22}
+ \DeclareMathAccent{\breve}{\mathalpha}{operators}{21}
+ \DeclareMathAccent{\check}{\mathalpha}{operators}{20}
+ \DeclareMathAccent{\hat}{\mathalpha}{operators}{94}
+ \DeclareMathAccent{\vec}{\mathord}{letters}{126}
+ \DeclareMathAccent{\dot}{\mathalpha}{operators}{5}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\else
+ \PackageWarningNoLine{lucidabr}
+ {Unknown Operator Encoding!\MessageBreak
+ Math accents may be wrong: assuming OT1 positions}
+\fi\fi\fi
+% \end{macrocode}
+%
+%
+% This section derives mostly from Berthold Horn's files
+% |lcdmacro.tex| and |amssymblb.tex|
+% \copyright 1991, 1992 Y\&Y. All Rights Reserved
+% Original from Version 1.2, 1992 June 14; updated \emph{ad hoc}.
+% \begin{macrocode}
+\@ifpackageloaded{amsmath}{%
+% \end{macrocode}
+% (From M J Downes): it's possible the factors 1.5, 2, 2.5, 3, 3.5
+% should be adjusted
+% for Lucida fonts. But that has to be determined by looking at
+% printed tests which I cannot do at the moment. [mjd,24-Jun-1993]
+% \begin{macrocode}
+ \def\biggg{\bBigg@\thr@@}
+ \def\Biggg{\bBigg@{3.5}}
+}{%
+ \def\big#1{{\hbox{$\left#1\vbox to8.20\p@{}\right.\n@space$}}}
+ \def\Big#1{{\hbox{$\left#1\vbox to10.80\p@{}\right.\n@space$}}}
+ \def\bigg#1{{\hbox{$\left#1\vbox to13.42\p@{}\right.\n@space$}}}
+ \def\Bigg#1{{\hbox{$\left#1\vbox to16.03\p@{}\right.\n@space$}}}
+ \def\biggg#1{{\hbox{$\left#1\vbox to17.72\p@{}\right.\n@space$}}}
+ \def\Biggg#1{{\hbox{$\left#1\vbox to21.25\p@{}\right.\n@space$}}}
+ \def\n@space{\nulldelimiterspace\z@ \m@th}
+}
+% \end{macrocode}
+% Define some extra large sizes --- always done using extensible parts
+% \begin{macrocode}
+\def\bigggl{\mathopen\biggg}
+\def\bigggr{\mathclose\biggg}
+\def\Bigggl{\mathopen\Biggg}
+\def\Bigggr{\mathclose\Biggg}
+% \end{macrocode}
+% Following is only really needed if the roman text font is not
+% LucidaBright.
+% Draw the small sizes of `[' and `]' from math italic instead of
+% roman font
+% \begin{macrocode}
+\DeclareMathSymbol{[}{\mathopen} {letters}{134}
+\DeclareMathDelimiter{[}{letters}{134}{largesymbols}{2}
+\DeclareMathSymbol{]}{\mathclose}{letters}{135}
+\DeclareMathDelimiter{]}{letters}{135}{largesymbols}{3}
+% \end{macrocode}
+% Draw the small sizes of `(' and `)' from math italic instead
+% of roman font
+% \begin{macrocode}
+\DeclareMathSymbol{(}{\mathopen} {letters}{132}
+\DeclareMathDelimiter{(}{letters}{132}{largesymbols}{0}
+\DeclareMathSymbol{)}{\mathclose}{letters}{133}
+\DeclareMathDelimiter{)}{letters}{133}{largesymbols}{1}
+% \end{macrocode}
+% Draw `=' and `+' from symbol font instead of roman
+% \begin{macrocode}
+\DeclareMathSymbol{=}{\mathrel} {symbols}{131}
+\DeclareMathSymbol{+}{\mathbin} {symbols}{130}
+% \end{macrocode}
+% Draw small `/' from math italic instead of roman font
+% \begin{macrocode}
+\DeclareMathSymbol{/}{\mathord} {letters}{61}
+\DeclareMathDelimiter{/}{letters}{61}{largesymbols}{14}
+% \end{macrocode}
+% Make open face brackets accessible, i.e. [[ and ]]
+% \begin{macrocode}
+\DeclareMathDelimiter{\ldbrack}
+ {\mathopen}{letters}{130}{largesymbols}{130}
+\DeclareMathDelimiter{\rdbrack}
+ {\mathclose}{letters}{131}{largesymbols}{131}
+% \end{macrocode}
+% Provide access to surface integral signs
+% (linked from text to display size)
+% \begin{macrocode}
+\DeclareMathSymbol{\surfintop}{\mathop}{largesymbols}{144}
+\def\surfint{\surfintop\nolimits}
+% \end{macrocode}
+% Make medium size integrals available (NOT linked to display size)
+% \begin{macrocode}
+\DeclareMathSymbol{\midintop}{\mathop}{largesymbols}{146}
+\def\midint{\midintop\nolimits}
+\DeclareMathSymbol{\midointop}{\mathop}{largesymbols}{147}
+\def\midoint{\midointop\nolimits}
+\DeclareMathSymbol{\midsurfintop}{\mathop}{largesymbols}{148}
+\def\midsurfint{\midsurfintop\nolimits}
+% \end{macrocode}
+% Extensible integral
+% (use with |\bigg|, |\Bigg|, |\biggg|, |\Biggg| etc)
+% \begin{macrocode}
+\DeclareMathDelimiter{\largeint}
+ {\mathop}{largesymbols}{90}{largesymbols}{149}
+% \end{macrocode}
+% To close up gaps in special math characters constructed from pieces
+% \begin{macrocode}
+\def\joinrel{\mathrel{\mkern-4mu}} % \def\joinrel{\mathrel{\mkern-3mu}}
+% \end{macrocode}
+% The |\mkern-2.5mu| undoes the bogus `italic correction'
+% after joiners in LBMA
+% \begin{macrocode}
+\DeclareMathSymbol{\relbar@}{\mathord}{arrows}{45}
+\def\relbar{\mathrel{\smash\relbar@}\mathrel{\mkern-2.5mu}}
+% \end{macrocode}
+% \changes{v4.04}{1997/03/12}
+% {Relbar is hex 3D not 2D}
+% \begin{macrocode}
+\DeclareMathSymbol{\Relbar@}{\mathrel}{arrows}{61}
+\def\Relbar{\Relbar@\mathrel{\mkern-2.5mu}}
+% \end{macrocode}
+% The |\mkern4mu| undoes the overhang at the ends of the joiners
+% (and more)
+% \begin{macrocode}
+\def\longleftarrow{\leftarrow\relbar\mathrel{\mkern4mu}}
+\def\longrightarrow{\mathrel{\mkern4mu}\relbar\rightarrow}
+\def\Longleftarrow{\Leftarrow\Relbar\mathrel{\mkern4mu}}
+\def\Longrightarrow{\mathrel{\mkern4mu}\Relbar\Rightarrow}
+% \end{macrocode}
+%
+% If \textsf{amsmath} is loaded, need to redefine the arrow fill commands
+% as the relative spacing around |\relbar| and |\rightarrow| is not what
+% the AMS code expects.
+% \changes{v4.04}{1997/03/12}
+% {Modify AMS arrowfill commands}
+% \begin{macrocode}
+\AtBeginDocument{%
+ \@ifpackageloaded{amsmath}{%
+ \def\rightarrowfill@#1{%
+ \m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
+ $#1\mkern4.5mu\mathrel{\copy\z@}%
+ \kern-\wd\z@
+ \cleaders\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill%
+ \mkern-4.5mu %
+ \rightarrow$}%
+ \def\leftarrowfill@#1{%
+ \m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
+ $#1\leftarrow
+ \mkern-4.5mu %
+ \cleaders\hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
+ \kern-\wd\z@
+ \mathrel{\box\z@}\mkern4.5mu$}
+ \def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
+ $#1\leftarrow
+ \mkern-12mu %
+ \cleaders\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+ \rightarrow$}}%
+ {}}
+% \end{macrocode}
+%
+% Some characters that need construction in CM exist complete in math
+% italic or math symbol font.
+% \begin{macrocode}
+\let\bowtie\undefined
+\let\models\undefined
+\let\doteq\undefined
+\let\cong\undefined
+\let\angle\undefined
+\DeclareMathSymbol{\bowtie}{\mathrel}{letters}{246}
+\DeclareMathSymbol{\models}{\mathrel}{symbols}{238}
+\DeclareMathSymbol{\doteq}{\mathrel}{symbols}{201}
+\DeclareMathSymbol{\cong}{\mathrel}{symbols}{155}
+\DeclareMathSymbol{\angle}{\mathord}{symbols}{139}
+% \end{macrocode}
+% These need undefining so that we can redeclare them.
+% \begin{macrocode}
+\let\Box\undefined
+\let\Diamond\undefined
+\let\leadsto\undefined
+\let\neq\undefined
+\let\hookleftarrow\undefined
+\let\hookrightarrow\undefined
+\let\mapsto\undefined
+\let\notin\undefined
+\let\rightleftharpoons\undefined
+% \end{macrocode}
+% Other characters may be found in LucidaNewMath-Arrows
+% (more negated later).
