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diff --git a/Master/texmf-dist/source/latex/stex/cmathml.dtx b/Master/texmf-dist/source/latex/stex/cmathml.dtx deleted file mode 100644 index dc101d12f38..00000000000 --- a/Master/texmf-dist/source/latex/stex/cmathml.dtx +++ /dev/null @@ -1,2442 +0,0 @@ -% \iffalse meta-comment -% Semantic Macros for Content MathML in LaTeX -% Copyright (c) 2006 Michael Kohlhase, all rights reserved -% this file is released under the -% Gnu Library Public Licences (LGPL) -% -% The development version of this file can be found at -% https://svn.kwarc.info/repos/kwarc/projects/stex/sty/cmathml.dtx -% \fi -% -% \iffalse -%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01] -%<package>\ProvidesPackage{cmathml}[2006/01/10 v0.1 CMathML Bindings] -% -%<*driver> -\documentclass{ltxdoc} -\usepackage{url,array,float,amsfonts,a4wide} -\usepackage{cmathml,cmathmlx,presentation} -\usepackage[show]{ed} -\usepackage{hyperref} -\makeindex -\floatstyle{boxed} -\newfloat{exfig}{thp}{lop} -\floatname{exfig}{Example} -\begin{document}\DocInput{cmathml.dtx}\end{document} -%</driver> -% \fi -% -%\CheckSum{1586} -% -% \changes{v0.1}{10. January 2006}{Initial Version} -% \changes{v0.2}{16. January 2006}{Added big operators} -% -% \GetFileInfo{cmathml.sty} -% -% \MakeShortVerb{\|} -% -% \def\scsys#1{{{\sc #1}}\index{#1@{\sc #1}}} -% \def\stex{{\raisebox{-.5ex}S\kern-.5ex\TeX}\index{sTeX}} -% \def\sTeX{\stex} -% \newenvironment{pcmtab}[1][5cm]{\begin{center}\begin{tabular}{|l|l|p{#1}|l|}\hline% -% macro & args & Example & Result\\\hline\hline}% -% {\end{tabular}\end{center}} -% \newenvironment{cmtab}{\begin{center}\begin{tabular}{|l|l|l|l|}\hline% -% macro & args & Example & Result\\\hline\hline}% -% {\end{tabular}\end{center}} -% -% \def\snippet#1{\hbox{\ttfamily{#1}}} -% \def\xml{{\scsys{Xml}}} -% \def\xslt{{\scsys{xslt}}} -% \def\element#1{{\ttfamily{#1}}} -% \def\mathml{{\scshape{MathML}}\index{MathML}} -% \def\latexml{\hbox{{\LaTeX}ML}\index{LaTexML}} -% \def\twin#1#2{\index{#1!#2}\index{#2!#1}} -% \def\twintoo#1#2{{#1 #2}\twin{#1}{#2}} -% \def\atwin#1#2#3{\index{#1!#2!#3}\index{#3!#2 (#1)}} -% \def\atwintoo#1#2#3{{#1 #2 #3}\atwin{#1}{#2}{#3}} -% -% \title{A {\TeX/\LaTeX}-based Syntax for Content -% {\mathml}\thanks{Version {\fileversion} (last revised {\filedate})}} -% \author{Michael Kohlhase\\ -% Jacobs University, Bremen\\ -% \url{http://kwarc.info/kohlhase}} -% \maketitle -% -% \begin{abstract} -% The |cmathml| packge is part of the {\stex} collection, a -% version of {\TeX/\LaTeX} that allows to markup {\TeX/\LaTeX} documents semantically -% without leaving the document format, essentially turning {\TeX/\LaTeX} into a document -% format for mathematical knowledge management (MKM). -% -% This package provides a collection of semantic macros for content {\mathml} and their -% {\latexml} bindings. These macros form the basis of a naive translation from -% semantically preloaded {\LaTeX} formulae into the content {\mathml} formulae via the -% {\latexml} system. -% \end{abstract} -% -% \newpage -% -%\section{Introduction}\label{sec:intro} -% -% This document describes the collection of semantic macros for content {\mathml} and -% their {\latexml} bindings. These macros can be used to mark up mathematical formulae, -% exposing their functional/logical structure. This structure can be used by MKM systems -% for added-value services, either directly from the {\sTeX} sources, or after -% translation. Even though it is part of the {\stex} collection, it can be used -% independently. Note that this documentation of the package presupposes the discussion of -% the {\stex} collection to be self-contained. -% -% \subsection{Encoding Content {\mathml} in {\TeX/\LaTeX}}\label{sec:encoding} -% -% The |cmathml| packge presented here addresses part of transformation problem: representing -% mathematical formulae in the {\LaTeX} workflow, so that content {\mathml} representations -% can be derived from them. The underlying problem is that run-of-the-mill {\TeX/\LaTeX} -% only specifies the presentation (i.e. what formulae look like) and not their content -% (their functional structure). Unfortunately, there are no good methods (yet) to infer the -% latter from the former, but there are ways to get presentation from content. -% -% The solution to this problem is to dump the extra work on the author (after all she knows -% what she is talking about) and give them the chance to specify the intended structure. The -% markup infrastructure supplied by the |cmathml| package lets the author do this without -% changing the visual appearance, so that the {\LaTeX} workflow is not disrupted. -% -% To use these |cmathml| macros in a {\LaTeX} document, you will have to include the -% |cmathml| package using |\usepackage{cmathml}| somewhere in the document preamble. Then -% you can use the macros -% \begin{verbatim} -% $\Ceq{\Cexp{\Ctimes{\Cimaginaryi,\Cpi}},\Cuminus{\Ccn{1}}}$ -% \end{verbatim} -% which will result in $e^{i\pi}=-1$ when the document is formatted in {\LaTeX}. If the -% document is converted to {\xml} using the {\latexml} conversion tool, then the result -% will be content {\mathml} representation: -% -%\begin{exfig} -% \begin{verbatim} -% <math xmlns="http://www.w3.org/1998/Math/MathML"> -% <apply> -% <eq/> -% <apply> -% <exp/> -% <apply><times><imaginaryi/><pi/></times></apply> -% </apply> -% <apply><minus/><cn>1</cn></apply> -% </apply> -% </math> -% \end{verbatim}\vspace*{-.6cm} -% \caption{Content {\mathml} Form of $e^{i\pi}=-1$}\label{fig:cmathml-eip} -% \end{exfig} -% -% \subsection{Changing the {\TeX/\LaTeX} Presentation}\label{sec:changing} -% -% It is possible to change the default presentation (i.e. the result under {\LaTeX} -% formatting): The semantic macros only function as interface control sequences, which -% call an internal macro that does the actual presentation. Thus we simply have to -% redefine the internal macro to change the presentation. This is possible locally or -% globally in the following way: -% \begin{verbatim} -% \makeatletter -% \gdef\CMathML@exp#1{exp(#1)} -% \def\CMathML@pi{\varpi} -% \makeatother -% \end{verbatim} -% -% The first line is needed to lift the {\LaTeX} redefinition protection for internal -% macros (those that contain the $\snippet{\@}$ character), and the last line restores it -% for the rest of the document. The second line has a {\em{global}} (i.e. the presentation -% will be changed from this point on to the end of the document.) redefinition of the -% presentation of the exponential function in the {\LaTeX} output. The third line has a -% {\em{local}} redefinition of the presentation (i.e. in the local group induced by -% {\LaTeX}'s $\snippet{begin}/\snippet{end}$ grouping or by {\TeX}'s grouping induced by -% curly braces). Note that the argument structure has to be respected by the presentation -% redefinitions. Given the redefinitions above, our equation above would come out as -% $exp(i\varpi)=-1$. -% -% \subsection{The Future: Heuristic Parsing}\label{sec:future} -% -% The current implementation of content {\mathml} transformation from {\LaTeX} to -% {\mathml} lays a heavy burden on the content author: the {\LaTeX} source must be -% semantically preloaded --- the structure of the formulae must be fully annotated. In our -% example above, we had to write {|\Ceq{A,B}|} instead of the more conventional (and more -% legible) {|A=B|}.\ednote{come up with a good mixed example} -% -% The reason for this is that this keeps the transformation to content {\mathml} very -% simple, predictable and robust at the expense of authoring convenience. The -% implementation described in this module should be considered as a first step and -% fallback solution only. Future versions of the $\latexml$ tool will feature more -% intelligent solutions for determining the implicit structure of more conventional -% mathematical notations (and {\LaTeX} representations), so that writing content {\mathml} -% via {\LaTeX} will become less tedious. -% -% However, such more advanced techniques usually rely on linguistic, structural, and -% semantic information about the mathematical objects and their preferred -% representations. They tend to be less predictable to casual users and may lead to -% semantically unexpected results.\ednote{talk about sTeX and extensibility in -% MathML/OpenMath/OMDoc} -% -% \newpage -% \section{The User Interface}\label{sec:modules} -% -% We will now tabulate the semantic macros for the Content {\mathml} elements. We have -% divided them into modules based on the sectional structure of the {\mathml}2 -% recommendation ($2^{nd}$ edition). Before we go into the specific elements one-by-one, -% we will discuss some general properties of the |cmatml| macros and their {\latexml} -% bindings. -% -% \subsection{Generalities of the Encoding}\label{sec:generalities} -% -% The semantic macros provided by the |cmatml| package differ mainly in the way they treat -% their arguments. The simplest case are those for constants~\ref{sec:constants} that do -% not take any. Others take one, two, three, or even four arguments, which have to be -% {\TeX} tokens or have to be wrapped in curly braces. For operators that are associative -% {\twin{associative}{operator}} like addition the argument sequence is provided as a -% single {\TeX} argument (wrapped in curly braces) that contains a comma-separated -% sequence of arguments (wrapped in curly braces where necessary). -% -% \DescribeMacro{\Capply} The current setup of the |cmathml| infrastructure minimizes the -% need of specifying the {\mathml} {\element{apply}} element, since the macros are all in -% applied form: As we have seen in the example in the Introduction~\ref{sec:intro}, a -% macro call like {|\Cexp{A}|} corresponds to the application of the exponential function -% to some object, so the necessary {\element{apply}} elements in the {\mathml} -% representation are implicit in the {\LaTeX} formulation and are thus added by the -% transformation. Of course this only works, if the function is a content {\mathml} -% element. Often, in mathematics we will have situations, where the function is a variable -% (or ``arbitrary but fixed'') function. Then the formula $f(x)$ represented as |$f(x)$| -% in {\TeX} could (and sometimes will) be misunderstood by the Math parser as $f\cdot x$, -% i.e. a product of the number $f$ with the number $x$, where $x$ has brackets for some -% reason. In this case, we can disambiguate by using |\Capply{f}x|, which will also format -% as $f(x)$.