+% \begin{macrocode}
+\DeclareMathSymbol{\neq}{\mathrel}{arrows}{148}
+\DeclareMathSymbol{\rightleftharpoons}{\mathrel}{arrows}{122}
+\DeclareMathSymbol{\leftrightharpoons}{\mathrel}{arrows}{121}
+\DeclareMathSymbol{\hookleftarrow}{\mathrel}{arrows}{60}
+\DeclareMathSymbol{\hookrightarrow}{\mathrel}{arrows}{62}
+\DeclareMathSymbol{\mapsto}{\mathrel}{arrows}{44}
+\def\longmapsto{\mapstochar\longrightarrow}
+% \end{macrocode}
+% Special \LaTeX\ character definitions
+% (originally from \LaTeX\ symbol font)
+% \begin{macrocode}
+\let\Join\undefined
+\let\rhd\undefined
+\let\lhd\undefined
+\let\unrhd\undefined
+\let\unlhd\undefined
+\DeclareMathSymbol{\Join}{\mathrel}{letters}{246}
+\DeclareMathSymbol{\rhd}{\mathrel}{letters}{46}
+\DeclareMathSymbol{\lhd}{\mathrel}{letters}{47}
+\DeclareMathSymbol{\unlhd}{\mathrel}{symbols}{244}
+\DeclareMathSymbol{\unrhd}{\mathrel}{symbols}{245}
+\DeclareMathSymbol{\Box}{\mathord}{arrows}{2}
+\DeclareMathSymbol{\Diamond}{\mathord}{arrows}{8}
+\DeclareMathSymbol{\leadsto}{\mathrel}{arrows}{142}
+\DeclareMathSymbol{\leadsfrom}{\mathrel}{arrows}{141}
+\def\mathstrut{\vphantom{f}}
+% \end{macrocode}
+% In n-th root, don't want the `n' to come too close to the radical
+% \begin{macrocode}
+\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1\sqrt{#2}$}%
+ \dimen@\ht\z@ \advance\dimen@-\dp\z@
+ \mkern5mu\raise.6\dimen@\copy\rootbox \mkern-7.5mu\box\z@}
+% \end{macrocode}
+% Here are some extra definitions of mathematical symbols and operators:
+% \begin{macrocode}
+\DeclareMathSymbol{\defineequal}{\mathrel}{symbols}{214}
+%\let\notleq\nleq
+%\let\notgeq\ngeq
+\DeclareMathSymbol{\notequiv}{\mathrel}{arrows}{149}
+%\let\notprec\nprec
+%\let\notsucc\nsucc
+\DeclareMathSymbol{\notapprox}{\mathrel}{arrows}{152}
+%\let\notpreceq\npreceq
+%\let\notsucceq\nsucceq
+\DeclareMathSymbol{\notasymp}{\mathrel}{arrows}{243}
+\DeclareMathSymbol{\notsubset}{\mathrel}{arrows}{198}
+\DeclareMathSymbol{\notsupset}{\mathrel}{arrows}{199}
+\DeclareMathSymbol{\notsim}{\mathrel}{arrows}{150}
+\DeclareMathSymbol{\notsubseteq}{\mathrel}{arrows}{200}
+\DeclareMathSymbol{\notsupseteq}{\mathrel}{arrows}{201}
+\DeclareMathSymbol{\notsimeq}{\mathrel}{arrows}{151}
+\DeclareMathSymbol{\notsqsubseteq}{\mathrel}{arrows}{212}
+\DeclareMathSymbol{\notsqsupseteq}{\mathrel}{arrows}{213}
+\DeclareMathSymbol{\notcong}{\mathrel}{arrows}{153}
+\DeclareMathSymbol{\notin}{\mathrel}{arrows}{29}
+\DeclareMathSymbol{\notni}{\mathrel}{arrows}{31}
+%\let\notvdash\nvdash
+%\let\notmodels\nvDash
+%\let\notparallelparallel
+%\let\noteq\neq
+%\let\notless\nless
+%\let\notgreater\ngtr
+%\let\notmid\nmid
+\let\Bbb\mathbb
+% \end{macrocode}
+% Normal \LaTeX\ draws upper case (upright) Greek from cmr10 ---
+% when using the Cork encoding, that isn't there.
+% \begin{macrocode}
+\iflucida@expert
+% \end{macrocode}
+% If we have the LucidaBright Expert set, we'll draw them from the
+% upright math font. That way we can get bold math to work on upright
+% upper case Greek.
+%
+% Why doesn't this work?
+%\begin{verbatim}
+% \documentclass{article}
+% \usepackage{lucidabr}
+% $\mathbf{\Sigma}$
+% \end{document}
+%\end{verbatim}
+% The answer lies in the meaning of |\mathbf|; as fntguide.tex says,
+% it is for alphabetic switching. The straight lucida style says
+%\begin{verbatim}
+% \DeclareMathSymbol{\Sigma}{\mathalpha}{largesymbols}{'326}
+%\end{verbatim}
+% and the |\mathalpha| signifies that the |\Sigma| can change with the
+% alphabet; so this in fact looks for |\char'326| in the ``mathbf''
+% alphabet when we ask for that. That is defined with
+%\begin{verbatim}
+% \SetMathAlphabet{\mathbf}{bold}{\operator@encoding}{\rmdefault}{b}{n}
+%\end{verbatim}
+% ie normal text Lucida bold. It all works in CMR because the text fonts
+% have Greek, which is why the symbols are defined as \mathalpha; in
+% addition, the alphabets like |\mathbf| \emph{explicitly} ask for OT1:
+%\begin{verbatim}
+%\DeclareMathAlphabet {\mathbf}{OT1}{cmr}{bx}{n}
+%\end{verbatim}
+% so it works in T1 encoding too.
+%
+% When we get the symbols from other fonts in Lucida, we should no
+% longer classify the fonts as |\mathalpha|, since the mechanism
+% doesn't function. So we use |\mathord| instead, and you
+% only get bold Greek if you change |\mathversion|.
+% At least it's consistent.
+%
+% If, however, we are using the Times mixture, we can keep
+% |\mathalpha|, as we have the right font layouts around.
+% \begin{macrocode}
+%<*!luctim>
+ \DeclareMathSymbol{\Gamma}{\mathord}{mathupright}{0}
+ \DeclareMathSymbol{\Delta}{\mathord}{mathupright}{1}
+ \DeclareMathSymbol{\Theta}{\mathord}{mathupright}{2}
+ \DeclareMathSymbol{\Lambda}{\mathord}{mathupright}{3}
+ \DeclareMathSymbol{\Xi}{\mathord}{mathupright}{4}
+ \DeclareMathSymbol{\Pi}{\mathord}{mathupright}{5}
+ \DeclareMathSymbol{\Sigma}{\mathord}{mathupright}{6}
+ \DeclareMathSymbol{\Upsilon}{\mathord}{mathupright}{7}
+ \DeclareMathSymbol{\Phi}{\mathord}{mathupright}{8}
+ \DeclareMathSymbol{\Psi}{\mathord}{mathupright}{9}
+ \DeclareMathSymbol{\Omega}{\mathord}{mathupright}{10}
+\else
+% \end{macrocode}
+% It's in the extension font (largesymbols)
+% \begin{macrocode}
+ \DeclareMathSymbol{\Gamma}{\mathord}{largesymbols}{'320}
+ \DeclareMathSymbol{\Delta}{\mathord}{largesymbols}{'321}
+ \DeclareMathSymbol{\Theta}{\mathord}{largesymbols}{'322}
+ \DeclareMathSymbol{\Lambda}{\mathord}{largesymbols}{'323}
+ \DeclareMathSymbol{\Xi}{\mathord}{largesymbols}{'324}
+ \DeclareMathSymbol{\Pi}{\mathord}{largesymbols}{'325}
+ \DeclareMathSymbol{\Sigma}{\mathord}{largesymbols}{'326}
+ \DeclareMathSymbol{\Upsilon}{\mathord}{largesymbols}{'327}
+ \DeclareMathSymbol{\Phi}{\mathord}{largesymbols}{'330}
+ \DeclareMathSymbol{\Psi}{\mathord}{largesymbols}{'331}