\ednote{what about $n$-ary functions?} -% -% By the same token, we do not need to represent the qualifier elements -% {\element{condition}} and {\element{domainofapplication}}\footnote{We do not support the -% {\element{fn}} element as it is deprecated in {\mathml}2 and the {\element{declare}} -% and {\element{sep}} elements, since their semantic status is unclear (to the author, -% if you feel it is needed, please gripe to me).}, for -% {\twintoo{binding}{operator}s}. They are are folded into the special forms of the -% semantic macros for the binding operators below (the ones with the {|Cond|} and {|DA|} -% endings): -% -% For operators that are {\index*{associative}}, {\index*{commutative}}, and -% {\index*{idempotent}} ({\index*{ACI}} i.e. {\index*{bracketing}}, -% order\twin{argument}{order}, and {\index*{multiplicity}} of arguments does not matter) -% {\mathml} supplies the a special form of application as a binding operator (often called -% the corresponding ``{\twintoo{big}{operator}})'', which ranges over a whole set of -% arguments. For instance for the ACI operator $\cup$ for set uinon has the ``big'' -% operator for unions over collections of sets e.g. used in the power set -% $\bigcup_{S\subseteq T}S$ of a set $T$. In some cases, the ``big'' operators are -% provided independently by {\mathml}, e.g. the ACI addition operator has the sum operator -% as a corresponding ``big operator'': $\sum_{x\in\Cnaturalnumbers}{x^i}$ is the sum of -% the powers of $x$ for all natural numbers. Where they are not, we will supply extra -% macros in the |cmathml| package, e.g. the |\CUnion| macro as the big operator for -% |\Cunion|. -% -% Finally, some of the binding operators have multiple content models flagged by the -% existence of various modifier elements. In these cases, we have provided different -% semantic macros for the different cases. -% -% \subsection{The Token Elements}\label{sec:tokens} -% -% The {\mathml} token elements are very simple containers that wrap some presentation -% {\mathml} text. The {\element{csymbol}} element is the extension element in -% {\mathml}. It's content is the presentation of symbol, and it has a |definitionURL| -% attribute that allows to specify a URI that specifies the semantics of the symbol. This -% URL can be specified in an optional argument to teh |\Ccsymbol| macro, in accordance -% with usual mathematical practice, the |definitionURL| is not presented. -% \DescribeMacro{\Ccn}\DescribeMacro{\Cci}\DescribeMacro{\Ccsymbol} -% \begin{cmtab} -% |\Ccn| & token & |\Ccn{t}| & $\Ccn{t}$\\\hline -% |\Cci| & token & |\Cci{t}| & $\Cci{t}$\\\hline -% |\Ccsymbol| & token, URI & |\Ccsymbol[http://w3.org]{t}| -% & $\Ccsymbol[http://w3.org]{t}$\\\hline -% \end{cmtab} -% Like the |\Ccsymbol| macro, all other macros in the |camthml| package take an optional -% argument\footnote{This may change into a KeyVaL argument in future versionss of the -% |cmathml| package.} for the |definitionURL| attribute in the corresponding {\mathml} -% element. -% -%\newpage -% \subsection{The Basic Content Elements}\label{sec:basic} -% -% The basic elements comprise various pieces of the {\mathml} infrastructure. Most of the -% semantic macros in this section are relatively uneventful. -% -% \DescribeMacro{\Cinverse}\DescribeMacro{\Ccompose}\DescribeMacro{\Cident} -% \DescribeMacro{\Cdomain}\DescribeMacro{\Ccodomain}\DescribeMacro{\Cimage} -% \begin{cmtab} -% |\Cinverse| & 1 & |\Cinverse{f}| & $\Cinverse{f}$\\\hline -% |\Ccompose| & 1 & |\Ccompose{f,g,h}| & $\Ccompose{f,g,h}$\\\hline -% |\Cident| & 0 & |\Cident| & $\Cident$\\\hline -% |\Cdomain| & 1 & |\Cdomain{f}| & $\Cdomain{f}$\\\hline -% |\Ccodomain| & 1 & |\Ccodomain{f}| & $\Ccodomain{f}$\\\hline -% |\Cimage| & 1 & |\Cimage{f}| & $\Cimage{f}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Clambda}\DescribeMacro{\ClambdaDA}\DescribeMacro{\Crestrict} For the -% {\element{lambda}} element, we only have the {\element{domainofapplication}} element, so -% that we have three forms a $\lambda$-construct can have. The first one is the simple one -% where the first element is a bound variable. The second one restricts the appliccability -% of the bound variable via a {\element{domainofapplication}} element, while the third one -% does not have a bound variable, so it is just a function restriction -% operator.\ednote{need ClambdaCond} -% -% \begin{cmtab} -% |\Clambda| & 2 & |\Clambda{x,y}{A}| & $\Clambda{x,y}{A}$\\\hline -% |\ClambdaDA| & 3 & |\ClambdaDA{x}{C}{A}| & $\ClambdaDA{x,y}{C}{A}$\\\hline -% |\Crestrict| & 2 & |\Crestrict{f}{S}| & $\Crestrict{f}{S}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{ccinterval}\DescribeMacro{cointerval} -% \DescribeMacro{ocinterval}\DescribeMacro{oointerval} -% The {\element{interval}} constructor actually represents four types of intervals in -% {\mathml}. Therefore we have four semantic macros, one for each combination of open and -% closed endings: -% \begin{cmtab} -% |\Cccinterval| & 2 & |\Cccinterval{1}{2}| & $\Cccinterval{1}{2}$\\\hline -% |\Ccointerval| & 2 & |\Ccointerval{1}{2}| & $\Ccointerval{1}{2}$\\\hline -% |\Cocinterval| & 2 & |\Cocinterval{1}{2}| & $\Cocinterval{1}{2}$\\\hline -% |\Coointerval| & 2 & |\Coointerval{1}{2}| & $\Coointerval{1}{2}$\\\hline -% \end{cmtab} -% -%\DescribeMacro{\Cpiecewise}\DescribeMacro{\Cpiece}\DescribeMacro{\Cotherwise} -% The final set of semantic macros are concerned with piecewise definition of functions. -% \begin{cmtab} -% |\Cpiecewise| & 1 & see below & see below\\\hline -% |\Cpiece| & 2 & |\Cpiece{A}{B}| & $\begin{array}{ll}\Cpiece{A}{B}\end{array}$\\\hline -% |\Cotherwise| & 1 & |\Cotherwise{B}| & $\begin{array}{ll}\Cotherwise{1}\end{array}$\\\hline -% \end{cmtab} -% -% For instance, we could define the abstract value function on the reals with the following -% markup -% -% \begin{center} -% \begin{tabular}{|l|l|}\hline -% Semantic Markup & Formatted\\\hline -% \begin{minipage}{8cm}\footnotesize -% \begin{verbatim} -% \Ceq{\Cabs{x}, -% \Cpiecewise{\Cpiece{\Cuminus{x}}{\Clt{x,0}} -% \Cpiece{0}{\Ceq{x,0}} -% \Cotherwise{x}}} -% \end{verbatim} -% \end{minipage} & -% $\Ceq{\Cabs{x},\Cpiecewise{\Cpiece{\Cuminus{x}}{\Clt{x,0}} -% \Cpiece{0}{\Ceq{x,0}} -% \Cotherwise{x}}}$ -% \\\hline -% \end{tabular} -% \end{center} -% -% \newpage -% \subsection{Elements for Arithmetic, Algebra, and Logic}\label{sec:arith} -% -% This section introduces the infrastructure for the basic arithmetic operators. The first -% set is very simple -% -% \DescribeMacro{\Cquotient}\DescribeMacro{\Cfactorial}\DescribeMacro{\Cdivide} -% \DescribeMacro{\Cminus}\DescribeMacro{\Cplus}\DescribeMacro{\Cpower} -% \DescribeMacro{\Crem}\DescribeMacro{\Ctimes}\DescribeMacro{\Croot} -% \begin{cmtab} -% |\Cquotient| & 2 & |\Cquotient{1}{2}| & $\Cquotient{1}{2}$\\\hline -% |\Cfactorial| & 1 & |\Cfactorial{7}| & $\Cfactorial{7}$\\\hline -% |\Cdivide| & 2 & |\Cdivide{1}{2}| & $\Cdivide{1}{2}$\\\hline -% |\Cminus| & 2 & |\Cminus{1}{2}| & $\Cminus{1}{2}$\\\hline -% |\Cplus| & 1 & |\Cplus{1}| & $\Cplus{1}$\\\hline -% |\Cpower| & 2 & |\Cpower{x}{2}| & $\Cpower{x}{2}$\\\hline -% |\Crem| & 2 & |\Crem{7}{2}| & $\Crem{7}{2}$\\\hline -% |\Ctimes| & 1 & |\Ctimes{1,2,3,4}| & $\Ctimes{1,2,3,4}$\\\hline -% |\Croot| & 2 & |\Croot{3}{2}| & $\Croot{3}{2}$\\\hline -% \end{cmtab} -% -% The second batch below is sligtly more complicated, since they take a set of -% arguments. In the |cmathml| package, we treat them like {\index*{associative}} -% operators, i.e. they act on a single argument that contains a sequence of -% comma-separated arguments\ednote{implement this in the latexml side} -% -% \DescribeMacro{\Cmax}\DescribeMacro{\Cmin}\DescribeMacro{\Cgcd}\DescribeMacro{\Clcm} -% \begin{cmtab} -% |\Cmax| & 1 & |\Cmax{1,3,6}| & $\Cmax{1,3,6}$\\\hline -% |\Cmin| & 1 & |\Cmin{1,4,5}| & $\Cmin{1,4,7}$\\\hline -% |\Cgcd| & 1 & |\Cgcd{7,3,5}| & $\Cgcd{7,3,5}$\\\hline -% |\Clcm| & 1 & |\Clcm{3,5,4}| & $\Clcm{3,5,4}$\\\hline -% \end{cmtab} -% -% The operators for the logical connectives are associative as well\ednote{maybe add some -% precedences here.}. Here, conjunction, (exclusive) disjunction are $n$-ary associative -% operators, therefore their semantic macro only has one {\TeX} argument which contains a -% comma-separated list of subformulae. -% \DescribeMacro{\Cand}\DescribeMacro{\Cor}\DescribeMacro{\Cxor}\DescribeMacro{\Cnot} -% \DescribeMacro{\Cimplies} -% \begin{cmtab} -% |\Cand| & 1 & |\Cand{A,B,C}| & $\Cand{A,B,C}$\\\hline -% |\Cor| & 1 & |\Cor{A,B,C}| & $\Cor{A,B,C}$\\\hline -% |\Cxor| & 1 & |\Cxor{A,B,C}| & $\Cxor{A,B,C}$\\\hline -% |\Cnot| & 1 & |\Cnot{A}| & $\Cnot{A}$\\\hline -% |\Cimplies| & 2 & |\Cimplies{A}{B}| & $\Cimplies{A}{B}$\\\hline -% \end{cmtab} -% -% The following are the corresponding big operators, where appropriate. -% \DescribeMacro{\CAndDA}\DescribeMacro{\CAndCond} -% \DescribeMacro{\COrDA}\DescribeMacro{\COrCond} -% \DescribeMacro{\CXorDA}\DescribeMacro{\CXorCond} -% \begin{cmtab} -% |\CAndDA| & 2 & |\CAndDA\Cnaturalnumbers\phi| & $\CAndDA\Cnaturalnumbers\phi$\\\hline -% |\CAndCond| & 3 & |\CAndCond{x}{\Cgt{x}5}{\psi(x)}| -% & $\CAndCond{x}{\Cgt{x}5}{\psi(x)}$\\\hline -% |\COrDA| & 2 & |\COrDA\Cnaturalnumbers\phi| & $\COrDa\Cnaturalnumbers\phi$\\\hline -% |\COrCond| & 3 & |\COrCond{x}{\Cgt{x}5}{\psi(x)}| -% & $\COrCond{x}{\Cgt{x}5}{\psi(x)}$\\\hline -% |\CXorDA| & 2 & |\CXorDA\Cnaturalnumbers\phi| & $\CXorDA\Cnaturalnumbers\phi$\\\hline -% |\CXorCond| & 3 & |\CXorCond{x}{\Cgt{x}5}{\psi(x)}| -% & $\CXorCond{x}{\Cgt{x}5}{\psi(x)}$\\\hline -% \end{cmtab} -% -% The semantic macros for the quantifiers come in two forms: with- and without a condition -% qualifier. In a restricted quantification of the form $\forall x,C:A$, the bound variable -% $x$ ranges over all values, such that $C$ holds ($x$ will usually occur in the condition -% $C$). In an unrestricted quantification of the form $\forall x:A$, the bound variable -% ranges over all possible values for $x$. -% \DescribeMacro{\Cforall}\DescribeMacro{\CforallCond} -% \DescribeMacro{\Cexists}\DescribeMacro{\CexistsCond} -% \begin{cmtab} -% |\Cforall| & 2 & |\Cforall{x,y}{A}| & $\Cforall{x,y}{A}$\\\hline -% |\CforallCond| & 3 & |\CforallCond{x}{C}{A}| & $\CforallCond{x}{C}{A}$\\\hline -% |\Cexists| & 2 & |\Cexists{x,y}{A}| & $\Cexists{x,y}{A}$\\\hline -% |\CexistsCond| & 3 & |\CexistsCond{x}{C}{A}| & $\CexistsCond{x}{C}{A}$\\\hline -% \end{cmtab} -% -% The rest of the operators are very simple in structure. -% \DescribeMacro{\Cabs}\DescribeMacro{\Cconjugate}\DescribeMacro{\Carg} -% \DescribeMacro{\Creal}\DescribeMacro{\Cimaginary}\DescribeMacro{\Cfloor} -% \DescribeMacro{\Cceiling} -% \begin{cmtab} -% |\Cabs| & 1 & |\Cabs{x}| & $\Cabs{x}$\\\hline -% |\Cconjugate| & 1 & |\Cconjugate{x}| & $\Cconjugate{x}$\\\hline -% |\Carg| & 1 & |\Carg{x}| & $\Carg{x}$\\\hline -% |\Creal| & 1 & |\Creal{x}| & $\Creal{x}$\\\hline -% |\Cimaginary| & 1 & |\Cimaginary{x}| & $\Cimaginary{x}$\\\hline -% |\Cfloor| & 1 & |\Cfloor{1.3}| & $\Cfloor{1.3}$\\\hline -% |\Cceiling| & 1 & |\Cceiling{x}| & $\Cceiling{x}$\\\hline -% \end{cmtab} -% -% \subsection{Relations}\label{sec:rels} -% -% The relation symbols in {\mathml} are mostly $n$-ary associative operators (taking a -% comma-separated list as an argument). -% -% \DescribeMacro{\Ceq}\DescribeMacro{\Cneq}\DescribeMacro{\Cgt}\DescribeMacro{\Clt} -% \DescribeMacro{\Cgeq}\DescribeMacro{\Cleq}\DescribeMacro{\Cequivalent} -% \DescribeMacro{\Capprox}\DescribeMacro{\Cfactorof} -% \begin{cmtab} -% |\Ceq| & 1 & |\CeqA,B,C| & $\Ceq{A,B,C}$\\\hline -% |\Cneq| & 2 & |\Cneq{1}{2}| & $\Cneq{1}{2}$\\\hline -% |\Cgt| & 1 & |\Cgt{A,B,C}| & $\Cgt{A,B,C}$\\\hline -% |\Clt| & 1 & |\Clt{A,B,C}| & $\Clt{A,B,C}$\\\hline -% |\Cgeq| & 1 & |\Cgeq{A,B,C}| & $\Cgeq{A,B,C}$\\\hline -% |\Cleq| & 1 & |\Cleq{A,B,C}| & $\Cleq{A,B,C}$\\\hline -% |\Cequivalent| & 1 & |\Cequivalent{A,B,C}| & $\Cequivalent{A,B,C}$\\\hline -% |\Capprox| & 2 & |\Capprox{1}{2}| & $\Capprox{1}{1.1}$\\\hline -% |\Cfactorof| & 2 & |\Cfactorof{7}{21}| & $\Cfactorof{7}{21}$\\\hline -% \end{cmtab} -% -% \subsection{Elements for Calculus and Vector Calculus}\label{sec:calculus-vector-calculus} -% -% The elements for calculus and vector calculus have the most varied forms. -% -% The integrals come in four forms: the first one is just an indefinite integral over a -% function, the second one specifies the bound variables, upper and lower limits. The -% third one specifies a set instead of an interval, and finally the last specifies a -% bound variable that ranges over a set specified by a condition. -% -% \DescribeMacro{\Cint}\DescribeMacro{\CintLimits}\DescribeMacro{\CintDA}\DescribeMacro{\CintCond} -% \begin{cmtab} -% |\Cint| & 1 & |\Cint{f}| & $\Cint{f}$\\\hline -% |\CintLimits| & 4 & |\CintLimits{x}{0}{\Cinfinit}{f(x)}| -% & $\CintLimits{x}{0}{\infty}{f(x)}$\\\hline -% |\CintDA| & 2 & |\CintDA{\Creals}{f}| -% & $\CintDA{\mathbb{R}}{f}$\\\hline -% |\CintCond| & 3 & |\CintCond{x}{\Cin{x}{D}}{f(x)}| -% & $\CintCond{x}{x\in D}{f(x)}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Cdiff}\DescribeMacro{\Cddiff} The differentiation operators are used in -% the usual way: simple differentiation is represented by the |\Cdiff| macro which takes -% the function to be differentiated as an argument, differentiation with the $d$-notation -% is possible by the |\Cddiff|, which takes the bound varible\ednote{really only one?} as -% the first argument and the function expression (in the bound variable) as a second -% argument. -% -% \DescribeMacro{\Cpartialdiff} Partial Differentiation is specified by the -% |\Cpartialdiff| macro. It takes the overall degree as the first argument (to leave it -% out, just pass the empty argument). The second argument is the list of bound variables -% (with their degrees; see below), and the last the function expression (in these bound -% variables). \DescribeMacro{\Cdegree} To specify the respective degrees of -% differentiation on the variables, we use the |\Cdegree| macro, which takes two arguments -% (but no optional argument), the first one is the degree (a natural number) and the -% second one takes the variable. Note that the overall degree has to be the sum of the -% degrees of the bound variables. -% -% \begin{pcmtab}[6cm] -% |\Cdiff| & 1 & |\Cdiff{f}| & $\Cdiff{f}$\\\hline -% |\Cddiff| & 2 & |\Cddiff{x}{f}| & $\Cddiff{x}{f}$\\\hline -% |\Cpartialdiff| & 3 & |\Cpartialdiff{3}{x,y,z}{f(x,y)}| -% & $\Cpartialdiff{3}{x,y,z}{f(x,y)}$\\\hline -% |\Cpartialdiff| & 3 & |\Cpartialdiff{7}| |{\Cdegree{2}{x},\Cdegree{4}{y},z}| |{f(x,y)}| -% & $\Cpartialdiff{7}{\Cdegree{2}{x},\Cdegree{4}{y},z}{f(x,y)}$\\\hline -% \end{pcmtab} -% -% \DescribeMacro{\Climit}\DescribeMacro{\ClimitCond} For content {\mathml}, there are two -% kinds of limit expressions: The simple one is specified by the |\Climit| macro, which -% takes three arguments: the bound variable, the target, and the limit expression. If we -% want to place additional conditions on the limit construction, then we use the -% |\ClimitCond| macro, which takes three arguments as well, the first one is a sequence of -% bound variables, the second one is the condition, and the third one is again the limit -% expression. -% -% \DescribeMacro{\Ctendsto}\DescribeMacro{\CtendstoAbove}\DescribeMacro{\CtendstoBelow} If -% we want to speak qualitatively about limit processes (e.g. in the condition of a -% |\ClimitCond| expression), then can use the {\mathml} {\element{tendsto}} element, which -% is represented by the |\Ctendsto| macro, wich takes two expressions arguments. In -% {\mathml}, the {\element{tendsto}} element can be further specialized by an attribute to -% indicate the direction from which a limit is approached. In the |cmathml| package, we -% supply two additional (specialized) macros for that: |\CtendstoAbove| and -% |\CtendstoBelow|. -% \begin{cmtab} -% |\Climit| & 3 & |\Climit{x}{0}{\Csin{x}}| & $\Climit{x}{0}{\Csin{x}}$\\\hline -% |\ClimitCond| & 3 & |\ClimitCond{x}{\Ctendsto{x}{0}}{\Ccos{x}}| -% & $\ClimitCond{x}{\Ctendsto{x}{0}}{\Ccos{x}}$\\\hline -% |\Ctendsto| & 2 & |\Ctendsto{f(x)}{2}| & $\Ctendsto{f(x)}{2}$\\\hline -% |\CtendstoAbove| & 2 & |\CtendstoAbove{x}{1}| & $\CtendstoAbove{x}{1}$\\\hline -% |\CtendstoBelow| & 2 & |\CtendstoBelow{x}{2}| & $\CtendstoBelow{x}{2}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Cdivergence}\DescribeMacro{\Cgrad}\DescribeMacro{\Ccurl} -% \DescribeMacro{\Claplacian} -% \begin{cmtab} -% |\Cdivergence| & 1 & |\Cdivergence{A}| & $\Cdivergence{A}$\\\hline -% |\Cgrad| & 1 & |\Cgrad{\Phi}| & $\Cgrad{\Phi}$\\\hline -% |\Ccurl| & 1 & |\Ccurl{\Xi}| & $\Ccurl{\Xi}$\\\hline -% |\Claplacian| & 1 & |\Claplacian{A}| & $\Claplacian{A}$\\\hline -% \end{cmtab} -% -% \subsection{Sets and their Operations}\label{sec:sets} -% -% \DescribeMacro{\Cset}\DescribeMacro{\Clist} -% \DescribeMacro{\CsetDA}\DescribeMacro{\CsetRes}\DescribeMacro{\CsetCond} -% The |\Cset| macros is used as the simple finite set constructor, it takes one argument -% that is a comma-separated sequence of members of the set. |\CsetRes| allows to specify a -% set by restricting a set of variables, and |\CsetCond| is the general form of the set -% construction.