+ \DeclareMathSymbol{\Omega}{\mathord}{largesymbols}{'332}
+\fi
+%</!luctim>
+%<*luctim>
+ \DeclareMathSymbol{\Gamma}{\mathalpha}{mathupright}{0}
+ \DeclareMathSymbol{\Delta}{\mathalpha}{mathupright}{1}
+ \DeclareMathSymbol{\Theta}{\mathalpha}{mathupright}{2}
+ \DeclareMathSymbol{\Lambda}{\mathalpha}{mathupright}{3}
+ \DeclareMathSymbol{\Xi}{\mathalpha}{mathupright}{4}
+ \DeclareMathSymbol{\Pi}{\mathalpha}{mathupright}{5}
+ \DeclareMathSymbol{\Sigma}{\mathalpha}{mathupright}{6}
+ \DeclareMathSymbol{\Upsilon}{\mathalpha}{mathupright}{7}
+ \DeclareMathSymbol{\Phi}{\mathalpha}{mathupright}{8}
+ \DeclareMathSymbol{\Psi}{\mathalpha}{mathupright}{9}
+ \DeclareMathSymbol{\Omega}{\mathalpha}{mathupright}{10}
+\else
+% \end{macrocode}
+% It's in the extension font (largesymbols)
+% \begin{macrocode}
+ \DeclareMathSymbol{\Gamma}{\mathord}{largesymbols}{'320}
+ \DeclareMathSymbol{\Delta}{\mathord}{largesymbols}{'321}
+ \DeclareMathSymbol{\Theta}{\mathord}{largesymbols}{'322}
+ \DeclareMathSymbol{\Lambda}{\mathord}{largesymbols}{'323}
+ \DeclareMathSymbol{\Xi}{\mathord}{largesymbols}{'324}
+ \DeclareMathSymbol{\Pi}{\mathord}{largesymbols}{'325}
+ \DeclareMathSymbol{\Sigma}{\mathord}{largesymbols}{'326}
+ \DeclareMathSymbol{\Upsilon}{\mathord}{largesymbols}{'327}
+ \DeclareMathSymbol{\Phi}{\mathord}{largesymbols}{'330}
+ \DeclareMathSymbol{\Psi}{\mathord}{largesymbols}{'331}
+ \DeclareMathSymbol{\Omega}{\mathord}{largesymbols}{'332}
+\fi
+%</luctim>
+% \end{macrocode}
+%
+% \begin{macrocode}
+\DeclareMathSymbol{\alpha}{\mathord}{\lcgreek@alphabet}{11}
+\DeclareMathSymbol{\beta}{\mathord}{\lcgreek@alphabet}{12}
+\DeclareMathSymbol{\gamma}{\mathord}{\lcgreek@alphabet}{13}
+\DeclareMathSymbol{\delta}{\mathord}{\lcgreek@alphabet}{14}
+\DeclareMathSymbol{\epsilon}{\mathord}{\lcgreek@alphabet}{15}
+\DeclareMathSymbol{\zeta}{\mathord}{\lcgreek@alphabet}{16}
+\DeclareMathSymbol{\eta}{\mathord}{\lcgreek@alphabet}{17}
+\DeclareMathSymbol{\theta}{\mathord}{\lcgreek@alphabet}{18}
+\DeclareMathSymbol{\iota}{\mathord}{\lcgreek@alphabet}{19}
+\DeclareMathSymbol{\kappa}{\mathord}{\lcgreek@alphabet}{20}
+\DeclareMathSymbol{\lambda}{\mathord}{\lcgreek@alphabet}{21}
+\DeclareMathSymbol{\mu}{\mathord}{\lcgreek@alphabet}{22}
+\DeclareMathSymbol{\nu}{\mathord}{\lcgreek@alphabet}{23}
+\DeclareMathSymbol{\xi}{\mathord}{\lcgreek@alphabet}{24}
+\DeclareMathSymbol{\pi}{\mathord}{\lcgreek@alphabet}{25}
+\DeclareMathSymbol{\rho}{\mathord}{\lcgreek@alphabet}{26}
+\DeclareMathSymbol{\sigma}{\mathord}{\lcgreek@alphabet}{27}
+\DeclareMathSymbol{\tau}{\mathord}{\lcgreek@alphabet}{28}
+\DeclareMathSymbol{\upsilon}{\mathord}{\lcgreek@alphabet}{29}
+\DeclareMathSymbol{\phi}{\mathord}{\lcgreek@alphabet}{30}
+\DeclareMathSymbol{\chi}{\mathord}{\lcgreek@alphabet}{31}
+\DeclareMathSymbol{\psi}{\mathord}{\lcgreek@alphabet}{32}
+\DeclareMathSymbol{\omega}{\mathord}{\lcgreek@alphabet}{33}
+\DeclareMathSymbol{\varepsilon}{\mathord}{\lcgreek@alphabet}{34}
+\DeclareMathSymbol{\vartheta}{\mathord}{\lcgreek@alphabet}{35}
+\DeclareMathSymbol{\varpi}{\mathord}{\lcgreek@alphabet}{36}
+\DeclareMathSymbol{\varrho}{\mathord}{\lcgreek@alphabet}{37}
+\DeclareMathSymbol{\varsigma}{\mathord}{\lcgreek@alphabet}{38}
+\DeclareMathSymbol{\varphi}{\mathord}{\lcgreek@alphabet}{39}
+% \end{macrocode}
+%
+% `Individual' Upright lowercase Greek (not currently activated).
+% \begin{macrocode}
+%<*upalpha>
+\ifx\upalpha\relax
+ \DeclareMathSymbol{\upalpha}{\mathord}{mathupright}{11}
+ \DeclareMathSymbol{\upbeta}{\mathord}{mathupright}{12}
+ \DeclareMathSymbol{\upgamma}{\mathord}{mathupright}{13}
+ \DeclareMathSymbol{\updelta}{\mathord}{mathupright}{14}
+ \DeclareMathSymbol{\upepsilon}{\mathord}{mathupright}{15}
+ \DeclareMathSymbol{\upzeta}{\mathord}{mathupright}{16}
+ \DeclareMathSymbol{\upeta}{\mathord}{mathupright}{17}
+ \DeclareMathSymbol{\uptheta}{\mathord}{mathupright}{18}
+ \DeclareMathSymbol{\upiota}{\mathord}{mathupright}{19}
+ \DeclareMathSymbol{\upkappa}{\mathord}{mathupright}{20}
+ \DeclareMathSymbol{\uplambda}{\mathord}{mathupright}{21}
+ \DeclareMathSymbol{\upmu}{\mathord}{mathupright}{22}
+ \DeclareMathSymbol{\upnu}{\mathord}{mathupright}{23}
+ \DeclareMathSymbol{\upxi}{\mathord}{mathupright}{24}
+ \DeclareMathSymbol{\uppi}{\mathord}{mathupright}{25}
+ \DeclareMathSymbol{\uprho}{\mathord}{mathupright}{26}
+ \DeclareMathSymbol{\upsigma}{\mathord}{mathupright}{27}
+ \DeclareMathSymbol{\uptau}{\mathord}{mathupright}{28}
+ \DeclareMathSymbol{\upupsilon}{\mathord}{mathupright}{29}
+ \DeclareMathSymbol{\upphi}{\mathord}{mathupright}{30}
+ \DeclareMathSymbol{\upchi}{\mathord}{mathupright}{31}
+ \DeclareMathSymbol{\uppsi}{\mathord}{mathupright}{32}
+ \DeclareMathSymbol{\upomega}{\mathord}{mathupright}{33}
+ \DeclareMathSymbol{\upvarepsilon}{\mathord}{mathupright}{34}
+\fi
+%</upalpha>
+% \end{macrocode}
+% Slanted upright Greek.
+% \begin{macrocode}
+%<*varGamma>
+\ifx\varGamma\relax
+ \DeclareMathSymbol{\varGamma}{\mathord}{letters}{0}
+ \DeclareMathSymbol{\varDelta}{\mathord}{letters}{1}
+ \DeclareMathSymbol{\varTheta}{\mathord}{letters}{2}
+ \DeclareMathSymbol{\varLambda}{\mathord}{letters}{3}
+ \DeclareMathSymbol{\varXi}{\mathord}{letters}{4}
+ \DeclareMathSymbol{\varPi}{\mathord}{letters}{5}
+ \DeclareMathSymbol{\varSigma}{\mathord}{letters}{6}
+ \DeclareMathSymbol{\varUpsilon}{\mathord}{letters}{7}
+ \DeclareMathSymbol{\varPhi}{\mathord}{letters}{8}
+ \DeclareMathSymbol{\varPsi}{\mathord}{letters}{9}
+ \DeclareMathSymbol{\varOmega}{\mathord}{letters}{10}
+\fi
+%</varGamma>
+% \end{macrocode}
+% Definitions for math symbols and operators
+% (normally found in the AMS symbol fonts)
+% using LucidaNewMath fonts
+% MSAM* equivalents:
+%
+% Stop here if noamssymbols option given.