\ednote{need to do this for lists as well? Probably} -% \begin{cmtab} -% |\Cset| & 1 & |\Cset{1,2,3}| & $\Cset{1,2,3}$\\\hline -% |\CsetRes| & 2 & |\CsetRes{x}{\Cgt{x}5}| -% & $\CsetRes{x}{\Cgt{x}5}$\\\hline -% |\CsetCond| & 3 & |\CsetCond{x}{\Cgt{x}5}{\Cpower{x}3}| -% & $\CsetCond{x}{\Cgt{x}5}{\Cpower{x}3}$\\\hline -% |\CsetDA| & 3 & |\CsetDA{x}{\Cgt{x}5}{S_x}}| -% & $\CsetDA{x}{\Cgt{x}5}{S_x}$\\\hline -% |\Clist| & 1 & |\Clist{3,2,1}| & $\Clist{3,2,1}$\\\hline -%\end{cmtab} -% -%\DescribeMacro{\Cunion}\DescribeMacro{\Cintersect}\DescribeMacro{\Ccartesianproduct} -% \DescribeMacro{\Csetdiff}\DescribeMacro{\Ccard}\DescribeMacro{\Cin}\DescribeMacro{\Cnotin} -% \begin{cmtab} -% |\Cunion| & 1 & |\Cunion{S,T,L}| & $\Cunion{S,T,L}$\\\hline -% |\Cintersect| & 1 & |\Cintersect{S,T,L}| & $\Cintersect{S,T,L}$\\\hline -% |\Ccartesianproduct| & 1 & |\Ccartesianproduct{A,B,C}| & $\Ccartesianproduct{A,B,C}$\\\hline -% |\Csetdiff| & 2 & |\Csetdiff{S}{L}| & $\Csetdiff{S}{L}$\\\hline -% |\Ccard| & 1 & |\Ccard{\Cnaturalnumbers}| & $\Ccard{\mathbb{N}}$\\\hline -% |\Cin| & 2 & |\Cin{a}{S}| & $\Cin{a}{S}$\\\hline -% |\Cnotin| & 2 & |\Cnotin{b}{S}| & $\Cnotin{b}{S}$\\\hline -%\end{cmtab} -% -% The following are the corresponding big operators for the first three binary ACI -% functions. \DescribeMacro{\CUnionDA}\DescribeMacro{\CUnionCond} -% \DescribeMacro{\CIntersectDA}\DescribeMacro{\CIntersectCond} -% \DescribeMacro{\CCartesianproductDA}\DescribeMacro{\CCartesianproductCond} -% \begin{cmtab} -% |\CUnionDA| & 2 & |\CUnionDA\Cnaturalnumbers{S_i}| -% & $\CUnionDA\Cnaturalnumbers{S_i}$\\\hline -% |\CUnionCond| & 3 & |\CUnionCond{x}{\Cgt{x}5}{S_x}}| -% & $\CUnionCond{x}{\Cgt{x}5}{S_x}$\\\hline -% |\CIntersectDA| & 2 & |\CIntersectDA\Cnaturalnumbers{S_i}| -% & $\CIntersectDa\Cnaturalnumbers{S_i}$\\\hline -% |\CIntersectCond| & 3 & |\CIntersectCond{x}{\Cgt{x}5}{S_x}| -% & $\CIntersectCond{x}{\Cgt{x}5}{S_x}$\\\hline -% |\CCartesianproductDA| & 2 & |\CCartesianproductDA\Cnaturalnumbers{S_i}| -% & $\CCartesianproductDA\Cnaturalnumbers{S_i}$\\\hline -% |\CCartesianproductCond| & 3 & |\CCartesianproductCond{x}{\Cgt{x}5}{S_x}| -% & $\CCartesianproductCond{x}{\Cgt{x}5}{S_x}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Csubset}\DescribeMacro{\Cprsubset} -% \DescribeMacro{\Cnotsubset}\DescribeMacro{\Cnotprsubset} For the set containment -% relations, we are in a somewhat peculiar situation: content {\mathml} only supplies the -% subset side of the reations and leaves out the superset relations. Of course they are -% not strictly needed, since they can be expressed in terms of the subset relation with -% reversed argument order. But for the |cmathml| package, the macros have a presentational -% side (for the {\LaTeX} workflow) and a content side (for the {\latexml} converter) -% therefore we will need macros for both relations. -% -% \begin{cmtab} -% |\Csubset| & 1 & |\Csubset{S,T,K}| & $\Csubset{S,T,K}$\\\hline -% |\Cprsubset| & 1 & |\Cprsubset{S,T,K}| & $\Cprsubset{S,T,K}$\\\hline -% |\Cnotsubset| & 2 & |\Cnotsubset{S}{K}| & $\Cnotsubset{S}{K}$\\\hline -% |\Cnotprsubset| & 2 & |\Cnotprsubset{S}{L}| & $\Cnotprsubset{S}{L}$\\\hline -% \end{cmtab} -% \DescribeMacro{\Csupset}\DescribeMacro{\Cprsupset} -% \DescribeMacro{\Cnotsupset}\DescribeMacro{\Cnotprsupset} -% The following set of macros are presented in {\LaTeX} as their name suggests, but upon -% transformation will generate content markup with the {\mathml} elements (i.e. in terms -% of the subset relation). -% -% \begin{cmtab} -% |\Csupset| & 1 & |\Csupset{S,T,K}| & $\Csupset{S,T,K}$\\\hline -% |\Cprsupset| & 1 & |\Cprsupset{S,T,K}| & $\Cprsupset{S,T,K}$\\\hline -% |\Cnotsupset| & 2 & |\Cnotsupset{S}{K}| & $\Cnotsupset{S}{K}$\\\hline -% |\Cnotprsupset| & 2 & |\Cnotprsupset{S}{L}| & $\Cnotprsupset{S}{L}$\\\hline -% \end{cmtab} -% -% \subsection{Sequences and Series}\label{sec:sequences} -% -% \DescribeMacro{\CsumLimits}\DescribeMacro{\CsumCond}\DescribeMacro{\CsumDA} -% \DescribeMacro{\CprodLimist}\DescribeMacro{\CprodCond}\DescribeMacro{\CprodDA} -% \begin{cmtab} -% |\CsumLimits| & 4 & |\CsumLimits{i}{0}{50}{x^i}| & $\CsumLimits{i}{0}{50}{x^i}$\\\hline -% |\CsumCond| & 3 & |\CsumCond{i}{\Cintegers}{i}| & $\CsumCond{i}{\mathbb{Z}}{i}$\\\hline -% |\CsumDA| & 2 & |\CsumDA{\Cintegers}{f}| & $\CsumDA{\mathbb{Z}}{f}$\\\hline -% |\CprodLimits| & 4 & |\CprodLimits{i}{0}{20}{x^i}| & $\CprodLimits{i}{0}{20}{x^i}$\\\hline -% |\CprodCond| & 3 & |\CprodCond{i}{\Cintegers}{i}| & $\CprodCond{i}{\mathbb{Z}}{i}$\\\hline -% |\CprodDA| & 2 & |\CprodDA{\Cintegers}{f}| & $\CprodDA{\mathbb{Z}}{f}$\\\hline -% \end{cmtab} -% -% \subsection{Elementary Classical Functions}\label{sec:specfun} -% -% \DescribeMacro{\Csin}\DescribeMacro{\Ccos}\DescribeMacro{\Ctan} -% \DescribeMacro{\Csec}\DescribeMacro{\Ccsc}\DescribeMacro{\Ccot} -% \begin{cmtab} -% |\Csin| & 1 & |\Csin{x}| & $\Csin{x}$\\\hline -% |\Ccos| & 1 & |\Ccos{x}| & $\Ccos{x}$\\\hline -% |\Ctan| & 1 & |\Ctan{x}| & $\Ctan{x}$\\\hline -% |\Csec| & 1 & |\Csec{x}| & $\Csec{x}$\\\hline -% |\Ccsc| & 1 & |\Ccsc{x}| & $\Ccsc{x}$\\\hline -% |\Ccot| & 1 & |\Ccot{x}| & $\Ccot{x}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Csinh}\DescribeMacro{\Ccosh}\DescribeMacro{\Ctanh} -% \DescribeMacro{\Csech}\DescribeMacro{\Ccsch}\DescribeMacro{\Ccoth} -% \begin{cmtab} -% |\Csinh| & 1 & |\Csinh{x}| & $\Csinh{x}$\\\hline -% |\Ccosh| & 1 & |\Ccosh{x}| & $\Ccosh{x}$\\\hline -% |\Ctanh| & 1 & |\Ctanh{x}| & $\Ctanh{x}$\\\hline -% |\Csech| & 1 & |\Csech{x}| & $\Csech{x}$\\\hline -% |\Ccsch| & 1 & |\Ccsch{x}| & $\Ccsch{x}$\\\hline -% |\Ccoth| & 1 & |\Ccoth{x}| & $\Ccoth{x}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Carcsin}\DescribeMacro{\Carccos}\DescribeMacro{\Carctan} -% \DescribeMacro{\Carcsec}\DescribeMacro{\Carccsc}\DescribeMacro{\Carccot} -% \begin{cmtab} -% |\Carcsin| & 1 & |\Carcsin{x}| & $\Carcsin{x}$\\\hline -% |\Carccos| & 1 & |\Carccos{x}| & $\Carccos{x}$\\\hline -% |\Carctan| & 1 & |\Carctan{x}| & $\Carctan{x}$\\\hline -% |\Carccosh| & 1 & |\Carccosh{x}| & $\Carccosh{x}$\\\hline -% |\Carccot| & 1 & |\Carccot{x}| & $\Carccot{x}$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Carcsinh}\DescribeMacro{\Carccosh}\DescribeMacro{\Carctanh} -% \DescribeMacro{\Carcsech}\DescribeMacro{\Carccsch}\DescribeMacro{\Carccoth} -% \begin{cmtab} -% |\Carccoth| & 1 & |\Carccoth{x}| & $\Carccoth{x}$\\\hline -% |\Carccsc| & 1 & |\Carccsc{x}| & $\Carccsc{x}$\\\hline -% |\Carcsinh| & 1 & |\Carcsinh{x}| & $\Carcsinh{x}$\\\hline -% |\Carctanh| & 1 & |\Carctanh{x}| & $\Carctanh{x}$\\\hline -% |\Cexp| & 1 & |\Cexp{x}| & $\Cexp{x}$\\\hline -% |\Cln| & 1 & |\Cln{x}| & $\Cln{x}$\\\hline -% |\Clog| & 2 & |\Clog{5}{x}| & $\Clog{5}{x}$\\\hline -% \end{cmtab} -% -% \subsection{Statistics}\label{sec:statistics} -% -% The only semantic macro that is non-standard in this module is the one for the -% {\element{moment}} and {\element{momentabout}} elements in {\mathml}. They are combined -% into the semantic macro {|CmomentA|}; its first argument is the degree, its -% second one the point in the distribution, the moment is taken about, and the third is -% the distribution. -% -% \DescribeMacro{\Cmean}\DescribeMacro{\Csdev}\DescribeMacro{\Cvar}\DescribeMacro{\Cmedian} -% \DescribeMacro{\Cmode}\DescribeMacro{\Cmoment}\DescribeMacro{\CmomentA} -% \begin{cmtab} -% |\Cmean| & 1 & |\Cmean{X}| & $\Cmean{X}$\\\hline -% |\Csdev| & 1 & |\Csdev{X}| & $\Csdev{X}$\\\hline -% |\Cvar| & 1 & |\Cvar{X}| & $\Cvar{X}$\\\hline -% |\Cmedian| & 1 & |\Cmedian{X}| & $\Cmedian{X}$\\\hline -% |\Cmode| & 1 & |\Cmode{X}| & $\Cmode{X}$\\\hline -% |\Cmoment| & 3 & |\Cmoment{3}{X}| & $\Cmoment{3}{X}$\\\hline -% |\CmomentA| & 3 & |\CmomentA{3}{p}{X}| & $\CmomentA{3}{p}{X}$\\\hline -% \end{cmtab} -% -% \subsection{Linear Algebra}\label{sec:linalg} -% -% In these semantic macros, only the matrix constructor is unusual; instead of -% constructing a matrix from {\element{matrixrow}} elements like {\mathml} does, the macro -% follows the {\TeX/\LaTeX} tradition allows to give a matrix as an array. The first -% argument of the macro is the column specification (it will only be used for presentation -% purposes), and the second one the rows. -% -% \DescribeMacro{\Cvector}\DescribeMacro{\Cmatrix}\DescribeMacro{\Cdeterminant} -% \DescribeMacro{\Ctranspose}\DescribeMacro{\Cselector} -% \DescribeMacro{\Cvectorproduct}\DescribeMacro{\Cscalarproduct}\DescribeMacro{\Couterproduct} -% \begin{cmtab} -% |\Cvector| & 1 & |\Cvector{1,2,3}| & $\Cvector{1,2,3}$\\\hline -% |\Cmatrix| & 2 & |\Cmatrix{ll}{1 & 2\\ 3 & 4}| & $\Cmatrix{ll}{1 & 2\\3 & 4}$\\\hline -% |\Cdeterminant| & 1 & |\Cdeterminant{A}| & $\Cdeterminant{A}$\\\hline -% |\Ctranspose| & 1 & |\Ctranspose{A}| & $\Ctranspose{A}$\\\hline -% |\Cselector| & 2 & |\Cselector{A}{2}| & $\Cselector{A}{2}$\\\hline -% |\Cvectproduct| & 2 & |\Cvectproduct{\phi}{\psi}| & $\Cvectproduct{\phi}{\psi}$\\\hline -% |\Cscalarproduct| & 2 & |\Cscalarproduct{\phi}{\psi}| & $\Cscalarproduct{\phi}{\psi}$\\\hline -% |\Couterproduct| & 2 & |\Couterproduct{\phi}{\psi}| & $\Couterproduct{\phi}{\psi}$\\\hline -% \end{cmtab} -% -% \subsection{Constant and Symbol Elements}\label{sec:constants} -% -% The semantic macros for the {\mathml} constant and symbol elements are very simple, they -% do not take any arguments, and their name is just the {\mathml} element name prefixed by -% a capital C. -% -% \DescribeMacro{\Cintegers}\DescribeMacro{\Creals}\DescribeMacro{\Crationals} -% \DescribeMacro{\Ccomplexes}\DescribeMacro{\Cprimes} -% \begin{cmtab} -% |\Cintegers| & & |\Cintegers| & $\Cintegers$\\\hline -% |\Creals| & & |\Creals| & $\Creals$\\\hline -% |\Crationals| & & |\Crationals| & $\Crationals$\\\hline -% |\Cnaturalnumbers| & & |\Cnaturalnumbers| & $\Cnaturalnumbers$\\\hline -% |\Ccomplexes| & & |\Ccomplexes| & $\Ccomplexes$\\\hline -% |\Cprimes| & & |\Cprimes| & $\Cprimes$\\\hline -% \end{cmtab} -% -% \DescribeMacro{\Cexponentiale}\DescribeMacro{\Cimaginaryi} -% \DescribeMacro{\Ctrue}\DescribeMacro{\Cfalse} \DescribeMacro{\Cemptyset} -% \DescribeMacro{\Cpi}\DescribeMacro{\Ceulergamma}\DescribeMacro{\Cinfinit} -% \begin{cmtab} -% |\Cexponemtiale| & & |\Cexponemtiale| & $\Cexponemtiale$\\\hline -% |\Cimaginaryi| & & |\Cimaginaryi| & $\Cimaginaryi$\\\hline -% |\Cnotanumber| & & |\Cnotanumber| & $\Cnotanumber$\\\hline -% |\Ctrue| & & |\Ctrue| & $\Ctrue$\\\hline -% |\Cfalse| & & |\Cfalse| & $\Cfalse$\\\hline -% |\Cemptyset| & & |\Cemptyset| & $\Cemptyset$\\\hline -% |\Cpi| & & |\Cpi| & $\Cpi$\\\hline -% |\Ceulergamma| & & |\Ceulergamma| & $\Ceulergamma$\\\hline -% |\Cinfinit| & & |\Cinfinit| & $\Cinfinit$\\\hline -% \end{cmtab} -% -% \subsection{Extensions}\label{sec:cmathmlx} -% Content MathML does not (even though it claims to cover M-14 Math) symbols for all the -% common mathematical notions. The |cmathmlx| attempts to collect these and provide -% {\TeX/\LaTeX} and {\latexml} bindings. -% -%\DescribeMacro{\Ccomplement} -% \begin{cmtab} -% |\Ccomplement| & 1 & |\Ccomplement{\Cnaturalnumbers}| & $\Ccomplement{\mathbb{N}}$\\\hline -%\end{cmtab} -% -% \StopEventually{\ednotemessage} -% -% \newpage -% \section{The Implementation}\label{sec:impl} -% -% In this file we document both the implementation of the |cmathml| package, as well as -% the corresponding {\latexml} bindings. This keeps similar items close to each other, -% even though they eventually go into differing files and helps promote consistency. We -% specify which code fragment goes into which file by the {\xml}-like grouping commands: -% The code between |<*sty>| and |</sty>| goes into the package file |cmathml.sty|, and the -% code between |<*ltxml>| and |</ltxml>| goes into |cmathml.ltxml|, the {\latexml} -% bindings. -% -% \subsection{Initialization and auxiliary functions}\label{sec:impl:init} -% -% We first make sure that the {\sTeX} |presentation| package is loaded. -% \begin{macrocode} -%<*sty|styx> -\RequirePackage{presentation} -%</sty|styx> -% \end{macrocode} -% -% Before we start im plementing the {\mathml} macros, we will need to set up the packages -% for perl in the {\latexml} bindings file. -% \begin{macrocode} -%<*ltxml|ltxmlx> -# -*- CPERL -*- -package LaTeXML::Package::Pool; -use strict; -use LaTeXML::Package; -use LaTeXML::Document; -RequirePackage('LaTeX'); -%</ltxml|ltxmlx> -% \end{macrocode} -% -% The next step is to itroduce two auxiliary functions, they are needed to work with -% $n$-ary function elements. The first one removes arbitrary tokens from a list, and the -% specializes that to commas. In particular |remove_tokens_from_list($List, $pattern, $math)| -% returns a new |List| (or |MathList| if |$math| is true) -% with all the tokens in |$List| except the ones which follow -% the pattern |$pattern|. -% -% \begin{macrocode} -%<*ltxml> -sub remove_tokens_from_list { - my ($list, $pattern, $math) = @_; - if (ref $list) { - my @toks = $list->unlist; - @toks = grep($_->toString !~ /$pattern/, @toks); - ($math ? (LaTeXML::MathList->new(@toks)) : (LaTeXML::List)->new(@toks)); } - else { undef; } } - -sub remove_math_commas { - my ($whatsit, $argno) = @_; - my @args = $whatsit ? $whatsit->getArgs() : undef; - $argno--; - if ($args[$argno]) { - $args[$argno] = remove_tokens_from_list($args[$argno], ',', 1); - $whatsit->setArgs(@args); - } - return; -} -%</ltxml> -% \end{macrocode} -% -% The structural macros are rather simple: -% -% \begin{macrocode} -%<*sty> -\newcommand{\Capply}[3][]{#2(#3)} -%</sty> -%<*ltxml> -DefConstructor('\Capply [] {} {}', - "<ltx:XMApp ?#1(definitionURL='#1')()>#2 #3</ltx:XMApp>"); -%</ltxml> -% after this, the implementation will always have the same form. We will first -% implement a block of {\LaTeX} macros via a |\newcommand| and then specify the -% corresponding {\latexml} bindings for them. -% -% \subsection{The Token Elements}\label{impl:tokens} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@cn#1{#1} -\newcommand{\Ccn}[2][]{\CMathML@cn{#2}} -\def\CMathML@ci#1{#1} -\newcommand{\Cci}[2][]{\CMathML@ci{#2}} -\def\CMathML@csymbol#1{#1} -\newcommand{\Ccsymbol}[2][]{\CMathML@csymbol{#2}} -%</sty> -%<*ltxml> -DefConstructor('\Ccn [] {}',"#2"); -DefConstructor('\Cci [] {}',"#2"); -DefConstructor('\Ccsymbol [] {}', - "<ltx:XMTok role='CSYMBOL' meaning='#2' ?#1(definitionURL='#1')()/>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{The Basic Elements}\label{impl:basic} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@ccinterval#1#2{[#1,#2]} -\newcommand{\Cccinterval}[3][]{\CMathML@ccinterval{#2}{#3}} -\def\CMathML@cointerval#1#2{[#1,#2)} -\newcommand{\Ccointerval}[3][]{\CMathML@cointerval{#2}{#3}} -\def\CMathML@ocinterval#1#2{(#1,#2]} -\newcommand{\Cocinterval}[3][]{\CMathML@ocinterval{#2}{#3}} -\def\CMathML@oointerval#1#2{(#1,#2)} -\newcommand{\Coointerval}[3][]{\CMathML@oointerval{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\Cccinterval [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONSTRUCTOR' meaning='ccinterval' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg></ltx:XMApp>"); -DefConstructor('\Ccointerval [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONSTRUCTOR' meaning='cointerval' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg></ltx:XMApp>"); -DefConstructor('\Cocinterval [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONSTRUCTOR' meaning='ocinterval' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg></ltx:XMApp>"); -DefConstructor('\Coointerval [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONSTRUCTOR' meaning='oointerval' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg></ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\newcommand{\Cinverse}[2][]{#2^{-1}} -% what about separator -%</sty> -%<*ltxml> -DefConstructor('\Cinverse [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='inverse' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@lambda#1#2{\lambda({#1},{#2})} -\newcommand{\Clambda}[3][]{\CMathML@lambda{#2}{#3}} -\def\CMathML@lambdaDA#1#2#3{\lambda({#1}\colon{#2},#3)} -\newcommand{\ClambdaDA}[4][]{\CMathML@lambdaDA{#2}{#3}{#4}} -\def\CMathML@restrict#1#2{\left.#1\right|_{#2}} -\newcommand{\Crestrict}[3][]{\CMathML@restrict{#2}{#3}} -%</sty> -%\ednote{need do deal with multiple variables!} -%<*ltxml> -DefConstructor('\Clambda [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BINDER' meaning='lambda' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\ClambdaDA [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BINDER' meaning='lambda' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Crestrict [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='restrict' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> - \def\CMathML@composeOp{\circ} - \newcommand{\CcomposeOp}{\CMathML@composeOp} -\def\CMathML@compose#1{\assoc[p=500,pi=500]{\CMathML@composeOp}{#1}} -\newcommand{\Ccompose}[2][]{\CMathML@compose{#2}} -\def\CMathML@ident#1{\mathrm{id}} -\newcommand{\Cident}[1][]{\CMathML@ident{#1}} -\def\CMathML@domain#1{\mbox{dom}(#1)} -\newcommand{\Cdomain}[2][]{\CMathML@domain{#2}} -\def\CMathML@codomain#1{\mbox{codom}(#1)} -\newcommand{\Ccodomain}[2][]{\CMathML@codomain{#2}} -\def\CMathML@image#1{{\mathbf{Im}}(#1)} -\newcommand{\Cimage}[2][]{\CMathML@image{#2}} -\def\CMathML@piecewise#1{\left\{\begin{array}{ll}#1\end{array}\right.} -\newcommand{\Cpiecewise}[2][]{\CMathML@piecewise{#2}} -\def\CMathML@piece#1#2{#1&{\mathrm{if}}\;{#2}\\} -\newcommand{\Cpiece}[3][]{\CMathML@piece{#2}{#3}} -\def\CMathML@otherwise#1{#1&else\\} -\newcommand{\Cotherwise}[2][]{\CMathML@otherwise{#2}} -%</sty> -%<*ltxml> -DefConstructor('\CcomposeOp []', - "<ltx:XMTok meaning='compose' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ccompose [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='MULOP' meaning='compose' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\Cident []', - "<ltx:XMTok meaning='ident' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cdomain [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='domain' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccodomain [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='codomain' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cimage [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='image' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cpiecewise [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='piecewise' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cpiece [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='piece' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cotherwise [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='otherwise' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Elements for Arithmetic, Algebra, and Logic}\label{impl:arith} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@quotient#1#2{\frac{#1}{#2}} -\newcommand{\Cquotient}[3][]{\CMathML@quotient{#2}{#3}} - \def\CMathML@factorialOp{!