+% \begin{macrocode}
+\ifx\blacksquare\endinput\endinput\fi
+% \end{macrocode}
+%
+% \begin{macrocode}
+\DeclareMathSymbol{\boxdot}{\mathbin}{symbols}{237}
+\DeclareMathSymbol{\boxplus}{\mathbin}{symbols}{234}
+\DeclareMathSymbol{\boxtimes}{\mathbin}{symbols}{236}
+\DeclareMathSymbol{\square}{\mathord}{arrows}{2}
+\DeclareMathSymbol{\blacksquare}{\mathord}{arrows}{3}
+\DeclareMathSymbol{\centerdot}{\mathbin}{arrows}{225}
+\DeclareMathSymbol{\lozenge}{\mathord}{arrows}{8}
+\DeclareMathSymbol{\blacklozenge}{\mathord}{arrows}{9}
+\DeclareMathSymbol{\circlearrowright}{\mathrel}{arrows}{140}
+\DeclareMathSymbol{\circlearrowleft}{\mathrel}{arrows}{139}
+\DeclareMathSymbol{\rightleftharpoons}{\mathrel}{arrows}{122}
+\DeclareMathSymbol{\leftrightharpoons}{\mathrel}{arrows}{121}
+\DeclareMathSymbol{\boxminus}{\mathbin}{symbols}{235}
+\DeclareMathSymbol{\Vdash}{\mathrel}{symbols}{240}
+\DeclareMathSymbol{\Vvdash}{\mathrel}{letters}{211}
+\DeclareMathSymbol{\vDash}{\mathrel}{symbols}{238}
+\DeclareMathSymbol{\twoheadrightarrow}{\mathrel}{arrows}{37}
+\DeclareMathSymbol{\twoheadleftarrow}{\mathrel}{arrows}{35}
+\DeclareMathSymbol{\leftleftarrows}{\mathrel}{arrows}{113}
+\DeclareMathSymbol{\rightrightarrows}{\mathrel}{arrows}{115}
+\DeclareMathSymbol{\upuparrows}{\mathrel}{arrows}{114}
+\DeclareMathSymbol{\downdownarrows}{\mathrel}{arrows}{116}
+\DeclareMathSymbol{\upharpoonright}{\mathrel}{arrows}{117}
+\DeclareMathSymbol{\downharpoonright}{\mathrel}{arrows}{119}
+\DeclareMathSymbol{\upharpoonleft}{\mathrel}{arrows}{118}
+\DeclareMathSymbol{\downharpoonleft}{\mathrel}{arrows}{120}
+\DeclareMathSymbol{\rightarrowtail}{\mathrel}{arrows}{41}
+\DeclareMathSymbol{\leftarrowtail}{\mathrel}{arrows}{40}
+\DeclareMathSymbol{\leftrightarrows}{\mathrel}{arrows}{110}
+\DeclareMathSymbol{\rightleftarrows}{\mathrel}{arrows}{109}
+\DeclareMathSymbol{\Lsh}{\mathrel}{arrows}{123}
+\DeclareMathSymbol{\Rsh}{\mathrel}{arrows}{125}
+\DeclareMathSymbol{\rightsquigarrow}{\mathrel}{arrows}{142}
+\DeclareMathSymbol{\leftsquigarrow}{\mathrel}{arrows}{141}
+\DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{arrows}{145}
+\DeclareMathSymbol{\looparrowleft}{\mathrel}{arrows}{63}
+\DeclareMathSymbol{\looparrowright}{\mathrel}{arrows}{64}
+\DeclareMathSymbol{\circeq}{\mathrel}{symbols}{208}
+\DeclareMathSymbol{\succsim}{\mathrel}{symbols}{225}
+\DeclareMathSymbol{\gtrsim}{\mathrel}{symbols}{221}
+\DeclareMathSymbol{\gtrapprox}{\mathrel}{letters}{219}
+\DeclareMathSymbol{\multimap}{\mathrel}{letters}{199}
+\DeclareMathSymbol{\image}{\mathrel}{letters}{198}
+\DeclareMathSymbol{\original}{\mathrel}{letters}{197}
+\DeclareMathSymbol{\therefore}{\mathrel}{symbols}{144}
+\DeclareMathSymbol{\because}{\mathrel}{symbols}{145}
+\DeclareMathSymbol{\doteqdot}{\mathrel}{symbols}{202}
+\DeclareMathSymbol{\triangleq}{\mathrel}{symbols}{213}
+\DeclareMathSymbol{\precsim}{\mathrel}{symbols}{224}
+\DeclareMathSymbol{\lesssim}{\mathrel}{symbols}{220}
+\DeclareMathSymbol{\lessapprox}{\mathrel}{letters}{218}
+\DeclareMathSymbol{\eqslantless}{\mathrel}{letters}{226}
+\DeclareMathSymbol{\eqslantgtr}{\mathrel}{letters}{227}
+\DeclareMathSymbol{\curlyeqprec}{\mathrel}{letters}{230}
+\DeclareMathSymbol{\curlyeqsucc}{\mathrel}{letters}{231}
+\DeclareMathSymbol{\preccurlyeq}{\mathrel}{letters}{228}
+\DeclareMathSymbol{\leqq}{\mathrel}{symbols}{218}
+\DeclareMathSymbol{\leqslant}{\mathrel}{letters}{224}
+\DeclareMathSymbol{\lessgtr}{\mathrel}{symbols}{222}
+\DeclareMathSymbol{\backprime}{\mathord}{letters}{200}
+\DeclareMathSymbol{\axisshort}{\mathord}{arrows}{57}
+\DeclareMathSymbol{\risingdotseq}{\mathrel}{symbols}{204}
+\DeclareMathSymbol{\fallingdotseq}{\mathrel}{symbols}{203}
+\DeclareMathSymbol{\succcurlyeq}{\mathrel}{letters}{229}
+\DeclareMathSymbol{\geqq}{\mathrel}{symbols}{219}
+\DeclareMathSymbol{\geqslant}{\mathrel}{letters}{225}
+\DeclareMathSymbol{\gtrless}{\mathrel}{symbols}{223}
+\let\sqsubset\undefined
+\let\sqsupset\undefined
+\DeclareMathSymbol{\sqsubset}{\mathrel}{symbols}{228}
+\DeclareMathSymbol{\sqsupset}{\mathrel}{symbols}{229}
+\DeclareMathSymbol{\vartriangleright}{\mathrel}{letters}{46}
+\DeclareMathSymbol{\vartriangleleft}{\mathrel}{letters}{47}
+\DeclareMathSymbol{\trianglerighteq}{\mathrel}{symbols}{245}
+\DeclareMathSymbol{\trianglelefteq}{\mathrel}{symbols}{244}
+\DeclareMathSymbol{\bigstar}{\mathord}{arrows}{171}
+\DeclareMathSymbol{\between}{\mathrel}{letters}{242}
+\DeclareMathSymbol{\blacktriangledown}{\mathord}{arrows}{7}
+\DeclareMathSymbol{\blacktriangleright}{\mathrel}{letters}{241}
+\DeclareMathSymbol{\blacktriangleleft}{\mathrel}{letters}{240}
+\DeclareMathSymbol{\arrowaxisright}{\mathord}{arrows}{55}
+\DeclareMathSymbol{\arrowaxisleft}{\mathord}{arrows}{54}
+\DeclareMathSymbol{\vartriangle}{\mathrel}{arrows}{4}
+\DeclareMathSymbol{\blacktriangle}{\mathord}{arrows}{5}
+\DeclareMathSymbol{\triangledown}{\mathord}{arrows}{6}
+\DeclareMathSymbol{\eqcirc}{\mathrel}{symbols}{207}
+\DeclareMathSymbol{\lesseqgtr}{\mathrel}{letters}{232}
+\DeclareMathSymbol{\gtreqless}{\mathrel}{letters}{233}
+\DeclareMathSymbol{\lesseqqgtr}{\mathrel}{letters}{234}
+\DeclareMathSymbol{\gtreqqless}{\mathrel}{letters}{235}
+\DeclareMathSymbol{\Rrightarrow}{\mathrel}{arrows}{108}
+\DeclareMathSymbol{\Lleftarrow}{\mathrel}{arrows}{106}
+\DeclareMathSymbol{\veebar}{\mathbin}{letters}{210}
+\DeclareMathSymbol{\barwedge}{\mathbin}{symbols}{246}
+\DeclareMathSymbol{\angle}{\mathord}{symbols}{139}
+\DeclareMathSymbol{\measuredangle}{\mathord}{symbols}{140}
+\DeclareMathSymbol{\sphericalangle}{\mathord}{symbols}{141}
+\DeclareMathSymbol{\varpropto}{\mathrel}{symbols}{47} % ?
+\DeclareMathSymbol{\smallsmile}{\mathrel}{letters}{94} % ?
+\DeclareMathSymbol{\smallfrown}{\mathrel}{letters}{95} % ?