} - \newcommand{\CfactorialOp}{\CMathML@factorialOp} -\def\CMathML@factorial#1{#1{\CMathML@factorialOp}} -\newcommand{\Cfactorial}[2][]{\CMathML@factorial{#2}} - \def\CMathML@divideOp{\div} - \newcommand{\CdivideOp}{\CMathML@divideOp} -\def\CMathML@divide#1#2{\infix[p=400]{\CMathML@divideOp}{#1}{#2}} -\newcommand{\Cdivide}[3][]{\CMathML@divide{#2}{#3}} - \def\CMathML@maxOp{\mathrm{max}} - \newcommand{\CmaxOp}{\CMathML@maxOp} -\def\CMathML@max#1{{\CMathML@maxOp}(#1)} -\newcommand{\Cmax}[2][]{\CMathML@max{#2}} - \def\CMathML@minOp{\mathrm{min}} - \newcommand{\CminOp}{\CMathML@minOp} -\def\CMathML@min#1{{\CMathML@minOp}(#1)} -\newcommand{\Cmin}[2][]{\CMathML@min{#2}} - \def\CMathML@minusOp{-} - \newcommand{\CminusOp}{\CMathML@minusOp} -\def\CMathML@minus#1#2{\infix[p=500]{\CMathML@minusOp}{#1}{#2}} -\newcommand{\Cminus}[3][]{\CMathML@minus{#2}{#3}} -\def\CMathML@uminus#1{\prefix[p=200]{\CMathML@minusOp}{#1}} -\newcommand{\Cuminus}[2][]{\CMathML@uminus{#2}} - \def\CMathML@plusOp{+} - \newcommand{\CplusOp}{\CMathML@plusOp} -\def\CMathML@plus#1{\assoc[p=500]{\CMathML@plusOp}{#1}} -\newcommand{\Cplus}[2][]{\CMathML@plus{#2}} -\def\CMathML@power#1#2{\infix[p=200]{^}{#1}{#2}} -\newcommand{\Cpower}[3][]{\CMathML@power{#2}{#3}} - \def\CMathML@remOp{\bmod} - \newcommand{\CremOp}{\CMathML@remOp} -\def\CMathML@rem#1#2{#1 \CMathML@remOp #2} -\newcommand{\Crem}[3][]{\CMathML@rem{#2}{#3}} - \def\CMathML@timesOp{\cdot} - \newcommand{\CtimesOp}{\CMathML@timesOp} -\def\CMathML@times#1{\assoc[p=400]{\CMathML@timesOp}{#1}} -\newcommand{\Ctimes}[2][]{\CMathML@times{#2}} - \def\CMathML@rootOp{\sqrt} - \newcommand{\CrootOp}{\CMathML@rootOp{}} -\def\CMathML@root#1#2{\CMathML@rootOp[#1]{#2}} -\newcommand{\Croot}[3][]{\CMathML@root{#2}{#3}} -\def\CMathML@gcd#1{\gcd(#1)} -\newcommand{\Cgcd}[2][]{\CMathML@gcd{#2}} - \def\CMathML@andOp{\wedge} - \newcommand{\CandOp}{\CMathML@andOp} -\def\CMathML@and#1{\assoc[p=400]{\CMathML@andOp}{#1}} -\newcommand{\Cand}[2][]{\CMathML@and{#2}} - \def\CMathML@orOp{\vee} - \newcommand{\CorOp}{\CMathML@orOp} -\def\CMathML@or#1{\assoc[p=500]{\CMathML@orOp}{#1}} -\newcommand{\Cor}[2][]{\CMathML@or{#2}} - \def\CMathML@xorOp{\oplus} - \newcommand{\CxorOp}{\CMathML@xorOp} -\def\CMathML@xor#1{\assoc[p=400]{\CMathML@xorOp}{#1}} -\newcommand{\Cxor}[2][]{\CMathML@xor{#2}} - \def\CMathML@notOp{\neg} - \newcommand{\CnotOp}{\CMathML@notOp} -\def\CMathML@not#1{\CMathML@notOp{#1}} -\newcommand{\Cnot}[2][]{\CMathML@not{#2}} - \def\CMathML@impliesOp{\Longrightarrow} - \newcommand{\CimpliesOp}{\CMathML@impliesOp} -\def\CMathML@implies#1#2{#1\CMathML@impliesOp{#2}} -\newcommand{\Cimplies}[3][]{\CMathML@implies{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\Cquotient [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='quotient' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CfactorialOp []', - "<ltx:XMTok meaning='factorial' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cfactorial [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='factorial' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CdivideOp []', - "<ltx:XMTok meaning='divide' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cdivide [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='divide' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CmaxOp []', - "<ltx:XMTok meaning='max' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cmax [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='max' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CminOp []', - "<ltx:XMTok meaning='min' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cmin [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='min' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CminusOp []', - "<ltx:XMTok meaning='minus' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cminus [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='ADDOP' meaning='minus' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cuminus [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='uminus' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CplusOp []', - "<ltx:XMTok meaning='plus' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cplus [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='ADDOP' meaning='plus' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\Cpower [] {} {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='power' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CremOp []', - "<ltx:XMTok meaning='rem' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Crem [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='rem' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CtimesOp []', - "<ltx:XMTok meaning='times' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ctimes [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='MULOP' meaning='times' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CrootOp []', - "<ltx:XMTok meaning='root' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Croot [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='root' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cgcd [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='gcd' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CandOp []', - "<ltx:XMTok meaning='and' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cand [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONNECTIVE' meaning='and' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CorOp []', - "<ltx:XMTok meaning='or' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cor [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONNECTIVE' meaning='or' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CxorOp []', - "<ltx:XMTok meaning='xor' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cxor [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONNECTIVE' meaning='xor' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CnotOp []', - "<ltx:XMTok meaning='not' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cnot [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONNECTIVE' meaning='not' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CimpliesOp []', - "<ltx:XMTok meaning='implies' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cimplies [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONNECTIVE' meaning='implies' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% \ednote{need to do something about the associative things in ltxml} -% \begin{macrocode} -%<*sty> -\def\CMathML@AndDA#1#2{\bigwedge_{#1}{#2}} % set, scope -\newcommand{\CAndDA}[3][]{\CMathML@AndDA{#2}{#3}} -\def\CMathML@AndCond#1#2#3{\bigwedge_{#2}{#3}} % bvars,condition, scope -\newcommand{\CAndCond}[4][]{\CMathML@AndCond{#2}{#2}{#3}} -\def\CMathML@OrDA#1#2{\bigvee_{#1}{#2}} % set, scope -\newcommand{\COrDa}[3][]{\CMathML@OrDA{#2}{#3}} -\def\CMathML@OrCond#1#2#3{\bigvee_{#2}{#3}}% bvars,condition, scope -\newcommand{\COrCond}[4][]{\CMathML@OrCond{#2}{#3}{#4}} -\def\CMathML@XorDA#1#2{\bigoplus_{#1}{#2}} % set, scope -\newcommand{\CXorDA}[3][]{\CMathML@XorDA{#2}{#3}} -\def\CMathML@XorCond#1#2#3{\bigoplus_{#2}{#3}}% bvars,condition, scope -\newcommand{\CXorCond}[4][]{\CMathML@XorCond{#2}{#3}{#4}} -% -\def\CMathML@forall#1#2{\forall{#1}\colon{#2}} -\newcommand{\Cforall}[3][]{\CMathML@forall{#2}{#3}} -\def\CMathML@forallCond#1#2#3{\forall{#1},{#2}\colon{#3}} % list), condition, scope -\newcommand{\CforallCond}[4][]{\CMathML@forallCond{#2}{#3}{#4}} -%</sty> -%<*ltxml> -DefConstructor('\CAndDa [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='and' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CAndCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='and' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\COrDa [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='or' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\COrCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='or' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CXorDa [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='xor' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CXorCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='xor' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cforall [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BINDER' meaning='forall' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CforallCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BINDER' meaning='forall' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@exists#1#2{\exists{#1}\colon{#2}} -\newcommand{\Cexists}[3][]{\CMathML@exists{#2}{#3}} -\def\CMathML@esistsCont#1#2#3{\exists{#1},{#2}\colon{#3}} -\newcommand{\CexistsCond}[4][]{\CMathML@esistsCont{#2}{#3}{#4}} -%</sty> -%<*ltxml> -DefConstructor('\Cexists [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BINDER' meaning='exists' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CexistsCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BINDER' meaning='exists' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@abs#1{\left|#1\right|} -\newcommand{\Cabs}[2][]{\CMathML@abs{#2}} -\def\CMathML@conjugate#1{\overline{#1}} -\newcommand{\Cconjugate}[2][]{\CMathML@conjugate{#2}} -\def\CMathML@arg#1{\angle #1} -\newcommand{\Carg}[2][]{\CMathML@arg{#2}} -\def\CMathML@real#1{\Re #1} -\newcommand{\Creal}[2][]{\CMathML@real{#2}} -\def\CMathML@imaginary#1{\Im #1} -\newcommand{\Cimaginary}[2][]{\CMathML@imaginary{#2}} -\def\CMathML@lcm#1{\mbox{lcm}(#1)} -\newcommand{\Clcm}[2][]{\CMathML@lcm{#2}} -\def\CMathML@floor#1{\left\lfloor{#1}\right\rfloor} -\newcommand{\Cfloor}[2][]{\CMathML@floor{#2}} -\def\CMathML@ceiling#1{\left\lceil{#1}\right\rceil} -\newcommand{\Cceiling}[2][]{\CMathML@ceiling{#2}} -%</sty> -%<*ltxml> -DefConstructor('\Cabs [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='abs' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cconjugate [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='conjugate' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carg [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='arg' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Creal [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='real' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cimaginary [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='imaginary' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Clcm [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='lcm' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cfloor [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='floor' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cceiling [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='ceiling' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Relations}\label{impl:rels} -% -% \begin{macrocode} -%<*sty> - \def\CMathML@eqOp{=} - \newcommand{\CeqOp}{\CMathML@eqOp} -\def\CMathML@eq#1{\assoc[p=700]{\CMathML@eqOp}{#1}} -\newcommand{\Ceq}[2][]{\CMathML@eq{#2}} - \def\CMathML@neqOp{\neq} - \newcommand{\CneqOp}{\CMathML@neqOp} -\def\CMathML@neq#1#2{\infix[p=700]{\CMathML@neqOp}{#1}{#2}} -\newcommand{\Cneq}[3][]{\CMathML@neq{#2}{#3}} - \def\CMathML@gtOp{>} - \newcommand{\CgtOp}{\CMathML@gtOp} -\def\CMathML@gt#1{\assoc[p=700]{\CMathML@gtOp}{#1}} -\newcommand{\Cgt}[2][]{\CMathML@gt{#2}} - \def\CMathML@ltOp{<} - \newcommand{\CltOp}{\CMathML@ltOp} -\def\CMathML@lt#1{\assoc[p=700]{\CMathML@ltOp}{#1}} -\newcommand{\Clt}[2][]{\CMathML@lt{#2}} - \def\CMathML@geqOp{\geq} - \newcommand{\CgeqOp}{\CMathML@geqOp} -\def\CMathML@geq#1{\assoc[p=700]{\CMathML@geqOp}{#1}} -\newcommand{\Cgeq}[2][]{\CMathML@geq{#2}} - \def\CMathML@leqOp{\leq} - \newcommand{\CleqOp}{\CMathML@leqOp} -\def\CMathML@leq#1{\assoc[p=700]{\CMathML@leqOp}{#1}} -\newcommand{\Cleq}[2][]{\CMathML@leq{#2}} - \def\CMathML@equivalentOp{\equiv} - \newcommand{\CequivalentOp}{\CMathML@equivalentOp} -\def\CMathML@equivalent#1{\assoc[p=700]{\CMathML@equivalentOp}{#1}} -\newcommand{\Cequivalent}[2][]{\CMathML@equivalent{#2}} - \def\CMathML@approxOp{\approx} - \newcommand{\CapproxOp}{\CMathML@approxOp} -\def\CMathML@approx#1#2{#1\CMathML@approxOp{#2}} -\newcommand{\Capprox}[3][]{\CMathML@approx{#2}{#3}} - \def\CMathML@factorofOp{\mid} - \newcommand{\CfactorofOp}{\CMathML@factorofOp} -\def\CMathML@factorof#1#2{#1\CMathML@factorofOp{#2}} -\newcommand{\Cfactorof}[3][]{\CMathML@factorof{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\CeqOp []', - "<ltx:XMTok meaning='eq' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ceq [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='eq' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CneqOp []', - "<ltx:XMTok meaning='neq' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cneq [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='neq' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CgtOp []', - "<ltx:XMTok meaning='gt' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cgt [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='gt' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CltOp []', - "<ltx:XMTok meaning='lt' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Clt [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='lt' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CgeqOp []', - "<ltx:XMTok meaning='geq' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cgeq [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='geq' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CleqOp []', - "<ltx:XMTok meaning='leq' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cleq [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='leq' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CequivalentOp []', - "<ltx:XMTok meaning='equivalent' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cequivalent [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='equivalent' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>"); -DefConstructor('\CapproxOp []', - "<ltx:XMTok meaning='approx' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Capprox [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='approx' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CfactorofOp []', - "<ltx:XMTok meaning='factorof' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cfactorof [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='factorof' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> - - \def\CMathML@intOp{\int} - \newcommand{\CintOp}{\CMathML@intOp} -\def\CMathML@int#1{\CMathML@intOp{#1}} -\newcommand{\Cint}[2][]{\CMathML@int{#2}} -\def\CMathML@intLimits#1#2#3#4{\CMathML@intOp_{#2}^{#3}{#4}d{#1}} %bvars,llimit, ulimit,body -\newcommand{\CintLimits}[5][]{\CMathML@intLimits{#2}{#3}{#4}{#5}} -\def\CMathML@intSet#1#2{\CMathML@intOp_{#1}{#2}}% set,function -\newcommand{\CintDA}[3][]{\CMathML@intSet{#2}{#3}} -\def\CMathML@intCond#1#2#3{\CMathML@intOp_{#2}{#3}d{#1}} %bvars, condition, body -\newcommand{\CintCond}[4][]{\CMathML@intCond{#2}{#3}{#4}} - -%</sty> -%<*ltxml> -DefConstructor('\CintOp []', - "<ltx:XMTok meaning='int' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cint [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='int' role='INTOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CintLimits [] {}{}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='int' role='INTOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "<ltx:XMArg>#5</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CintDA [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='int' role='INTOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CintCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='int' role='INTOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@diff#1{#1'} -\newcommand{\Cdiff}[2][]{\CMathML@diff{#2}} -\def\CMathML@ddiff#1#2{{d{#2}(#1)\over{d{#1}}}} -\newcommand{\Cddiff}[3][]{\CMathML@ddiff{#2}{#3}} -\def\CMathML@partialdiff#1#2#3{{\partial^{#1}\over\partial{#2}}{#3}}% degree, bvars, body -\newcommand{\Cpartialdiff}[4][]{\CMathML@partialdiff{#2}{#3}{#4}} -\newcommand{\Cdegree}[2]{#1^{#2}} -%</sty> -%<*ltxml> -DefConstructor('\Cdiff [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='diff' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cddiff [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='diff' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cpartialdiff [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='diff' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "?#2(<ltx:XMArg>#2</ltx:XMArg>)()" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cdegree {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='degree'/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#1</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@limit#1#2#3{\lim_{#1\rightarrow{#2}}{#3}} -\newcommand{\Climit}[4][]{\CMathML@limit{#2}{#3}{#4}} % bvar, lowlimit, scope -\def\CMathML@limitCond#1#2#3{\lim_{#2}{#3}} -\newcommand{\ClimitCond}[4][]{\CMathML@limitCond{#2}{#3}{#4}} % bvars, condition, scope -%</sty> -%<*ltxml> -DefConstructor('\Climit [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='limit' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\ClimitCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='limit' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> - \def\CMathML@tendstoOp{\rightarrow} - \newcommand{\CtendstoOp}{\CMathML@tendstoOp} -\def\CMathML@tendsto#1#2{#1\CMathML@tendstoOp{#2}} -\newcommand{\Ctendsto}[3][]{\CMathML@tendsto{#2}{#3}} - \def\CMathML@tendstoAboveOp{\searrow} - \newcommand{\CtendstoAboveOp}{\CMathML@tendstoAboveOp} -\def\CMathML@tendstoAbove#1#2{#1\searrow{#2}} -\newcommand{\CtendstoAbove}[3][]{\CMathML@tendstoAbove{#2}{#3}} - \def\CMathML@tendstoBelowOp{\nearrow} - \newcommand{\CtendstoBelowOp}{\CMathML@tendstoBelowOp} -\def\CMathML@tendstoBelow#1#2{#1\CMathML@tendstoBelowOp{#2}} -\newcommand{\CtendstoBelow}[3][]{\CMathML@tendstoBelow{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\CtendstoOp []', - "<ltx:XMTok meaning='tendsto' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ctendsto [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='RELOP' meaning='tendsto' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CtendstoAboveOp []', - "<ltx:XMTok meaning='tendsto' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CtendstoAbove [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='RELOP'meaning='tendsto' type='above' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CtendstoBelowOp []', - "<ltx:XMTok meaning='tendsto' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CtendstoBelow [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='RELOP' meaning='tendsto' type='below' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@divergence#1{\nabla\cdot{#1}} -\newcommand{\Cdivergence}[2][]{\CMathML@divergence{#2}} -\def\CMathML@grad#1{\nabla{#1}} -\newcommand{\Cgrad}[2][]{\CMathML@grad{#2}} -\def\CMathML@curl#1{\nabla\times{#1}} -\newcommand{\Ccurl}[2][]{\CMathML@curl{#2}} -\def\CMathML@laplacian#1{\nabla^2#1} -\newcommand{\Claplacian}[2][]{\CMathML@laplacian{#2}} -%</sty> -%<*ltxml> -DefConstructor('\Cdivergence [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='divergence' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cgrad [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='grad' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Curl [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='url' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Claplacian [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='OPFUNCTION' meaning='laplacian' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Sets and their