+\DeclareMathSymbol{\Subset}{\mathrel}{symbols}{248}
+\DeclareMathSymbol{\Supset}{\mathrel}{symbols}{249}
+\DeclareMathSymbol{\Cup}{\mathbin}{symbols}{250}
+\DeclareMathSymbol{\Cap}{\mathbin}{symbols}{251}
+\DeclareMathSymbol{\curlywedge}{\mathbin}{symbols}{132}
+\DeclareMathSymbol{\curlyvee}{\mathbin}{symbols}{133}
+\DeclareMathSymbol{\leftthreetimes}{\mathbin}{letters}{208}
+\DeclareMathSymbol{\rightthreetimes}{\mathbin}{letters}{209}
+\DeclareMathSymbol{\subseteqq}{\mathrel}{letters}{238}
+\DeclareMathSymbol{\supseteqq}{\mathrel}{letters}{239}
+\DeclareMathSymbol{\bumpeq}{\mathrel}{symbols}{200}
+\DeclareMathSymbol{\Bumpeq}{\mathrel}{symbols}{199}
+\DeclareMathSymbol{\lll}{\mathrel}{letters}{222}
+\DeclareMathSymbol{\ggg}{\mathrel}{letters}{223}
+\DeclareMathSymbol{\circledS}{\mathord}{letters}{202}
+\DeclareMathSymbol{\pitchfork}{\mathrel}{letters}{243}
+\DeclareMathSymbol{\dotplus}{\mathbin}{symbols}{137}
+\DeclareMathSymbol{\backsim}{\mathrel}{letters}{248}
+\DeclareMathSymbol{\backsimeq}{\mathrel}{letters}{249}
+\DeclareMathSymbol{\complement}{\mathord}{letters}{148}
+\DeclareMathSymbol{\intercal}{\mathbin}{letters}{217}
+\DeclareMathSymbol{\circledcirc}{\mathbin}{symbols}{230}
+\DeclareMathSymbol{\circledast}{\mathbin}{symbols}{231}
+\DeclareMathSymbol{\circleddash}{\mathbin}{letters}{204}
+% \end{macrocode}
+% MSBM* equivalents
+% \begin{macrocode}
+\DeclareMathSymbol{\lvertneqq}{\mathrel}{arrows}{222}
+\DeclareMathSymbol{\gvertneqq}{\mathrel}{arrows}{223}
+\DeclareMathSymbol{\nleq}{\mathrel}{arrows}{156}
+\DeclareMathSymbol{\ngeq}{\mathrel}{arrows}{157}
+\DeclareMathSymbol{\nless}{\mathrel}{arrows}{154}
+\DeclareMathSymbol{\ngtr}{\mathrel}{arrows}{155}
+\DeclareMathSymbol{\nprec}{\mathrel}{arrows}{229}
+\DeclareMathSymbol{\nsucc}{\mathrel}{arrows}{230}
+\DeclareMathSymbol{\lneqq}{\mathrel}{arrows}{220}
+\DeclareMathSymbol{\gneqq}{\mathrel}{arrows}{221}
+\DeclareMathSymbol{\nleqslant}{\mathrel}{arrows}{214}
+\DeclareMathSymbol{\ngeqslant}{\mathrel}{arrows}{215}
+\DeclareMathSymbol{\lneq}{\mathrel}{arrows}{218}
+\DeclareMathSymbol{\gneq}{\mathrel}{arrows}{219}
+\DeclareMathSymbol{\npreceq}{\mathrel}{arrows}{231}
+\DeclareMathSymbol{\nsucceq}{\mathrel}{arrows}{232}
+\DeclareMathSymbol{\precnsim}{\mathrel}{arrows}{235}
+\DeclareMathSymbol{\succnsim}{\mathrel}{arrows}{236}
+\DeclareMathSymbol{\lnsim}{\mathrel}{arrows}{224}
+\DeclareMathSymbol{\gnsim}{\mathrel}{arrows}{226}
+\DeclareMathSymbol{\nleqq}{\mathrel}{arrows}{216}
+\DeclareMathSymbol{\ngeqq}{\mathrel}{arrows}{217}
+\DeclareMathSymbol{\precneqq}{\mathrel}{arrows}{233}
+\DeclareMathSymbol{\succneqq}{\mathrel}{arrows}{234}
+\DeclareMathSymbol{\precnapprox}{\mathrel}{arrows}{237}
+\DeclareMathSymbol{\succnapprox}{\mathrel}{arrows}{238}
+\DeclareMathSymbol{\lnapprox}{\mathrel}{arrows}{227}
+\DeclareMathSymbol{\gnapprox}{\mathrel}{arrows}{228}
+\DeclareMathSymbol{\nsim}{\mathrel}{arrows}{150}
+\DeclareMathSymbol{\ncong}{\mathrel}{arrows}{153}
+\DeclareMathSymbol{\diagup}{\mathrel}{arrows}{11}
+\DeclareMathSymbol{\diagdown}{\mathrel}{arrows}{12}
+\DeclareMathSymbol{\varsubsetneq}{\mathrel}{arrows}{208}
+\DeclareMathSymbol{\varsupsetneq}{\mathrel}{arrows}{209}
+\DeclareMathSymbol{\nsubseteqq}{\mathrel}{arrows}{202}
+\DeclareMathSymbol{\nsupseteqq}{\mathrel}{arrows}{203}
+\DeclareMathSymbol{\subsetneqq}{\mathrel}{arrows}{206}
+\DeclareMathSymbol{\supsetneqq}{\mathrel}{arrows}{207}
+\DeclareMathSymbol{\varsubsetneqq}{\mathrel}{arrows}{210}
+\DeclareMathSymbol{\varsupsetneqq}{\mathrel}{arrows}{211}
+\DeclareMathSymbol{\subsetneq}{\mathrel}{arrows}{204}
+\DeclareMathSymbol{\supsetneq}{\mathrel}{arrows}{205}
+\DeclareMathSymbol{\nsubseteq}{\mathrel}{arrows}{200}
+\DeclareMathSymbol{\nsupseteq}{\mathrel}{arrows}{201}
+\DeclareMathSymbol{\nparallel}{\mathrel}{arrows}{247}
+\DeclareMathSymbol{\nmid}{\mathrel}{arrows}{246}
+\DeclareMathSymbol{\nshortmid}{\mathrel}{arrows}{244}
+\DeclareMathSymbol{\nshortparallel}{\mathrel}{arrows}{245}
+\DeclareMathSymbol{\nvdash}{\mathrel}{arrows}{248}
+\DeclareMathSymbol{\nVdash}{\mathrel}{arrows}{250}
+\DeclareMathSymbol{\nvDash}{\mathrel}{arrows}{249}
+\DeclareMathSymbol{\nVDash}{\mathrel}{arrows}{251}
+\DeclareMathSymbol{\ntrianglerighteq}{\mathrel}{arrows}{242}
+\DeclareMathSymbol{\ntrianglelefteq}{\mathrel}{arrows}{241}
+\DeclareMathSymbol{\ntriangleleft}{\mathrel}{arrows}{239}
+\DeclareMathSymbol{\ntriangleright}{\mathrel}{arrows}{240}
+\DeclareMathSymbol{\nleftarrow}{\mathrel}{arrows}{50}
+\DeclareMathSymbol{\nrightarrow}{\mathrel}{arrows}{51}
+\DeclareMathSymbol{\nLeftarrow}{\mathrel}{arrows}{102}
+\DeclareMathSymbol{\nRightarrow}{\mathrel}{arrows}{104}
+\DeclareMathSymbol{\nLeftrightarrow}{\mathrel}{arrows}{103}
+\DeclareMathSymbol{\nleftrightarrow}{\mathrel}{arrows}{52}
+\DeclareMathSymbol{\divideontimes}{\mathbin}{letters}{247}
+\DeclareMathSymbol{\varnothing}{\mathord}{letters}{156}
+\DeclareMathSymbol{\nexists}{\mathord}{arrows}{32}
+\DeclareMathSymbol{\Finv}{\mathord}{letters}{144}
+\DeclareMathSymbol{\Game}{\mathord}{letters}{145}
+\let\mho\undefined
+\DeclareMathSymbol{\mho}{\mathord}{letters}{146}
+\DeclareMathSymbol{\simeq}{\mathrel}{symbols}{39}
+\DeclareMathSymbol{\eqsim}{\mathrel}{symbols}{153}
+\DeclareMathSymbol{\beth}{\mathord}{letters}{149}
+\DeclareMathSymbol{\gimel}{\mathord}{letters}{150}
+\DeclareMathSymbol{\daleth}{\mathord}{letters}{151}
+\DeclareMathSymbol{\lessdot}{\mathrel}{letters}{220}
+\DeclareMathSymbol{\gtrdot}{\mathrel}{letters}{221}
+\DeclareMathSymbol{\ltimes}{\mathbin}{letters}{206}
+\DeclareMathSymbol{\rtimes}{\mathbin}{letters}{207}
+\DeclareMathSymbol{\shortmid}{\mathrel}{letters}{244}
+\DeclareMathSymbol{\shortparallel}{\mathrel}{letters}{245}
+\DeclareMathSymbol{\smallsetminus}{\mathbin}{letters}{216} %?
+\DeclareMathSymbol{\thicksim}{\mathrel}{symbols}{24} %?
+\DeclareMathSymbol{\thickapprox}{\mathrel}{symbols}{25} %?
+\DeclareMathSymbol{\approxeq}{\mathrel}{symbols}{157}
+\DeclareMathSymbol{\succapprox}{\mathrel}{letters}{237}
+\DeclareMathSymbol{\precapprox}{\mathrel}{letters}{236}
+\DeclareMathSymbol{\curvearrowleft}{\mathrel}{arrows}{135}
+\DeclareMathSymbol{\curvearrowright}{\mathrel}{arrows}{136}
+\DeclareMathSymbol{\digamma}{\mathord}{letters}{70} %?
+\DeclareMathSymbol{\varkappa}{\mathord}{letters}{155}
+\DeclareMathSymbol{\Bbbk}{\mathord}{arrows}{107}
+\DeclareMathSymbol{\hslash}{\mathord}{letters}{157}
+\DeclareMathSymbol{\hbar}{\mathord}{arrows}{27}
+\DeclareMathSymbol{\backepsilon}{\mathrel}{letters}{251} %?
+\DeclareMathSymbol{\dashrightarrow}{\mathord}{arrows}{58}
+\DeclareMathSymbol{\dashleftarrow}{\mathord}{arrows}{56}
+\DeclareMathSymbol{\dashuparrow}{\mathord}{arrows}{57}
+\DeclareMathSymbol{\dashdownarrow}{\mathord}{arrows}{59}
+% \end{macrocode}
+% \changes{v4.10}{1998/01/19}
+% {(Patrick Daly) Fix codes in corner delimiters}
+% \begin{macrocode}
+\DeclareMathDelimiter\ulcorner{\mathopen}{arrows}{91}{arrows}{91}
+\DeclareMathDelimiter\urcorner{\mathclose}{arrows}{92}{arrows}{92}
+\DeclareMathDelimiter\llcorner{\mathopen}{arrows}{93}{arrows}{93}
+\DeclareMathDelimiter\lrcorner{\mathclose}{arrows}{94}{arrows}{94}
+\edef\checkmark{\noexpand\mathhexbox{\hexnumber@\symarrows}AC}
+\edef\circledR{\noexpand\mathhexbox{\hexnumber@\symletters}C9}
+\edef\maltese{\noexpand\mathhexbox{\hexnumber@\symletters}CB}
+% \end{macrocode}
+% Changes to default for |\Leftrightarrow|. I (SPQR) don't like 22C, so:
+% \begin{macrocode}
+\let\Leftrightarrow\undefined
+\DeclareMathSymbol{\Leftrightarrow}{\mathrel}{arrows}{97}
+% \end{macrocode}
+%
+% Override AMS logo, just to ensure we don't use any CM fonts!
+% (Not done in this version.)
+%\begin{verbatim}
+%\def\AmS{{\protect\AmSfont
+% A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
+%<lucidabright|lucbmath>%\def\AmSfont{\usefont{OMS}{hlcy}{m}{n}}
+%\end{verbatim}
+%
+% \begin{macrocode}
+%</lucbmath>
+% \end{macrocode}
+%
+% \subsection{Lucfont test file}
+% A test file for the Lucida fonts.
+% \begin{macrocode}
+%<*lucfont>
+\documentclass{article}
+%<T1>\usepackage[T1]{fontenc}
+%<LY1>\usepackage[LY1]{fontenc}
+\begin{document}
+\title{All the Lucida text fonts}
+\author{prepared by Sebastian Rahtz}
+\date{February 19th 1995}
+\maketitle
+\def\test#1#2#3#4#5{%
+ \item[#1/#2/#3]#4 (#5):
+ {\fontfamily{#1}\fontseries{#2}\fontshape{#3}\selectfont
+ Animadversion for a giraffe costs \pounds123. Wa\ss\ ist
+ das f\"ur ein Klopf?
+ We are often na{\"\i}ve vis-\`{a}-vis
+the d{\ae}monic ph{\oe}nix's official r\^{o}le in fluffy souffl\'{e}s}
+}
+
+\begin{description}
+\test{hlx}{b}{it}{hlxdi8t}{LucidaFax-DemiItalic}
+\test{hlx}{b}{n}{hlxd8t}{LucidaFax-Demi}
+\test{hlx}{m}{it}{hlxrir8t}{LucidaFax-Italic}
+\test{hlx}{m}{n}{hlxr8t}{LucidaFax}
+
+\test{hlh}{b}{it}{hlcdib8t}{LucidaBright-DemiItalic}
+\test{hlh}{b}{n}{hlcdb8t}{LucidaBright-Demi}
+\test{hlh}{m}{it}{hlcrib8t}{LucidaBright-Italic}
+\test{hlh}{m}{n}{hlcrb8t}{LucidaBright}
+
+\test{hlce}{m}{it}{hlcrie8t}{LucidaCalligraphy-Italic}
+
+\test{hlcf}{m}{n}{hlcrf8t}{LucidaBlackletter}
+
+\test{hlcn}{m}{it}{hlcrin8t}{LucidaCasual-Italic}
+\test{hlcn}{m}{n}{hlcrn8t}{LucidaCasual}
+
+\test{hlst}{b}{n}{hlsbt8t}{LucidaSans-TypewriterBold}
+\test{hlst}{b}{sl}{hlsbot8t}{LucidaSans-TypewriterBoldOblique}
+
+\test{hls}{ub}{it}{hlsbi8t}{LucidaSans-BoldItalic}
+\test{hls}{ub}{n}{hlsb8t}{LucidaSans-Bold}
+\test{hls}{b}{it}{hlsdi8t}{LucidaSans-DemiItalic}
+\test{hls}{b}{n}{hlsd8t}{LucidaSans-Demi}
+\test{hls}{m}{it}{hlsri8t}{LucidaSans-Italic}
+\test{hls}{m}{n}{hlsr8t}{LucidaSans}
+
+\test{hlct}{b}{n}{hlcbt8t}{LucidaTypewriterBold}
+\test{hlct}{b}{sl}{hlcbot8t}{LucidaTypewriterOblique}
+\test{hlcw}{m}{it}{hlcriw8t}{LucidaHandwriting-Italic}
+
+\end{description}
+\end{document}
+%</lucfont>
+% \end{macrocode}
+% \Finale
diff --git a/texmf-dist/doc/latex/lucidabr/lucidabr.fdd b/texmf-dist/doc/latex/lucidabr/lucidabr.fdd
new file mode 100644
index 00000000..68da3d3b
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucidabr.fdd
@@ -0,0 +1,316 @@
+% \iffalse
+% lucidabr.fdd - generate math-related .fd files for Lucida.
+%%
+%% Copyright 1995, 1996 Sebastian Rahtz
+%% Copyright 1997 Sebastian Rahtz, David Carlisle
+%% Copyright 2005 TeX Users Group
+%%
+%% This file is part of the lucidabr package.
+%%
+%% 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 2003/12/01 or later.
+%%
+%% This work has the LPPL maintenance status "maintained".
+%%
+%% The Current Maintainer of this work is the TeX Users Group;
+%% (http://tug.org/lucida).
+%%
+%% The list of all files belonging to the lucidabr package is
+%% given in the file `manifest.txt'.
+%%
+%% The list of derived (unpacked) files belonging to the distribution
+%% and covered by LPPL is defined by the unpacking scripts (with
+%% extension .ins) which are part of the distribution.
+%%
+%<*dtx>
+ \ProvidesFile{lucidabr.fdd}
+%</dtx>
+%<LY1hlh>\ProvidesFile{ly1hlh.fd}
+%<LY1hls>\ProvidesFile{ly1hls.fd}
+%<LY1hlst>\ProvidesFile{ly1hlst.fd}
+%<LY1hlct>\ProvidesFile{ly1hlct.fd}
+%<LY1hlx>\ProvidesFile{ly1hlx.fd}
+%<LY1hlce>\ProvidesFile{ly1hlce.fd}
+%<LY1hlcw>\ProvidesFile{ly1hlcw.fd}
+%<LY1hlcf>\ProvidesFile{ly1hlcf.fd}
+%<LY1hlcn>\ProvidesFile{ly1hcn.fd}
+%<OMLhlcm>\ProvidesFile{omlhlcm.fd}
+%<OMShlcy>\ProvidesFile{omshlcy.fd}
+%<OMXhlcv>\ProvidesFile{omxhlcv.fd}
+%<LMRhlcm>\ProvidesFile{lmrhlcm.fd}
+%<OMLhlh>\ProvidesFile{omlhlh.fd}
+%<OMShlh>\ProvidesFile{omshlh.fd}
+%<driver>\ProvidesFile{lucidayy.drv}
+% \fi
+% \ProvidesFile{lucidabr.fdd}
+ [2005/11/28 v4.3 %
+%<LY1hlh> Lucida Bright
+%<LY1hls> Lucida Bright Sans
+%<LY1hlst> Lucida Bright Sans Typewriter
+%<LY1hlct> Lucida Bright Typewriter
+%<LY1hlx> Lucida Fax
+%<LY1hlce> Lucida Calligraphy
+%<LY1hlcw> Lucida Handwriting
+%<LY1hlcf> Lucida Black Letter
+%<LY1hlcn> Lucida Casual
+%<OMLhlcm> Lucida New Math Italic
+%<OMShlcy> Lucida New Math Symbols
+%<OMXhlcv> Lucida New Math Extension
+%<LMRhlcm> Lucida New Math Arrows
+%<OMLhlh> Lucida Bright
+%<OMShlh> Lucida Bright
+%<yy> (Y&Y Names)
+ (SPQR/DPC/TUG)]
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\DocInput{lucidabr.fdd}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{140}
+%
+% \GetFileInfo{lucida.dtx}
+%
+% \begin{document}
+% \title{The \textsf{lucidabr} fd files\thanks{This file
+% has version number \fileversion, last
+% revised \filedate.}}
+% \author{Sebastian Rahtz, David Carlisle}
+% \date{\filedate}
+%
+% \maketitle
+%
+% \StopEventually{}
+%
+% \section{Text Font description files}
+%
+%
+% \begin{macrocode}
+\providecommand\DeclareLucidaFontShape[6]{%
+ \DeclareFontShape{#1}{#2}{#3}{#4}{<->#5}{#6}}
+% \end{macrocode}
+%
+% \subsection{Lucida Bright font description files}
+% \begin{macrocode}
+%<*LY1hlh>
+\DeclareFontFamily{LY1}{hlh}{}
+\DeclareLucidaFontShape{LY1}{hlh}{m}{n}{lbr}{}
+\DeclareLucidaFontShape{LY1}{hlh}{m}{it}{lbi}{}
+\DeclareLucidaFontShape{LY1}{hlh}{m}{sl}{lbsl}{}
+\DeclareLucidaFontShape{LY1}{hlh}{m}{sc}{lbrsc}{}
+\DeclareLucidaFontShape{LY1}{hlh}{b}{n}{lbd}{}
+\DeclareLucidaFontShape{LY1}{hlh}{b}{it}{lbdi}{}
+\DeclareLucidaFontShape{LY1}{hlh}{b}{sc}{lbdsc}{}
+\DeclareFontShape{LY1}{hlh}{b} {sl}{<->ssub * hlh/b/it}{}
+\DeclareFontShape{LY1}{hlh}{bx}{n} {<->ssub * hlh/b/n}{}
+\DeclareFontShape{LY1}{hlh}{bx}{it}{<->ssub * hlh/b/it}{}
+\DeclareFontShape{LY1}{hlh}{bx}{sl}{<->ssub * hlh/b/it}{}
+\DeclareFontShape{LY1}{hlh}{bx}{sc}{<->ssub * hlh/b/sc}{}
+%</LY1hlh>
+% \end{macrocode}
+%
+% \subsection{Lucida Sans font description files}
+% \begin{macrocode}
+%<*LY1hls>
+\DeclareFontFamily{LY1}{hls}{}
+\DeclareLucidaFontShape{LY1}{hls}{m}{n}{lsr}{}
+\DeclareLucidaFontShape{LY1}{hls}{m}{it}{lsi}{}
+\DeclareLucidaFontShape{LY1}{hls}{b}{n}{lsd}{}
+\DeclareLucidaFontShape{LY1}{hls}{b}{it}{lsdi}{}
+\DeclareLucidaFontShape{LY1}{hls}{ub}{n}{lsb}{}
+\DeclareLucidaFontShape{LY1}{hls}{ub}{it}{lsbi}{}
+\DeclareFontShape{LY1}{hls}{m}{sl}{<->ssub * hls/m/it}{}
+\DeclareFontShape{LY1}{hls}{m}{sc}{<->ssub * hls/m/n}{}
+\DeclareFontShape{LY1}{hls}{b}{sc}{<->ssub * hls/m/sc}{}
+\DeclareFontShape{LY1}{hls}{bx}{sc}{<->ssub * hls/b/sc}{}
+\DeclareFontShape{LY1}{hls}{b}{sl}{<->ssub * hls/b/it}{}
+\DeclareFontShape{LY1}{hls}{bx}{n}{<->ssub * hls/ub/n}{}
+\DeclareFontShape{LY1}{hls}{bx}{it}{<->ssub * hls/ub/it}{}
+\DeclareFontShape{LY1}{hls}{bx}{sl}{<->ssub * hls/ub/it}{}
+%</LY1hls>
+% \end{macrocode}
+%
+% \subsection{Lucida Bright Typewriter font description files}
+% \begin{macrocode}
+%<*LY1hlst>
+\DeclareFontFamily{LY1}{hlst}{\hyphenchar \font\m@ne}%
+\DeclareLucidaFontShape{LY1}{hlst}{m}{n}{lstr}{}
+\DeclareFontShape{LY1}{hlst}{m}{sc}{<->ssub * hlst/m/n}{}
+\DeclareLucidaFontShape{LY1}{hlst}{m}{it}{lsto}{}
+\DeclareFontShape{LY1}{hlst}{m}{sl}{<->ssub * hlst/m/it}{}
+\DeclareLucidaFontShape{LY1}{hlst}{b}{n}{lstb}{}
+\DeclareLucidaFontShape{LY1}{hlst}{b}{it}{lstbo}{}
+\DeclareFontShape{LY1}{hlst}{b}{sc} {<->ssub * hlst/m/sc}{}
+\DeclareFontShape{LY1}{hlst}{b}{sl} {<->ssub * hlst/b/it}{}
+\DeclareFontShape{LY1}{hlst}{m}{sl} {<->ssub * hlst/m/it}{}
+\DeclareFontShape{LY1}{hlst}{bx}{n} {<->ssub * hlst/b/n}{}
+\DeclareFontShape{LY1}{hlst}{bx}{it}{<->ssub * hlst/b/it}{}
+\DeclareFontShape{LY1}{hlst}{bx}{sc}{<->ssub * hlst/b/sc}{}
+\DeclareFontShape{LY1}{hlst}{bx}{sl}{<->ssub * hlst/m/sl}{}
+%</LY1hlst>
+% \end{macrocode}
+% \subsection{Lucida Bright Serif Typewriter font description files}
+% \begin{macrocode}
+%<*LY1hlct>
+\DeclareFontFamily{LY1}{hlct}{\hyphenchar \font\m@ne}%
+\DeclareLucidaFontShape{LY1}{hlct}{m}{n}{lbtr}{}
+\DeclareFontShape{LY1}{hlct}{m}{sc}{<->ssub * hlct/m/n}{}
+\DeclareLucidaFontShape{LY1}{hlct}{m}{it}{lbto}{}
+\DeclareFontShape{LY1}{hlct}{m}{sl}{<->ssub * hlct/m/it}{}
+\DeclareLucidaFontShape{LY1}{hlct}{b}{n}{lbtb}{}
+\DeclareLucidaFontShape{LY1}{hlct}{b}{it}{lbtbo}{}
+\DeclareFontShape{LY1}{hlct}{b}{sc}{<->ssub * hlct/m/sc}{}
+\DeclareFontShape{LY1}{hlct}{b}{sl}{<->ssub * hlct/b/it}{}
+\DeclareFontShape{LY1}{hlct}{m}{sl}{<->ssub * hlct/m/it}{}
+\DeclareFontShape{LY1}{hlct}{bx}{n}{<->ssub * hlct/b/n}{}
+\DeclareFontShape{LY1}{hlct}{bx}{it}{<->ssub * hlct/b/it}{}
+\DeclareFontShape{LY1}{hlct}{bx}{sc}{<->ssub * hlct/b/sc}{}
+\DeclareFontShape{LY1}{hlct}{bx}{sl}{<->ssub * hlct/m/sl}{}
+%</LY1hlct>
+% \end{macrocode}
+%
+% \subsection{Lucida Fax font description files}
+% \begin{macrocode}
+%<*LY1hlx>
+\DeclareFontFamily{LY1}{hlx}{}
+\DeclareLucidaFontShape{LY1}{hlx}{m}{n}{lfr}{}
+\DeclareLucidaFontShape{LY1}{hlx}{b}{n}{lfd}{}
+\DeclareLucidaFontShape{LY1}{hlx}{m}{it}{lfi}{}
+\DeclareLucidaFontShape{LY1}{hlx}{b}{it}{lfdi}{}
+%</LY1hlx>
+% \end{macrocode}
+%
+% \subsection{Lucida Calligraphic font description files}
+% \begin{macrocode}
+%<*LY1hlce>
+\DeclareFontFamily{LY1}{hlce}{}
+\DeclareLucidaFontShape{LY1}{hlce}{m}{it}{lbc}{}
+\DeclareFontShape{LY1}{hlce}{m}{n}{<-> ssub * hlce/m/it}{}
+\DeclareFontShape{LY1}{hlce}{b}{n}{<-> ssub * hlce/m/it}{}
+\DeclareFontShape{LY1}{hlce}{b}{it}{<-> ssub * hlce/m/it}{}
+%</LY1hlce>
+% \end{macrocode}
+%
+% \subsection{Lucida Handwriting font description files}
+% \begin{macrocode}
+%<*LY1hlcw>
+\DeclareFontFamily{LY1}{hlcw}{}
+\DeclareLucidaFontShape{LY1}{hlcw}{m}{it}{lbh}{}
+\DeclareFontShape{LY1}{hlcw}{m}{n}{<-> ssub * hlcw/m/it}{}
+\DeclareFontShape{LY1}{hlcw}{b}{n}{<-> ssub * hlcw/m/it}{}
+\DeclareFontShape{LY1}{hlcw}{b}{it}{<-> ssub * hlcw/m/it}{}
+%</LY1hlcw>
+% \end{macrocode}
+%
+% \subsection{Lucida Black Letter font description files}
+% \begin{macrocode}
+%<*LY1hlcf>
+\DeclareFontFamily{LY1}{hlcf}{}
+\DeclareLucidaFontShape{LY1}{hlcf}{m}{n}{lbl}{}
+\DeclareFontShape{LY1}{hlcf}{m}{it}{<-> ssub * hlcf/m/n}{}
+\DeclareFontShape{LY1}{hlcf}{b}{n}{<-> ssub * hlcf/m/n}{}
+\DeclareFontShape{LY1}{hlcf}{b}{it}{<-> ssub * hlcf/m/n}{}
+%</LY1hlcf>
+% \end{macrocode}
+%
+% \subsection{Lucida Casual font description files}
+% \begin{macrocode}
+%<*LY1hlcn>
+\DeclareFontFamily{LY1}{hlcn}{}
+\DeclareLucidaFontShape{LY1}{hlcn}{m}{n}{lbkr}{}
+\DeclareFontShape{LY1}{hlcn}{m}{b}{<-> ssub * hlcn/m/n}{}
+\DeclareLucidaFontShape{LY1}{hlcn}{m}{it}{lbki}{}
+\DeclareFontShape{LY1}{hlcn}{b}{it}{<-> ssub * hlcn/m/it}{}
+%</LY1hlcn>
+% \end{macrocode}
+%
+% \section{Maths fonts font description files}
+%
+% \subsection{Lucida Math Italics font description files}
+% \begin{macrocode}
+%<*OMLhlcm>
+\DeclareFontFamily{OML}{hlcm}{\skewchar\font=127}
+%<yy>\DeclareLucidaFontShape{OML}{hlcm}{m}{n}{lbmr}{}
+%<kb>\DeclareLucidaFontShape{OML}{hlcm}{m}{n}{hlcrm}{}
+%<yy>\DeclareLucidaFontShape{OML}{hlcm}{b}{n}{lbmd}{}
+%<kb>\DeclareLucidaFontShape{OML}{hlcm}{b}{n}{hlcdm}{}
+%<yy>\DeclareLucidaFontShape{OML}{hlcm}{m}{it}{lbmo}{}
+%<kb>\DeclareLucidaFontShape{OML}{hlcm}{m}{it}{hlcrima}{}
+%<yy>\DeclareLucidaFontShape{OML}{hlcm}{b}{it}{lbmdo}{}
+%<kb>\DeclareLucidaFontShape{OML}{hlcm}{b}{it}{hlcdima}{}
+%<yy>\DeclareLucidaFontShape{OML}{hlcm}{m}{itx}{lbmi}{}
+%<kb>\DeclareLucidaFontShape{OML}{hlcm}{m}{itx}{hlcrim}{}
+%<yy>\DeclareLucidaFontShape{OML}{hlcm}{b}{itx}{lbmdi}{}
+%<kb>\DeclareLucidaFontShape{OML}{hlcm}{b}{itx}{hlcdim}{}
+%</OMLhlcm>
+% \end{macrocode}
+%
+% \subsection{Lucida Math Italics font description files}
+% \begin{macrocode}
+%<*OMLhlh>
+\DeclareFontFamily{OML}{hlh}{}
+\DeclareFontShape{OML}{hlh}{m}{n} {<-> ssub * hlcm/m/n}{}
+\DeclareFontShape{OML}{hlh}{m}{it} {<-> ssub * hlcm/m/n}{}
+\DeclareFontShape{OML}{hlh}{m}{sl} {<-> ssub * hlcm/m/n}{}
+\DeclareFontShape{OML}{hlh}{m}{sc} {<-> ssub * hlcm/m/n}{}
+\DeclareFontShape{OML}{hlh}{bx}{n} {<-> ssub * hlcm/b/n}{}
+\DeclareFontShape{OML}{hlh}{bx}{it} {<-> ssub * hlcm/b/n}{}
+\DeclareFontShape{OML}{hlh}{bx}{sl} {<-> ssub * hlcm/b/n}{}
+\DeclareFontShape{OML}{hlh}{bx}{sc} {<-> ssub * hlcm/b/n}{}
+%</OMLhlh>
+% \end{macrocode}
+%
+% \subsection{Lucida Math Symbols font description files}
+% \begin{macrocode}
+%<*OMShlh>
+\DeclareFontFamily{OMS}{hlh}{\skewchar\font=48}
+\DeclareFontShape{OMS}{hlh}{m}{n} {<-> ssub * hlcy/m/n}{}
+\DeclareFontShape{OMS}{hlh}{m}{it} {<-> ssub * hlcy/m/n}{}
+\DeclareFontShape{OMS}{hlh}{m}{sl} {<-> ssub * hlcy/m/n}{}
+\DeclareFontShape{OMS}{hlh}{m}{sc} {<-> ssub * hlcy/m/n}{}
+\DeclareFontShape{OMS}{hlh}{bx}{n} {<-> ssub * hlcy/b/n}{}
+\DeclareFontShape{OMS}{hlh}{bx}{it} {<-> ssub * hlcy/b/n}{}
+\DeclareFontShape{OMS}{hlh}{bx}{sl} {<-> ssub * hlcy/b/n}{}
+\DeclareFontShape{OMS}{hlh}{bx}{sc} {<-> ssub * hlcy/b/n}{}
+%</OMShlh>
+% \end{macrocode}
+%
+% \subsection{LucidaNewMath-Symbols font description files}
+% \begin{macrocode}
+%<*OMShlcy>
+\DeclareFontFamily{OMS}{hlcy}{\skewchar\font=48}
+%<yy>\DeclareLucidaFontShape{OMS}{hlcy}{m}{n}{lbms}{}
+%<kb>\DeclareLucidaFontShape{OMS}{hlcy}{m}{n}{hlcry}{}
+%<yy>\DeclareLucidaFontShape{OMS}{hlcy}{b}{n}{lbmsd}{}
+%<kb>\DeclareLucidaFontShape{OMS}{hlcy}{b}{n}{hlcdy}{}
+%</OMShlcy>
+% \end{macrocode}
+%
+% \subsection{LucidaNewMath-Extension font description files}
+% \begin{macrocode}
+%<*OMXhlcv>
+\DeclareFontFamily{OMX}{hlcv}{}
+%<yy>\DeclareLucidaFontShape{OMX}{hlcv}{m}{n}{lbme}{}
+%<kb>\DeclareLucidaFontShape{OMX}{hlcv}{m}{n}{hlcrv}{}
+%</OMXhlcv>
+% \end{macrocode}
+%
+% \subsection{LucidaNewMath-Arrows font description files}
+% \begin{macrocode}
+%<*LMRhlcm>
+\DeclareFontFamily{LMR}{hlcm}{}
+%<yy>\DeclareLucidaFontShape{LMR}{hlcm}{m}{n}{lbma}{}
+%<kb>\DeclareLucidaFontShape{LMR}{hlcm}{m}{n}{hlcra}{}
+%<yy>\DeclareLucidaFontShape{LMR}{hlcm}{b}{n}{lbmad}{}
+%<kb>\DeclareLucidaFontShape{LMR}{hlcm}{b}{n}{hlcda}{}
+%</LMRhlcm>
+% \end{macrocode}
+%
+% \Finale
diff --git a/texmf-dist/doc/latex/lucidabr/lucidabr.ins b/texmf-dist/doc/latex/lucidabr/lucidabr.ins
new file mode 100644
index 00000000..47a37831
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucidabr.ins
@@ -0,0 +1,75 @@
+% lucidabr.ins
+%% Generate fast loadable files and documentation driver files from the
+%% doc files in this package when run through LaTeX or TeX.
+%%
+%% Copyright 1995, 1996 Sebastian Rahtz
+%% Copyright 1997 Sebastian Rahtz, David Carlisle
+%% Copyright 2005 TeX Users Group
+%%
+%% This file is part of the lucidabr package.
+%%
+%% 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 2003/12/01 or later.
+%%
+%% This work has the LPPL maintenance status "maintained".
+%%
+%% The Current Maintainer of this work is the TeX Users Group
+%% (http://tug.org/lucida).
+%%
+%% The list of all files belonging to the lucidabr package is
+%% given in the file `manifest.txt'.
+%%
+%% The list of derived (unpacked) files belonging to the distribution
+%% and covered by LPPL is defined by the unpacking scripts (with
+%% extension .ins) which are part of the distribution.
+%%
+\def\batchfile{lucidabr.ins}
+\input docstrip
+
+\keepsilent
+\askforoverwritefalse
+
+\preamble
+\endpreamble
+
+
+% the style files.
+\generate{%
+ \file{lucidabr.sty}{\from{lucidabr.dtx}{lucidabright,upalpha,varGamma,lucbmath}}
+ \file{lucidbrb.sty}{\from{lucidabr.dtx}{lucidbrb}}
+ \file{lucidbry.sty}{\from{lucidabr.dtx}{lucidbry}}
+ \file{luctime.sty}{\from{lucidabr.dtx}{luctime,lucbmath,luctim}}
+ \file{lucmtime.sty}{\from{lucidabr.dtx}{lucmtime,lucbmath,luctim}}
+ \file{lucmin.sty}{\from{lucidabr.dtx}{lucmin,lucbmath,luctim}}
+ \file{lucbmath.sty}{\from{lucidabr.dtx}{lucbmath}}
+ \file{lucfont.tex}{\from{lucidabr.dtx}{T1,lucfont}}}
+
+
+% the math-related fd files. The text fd files are generated through
+% fontinst, and are part of the (separate) lucida package, not the
+% present (lucidabr) package.
+%
+\generate{%
+ \file{omlhlcm.fd}{\from{lucidabr.fdd}{lucidascale,OMLhlcm,kb}}
+ \file{omshlcy.fd}{\from{lucidabr.fdd}{lucidascale,OMShlcy,kb}}
+ \file{omxhlcv.fd}{\from{lucidabr.fdd}{lucidascale,OMXhlcv,kb}}
+ \file{lmrhlcm.fd}{\from{lucidabr.fdd}{lucidascale,LMRhlcm,kb}}}
+
+\generate{%
+ \file{omlhlh.fd}{\from{lucidabr.fdd}{OMLhlh,kb}}
+ \file{omshlh.fd}{\from{lucidabr.fdd}{OMShlh,kb}}}
+
+\Msg{***************************************************************}
+\Msg{*}
+\Msg{* \space To finish the installation you have to copy the files }
+\Msg{* \space *.sty and *.fd into a directory searched by TeX}
+\Msg{* \space (TDS directory: texmf/tex/latex/lucidabr/).}
+\Msg{*}
+\Msg{***************************************************************}
+
+\endinput
diff --git a/texmf-dist/doc/latex/lucidabr/lucidabr.pdf b/texmf-dist/doc/latex/lucidabr/lucidabr.pdf
new file mode 100644
index 00000000..55e8e815
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/lucidabr.pdf
Binary files differ
diff --git a/texmf-dist/doc/latex/lucidabr/manifest.txt b/texmf-dist/doc/latex/lucidabr/manifest.txt
new file mode 100644
index 00000000..29214a99
--- /dev/null
+++ b/texmf-dist/doc/latex/lucidabr/manifest.txt
@@ -0,0 +1,16 @@
+Files covered by the LPPL:
+lucidabr.dtx
+lucidar.fdd
+lucida.ins
+(and derivatives)
+
+Files with all-permissive licenses:
+Makefile
+README
+README.TUG
+lucida-amsmath.tex
+lucida-oneline-samples.tex
+lucida-sample.tex
+manifest.txt :)
+(and derivatives)
+