Operations}\label{impl:sets} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@set#1{\left\{#1\right\}} -\newcommand{\Cset}[2][]{\CMathML@set{#2}} -\def\CMathML@setRes#1#2{\{#1|#2\}} -\newcommand{\CsetRes}[3][]{\CMathML@setRes{#2}{#3}} -\def\CMathML@setCond#1#2#3{\{#2|#3\}} -\newcommand{\CsetCond}[4][]{\CMathML@setCond{#2}{#3}{#4}} -\def\CMathML@setDA#1#2#3{\{#1\in{#2}|#3\}} -\newcommand{\CsetDA}[4][]{\CMathML@setDA{#2}{#3}{#4}} - \def\CMathML@listOp{\mbox{list}} - \newcommand{\ClistOp}{\CMathML@listOp} -\def\CMathML@list#1{\CMathML@listOp({#1})} -\newcommand{\Clist}[2][]{\CMathML@list{#2}} - \def\CMathML@unionOp{\cup} - \newcommand{\CunionOp}{\CMathML@unionOp} -\def\CMathML@union#1{\assoc[p=500]{\CMathML@unionOp}{#1}} -\newcommand{\Cunion}[2][]{\CMathML@union{#2}} - \def\CMathML@intersectOp{\cap} - \newcommand{\CintersectOp}{\CMathML@intersectOp} -\def\CMathML@intersect#1{\assoc[p=400]{\CMathML@intersectOp}{#1}} -\newcommand{\Cintersect}[2][]{\CMathML@intersect{#2}} - \def\CMathML@inOp{\in} - \newcommand{\CinOp}{\CMathML@inOp} -\def\CMathML@in#1#2{#1\CMathML@inOp{#2}} -\newcommand{\Cin}[3][]{\CMathML@in{#2}{#3}} - \def\CMathML@notinOp{\notin} - \newcommand{\CnotinOp}{\CMathML@notinOp} -\def\CMathML@notin#1#2{#1\CMathML@notinOp{#2}} -\newcommand{\Cnotin}[3][]{\CMathML@notin{#2}{#3}} - \def\CMathML@setdiffOp{\setminus} - \newcommand{\CsetdiffOp}{\CMathML@setdiffOp} -\def\CMathML@setdiff#1#2{#1\CMathML@setdiffOp{#2}} -\newcommand{\Csetdiff}[3][]{\CMathML@setdiff{#2}{#3}} - \def\CMathML@cardOp{\#} - \newcommand{\CcardOp}{\CMathML@cardOp} -\def\CMathML@card#1{\CMathML@cardOp #1} -\newcommand{\Ccard}[2][]{\CMathML@card{#2}} - \def\CMathML@cartesianproductOp{\times} - \newcommand{\CcartesianproductOp}{\CMathML@cartesianproductOp} -\def\CMathML@cartesianproduct#1{\assoc[p=400]{\CMathML@cartesianproductOp}{#1}} -\newcommand{\Ccartesianproduct}[2][]{\CMathML@cartesianproduct{#2}} - \def\CMathML@subsetOp{\subseteq} - \newcommand{\CsubsetOp}{\CMathML@subsetOp} -\def\CMathML@subset#1{\assoc[p=700]{\CMathML@subsetOp}{#1}} -\newcommand{\Csubset}[2][]{\CMathML@subset{#2}} - \def\CMathML@prsubsetOp{\subset} - \newcommand{\CprsubsetOp}{\CMathML@prsubsetOp} -\def\CMathML@prsubset#1{\assoc[p=700]{\CMathML@prsubsetOp}{#1}} -\newcommand{\Cprsubset}[2][]{\CMathML@prsubset{#2}} - \def\CMathML@notsubsetOp{\not\subseteq} - \newcommand{\CnotsubsetOp}{\CMathML@notsubsetOp} -\def\CMathML@notsubset#1#2{#1\CMathML@notsubsetOp{#2}} -\newcommand{\Cnotsubset}[3][]{\CMathML@notsubset{#2}{#3}} - \def\CMathML@notprsubsetOp{\not\subset} - \newcommand{\CnotprsubsetOp}{\CMathML@notprsubsetOp} -\def\CMathML@notprsubset#1#2{#1\CMathML@notprsubsetOp{#2}} -\newcommand{\Cnotprsubset}[3][]{\CMathML@notprsubset{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\Cset [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='set' role='CONSTRUCTOR' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CsetRes [] {}{}', - "<ltx:XMApp role='BIGOP'>" - . "<ltx:XMTok role='BIGOP' meaning='set' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg role='BVAR'>#2</ltx:XMArg>" - . "<ltx:XMArg role='CONDITION'>#3</ltx:XMArg>" - . "<ltx:XMArg role='SCOPE'>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CsetCond [] {}{}{}', - "<ltx:XMApp role='BIGOP'>" - . "<ltx:XMTok role='BIGOP' meaning='set' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg role='BVAR'>#2</ltx:XMArg>" - . "<ltx:XMArg role='CONDITION'>#3</ltx:XMArg>" - . "<ltx:XMArg role='SCOPE'>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CsetDA [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='set' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg role='BVAR'>#2</ltx:XMArg>" - . "<ltx:XMArg role='DOMAINOFAPPLICATION'>#3</ltx:XMArg>" - . "<ltx:XMArg role='SCOPE'>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\ClistOp []', - "<ltx:XMTok meaning='list' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Clist [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='list' role='CONSTRUCTOR' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CunionOp []', - "<ltx:XMTok meaning='union' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cunion [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='union' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CintersectOp []', - "<ltx:XMTok meaning='intersect' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cintersect [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='intersect' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CinOp []', - "<ltx:XMTok meaning='in' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cin [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='in' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CnotinOp []', - "<ltx:XMTok meaning='notin' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cnotin [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='notin' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CsubsetOp []', - "<ltx:XMTok meaning='subset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Csubset [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='subset' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CprsubsetOp []', - "<ltx:XMTok meaning='prsubset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cprsubset [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='prsubset' role='RELOP' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\CnotsubsetOp []', - "<ltx:XMTok meaning='notsubset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cnotsubset [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='notsubset' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CnotprsubsetOp []', - "<ltx:XMTok meaning='notprsubset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cnotprsubset [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='notprsubset' role='RELOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CsetdiffOp []', - "<ltx:XMTok meaning='setdiff' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Csetdiff [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='setdiff' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CcardOp []', - "<ltx:XMTok meaning='card' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ccard [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='card' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CcartesianproductOp []', - "<ltx:XMTok meaning='cartesianproduct' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ccartesianproduct [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='cartesianproduct' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -%</ltxml> -% \end{macrocode} -% The next set of macros are needed, since they are presentational. -% \begin{macrocode} -%<*sty> - \def\CMathML@supsetOp{\supseteq} - \newcommand{\CsupsetOp}{\CMathML@supsetOp} -\def\CMathML@supset#1{\assoc[p=700]{\CMathML@supsetOp}{#1}} -\newcommand{\Csupset}[2][]{\CMathML@supset{#2}} - \def\CMathML@prsupsetOp{\supset} - \newcommand{\CprsupsetOp}{\CMathML@prsupsetOp} -\def\CMathML@prsupset#1{\assoc[p=700]{\CMathML@prsupsetOp}{#1}} -\newcommand{\Cprsupset}[2][]{\CMathML@prsupset{#2}} - \def\CMathML@notsupsetOp{\not\supseteq} - \newcommand{\CnotsupsetOp}{\CMathML@notsupsetOp} -\def\CMathML@notsupset#1#2{#1\CMathML@notsupsetOp{#2}} -\newcommand{\Cnotsupset}[3][]{\CMathML@notsupset{#2}{#3}} - \def\CMathML@notprsupsetOp{\not\supset} - \newcommand{\CnotprsupsetOp}{\CMathML@notprsupsetOp} -\def\CMathML@notprsupset#1#2{#1\CMathML@notprsupsetOp{#2}} -\newcommand{\Cnotprsupset}[3][]{\CMathML@notprsupset{#2}{#3}} -%</sty> -% \end{macrocode} -% -% On the semantic side (in {\latexml}), we need to implement them in terms of the -% {\mathml} elements. Fortunately, we can just turn them around. \ednote{ooooops, this -% does not work for the associative ones.} -% -% \begin{macrocode} -%<*ltxml> -DefConstructor('\CsupsetOp []', - "<ltx:XMTok meaning='supset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CprsupsetOp []', - "<ltx:XMTok meaning='prsupset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CnotsupsetOp []', - "<ltx:XMTok meaning='notsupset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CnotprsupsetOp []', - "<ltx:XMTok meaning='notprsupset' role='ID' ?#1(definitionURL='#1')()/>"); -DefMacro('\Csupset[]{}','\Csubset[#1]{#2}'); -DefMacro('\Cprsupset[]{}','\Cprsubset[#1]{#2}'); -DefMacro('\Cnotsupset[]{}{}','\Cnotsubset[#1]{#3}{#2}'); -DefMacro('\Cnotprsupset[]{}{}','\Cnotprsubset[#1]{#3}{#2}'); -%</ltxml> -% \end{macrocode} -% -% \begin{macrocode} -%<*sty> - \def\CMathML@UnionDAOp{\bigwedge} - \newcommand{\CUnionDAOp}{\CMathML@UnionDAOp} -\def\CMathML@UnionDA#1#2{\CMathML@UnionDAOp_{#1}{#2}} % set, scope -\newcommand{\CUnionDA}[3][]{\CMathML@UnionDA{#2}{#3}} -\def\CMathML@UnionCond#1#2#3{\CMathML@UnionDAOp_{#2}{#3}} % bvars,condition, scope -\newcommand{\CUnionCond}[4][]{\CMathML@UnionCond{#2}{#2}{#3}} - \def\CMathML@IntersectDAOp{\bigvee} - \newcommand{\CIntersectDAOp}{\CMathML@IntersectDAOp} -\def\CMathML@IntersectDA#1#2{\CMathML@IntersectDAOp_{#1}{#2}} % set, scope -\newcommand{\CIntersectDa}[3][]{\CMathML@IntersectDA{#2}{#3}} -\def\CMathML@IntersectCond#1#2#3{\CMathML@IntersectDAOp_{#2}{#3}}% bvars,condition, scope -\newcommand{\CIntersectCond}[4][]{\CMathML@IntersectCond{#2}{#3}{#4}} - \def\CMathML@CartesianproductDAOp{\bigoplus} - \newcommand{\CCartesianproductDAOp}{\CMathML@CartesianproductDAOp} -\def\CMathML@CartesianproductDA#1#2{\CMathML@CartesianproductDAOp_{#1}{#2}} % set, scope -\newcommand{\CCartesianproductDA}[3][]{\CMathML@CartesianproductDA{#2}{#3}} -\def\CMathML@CartesianproductCond#1#2#3{\CMathML@CartesianproductDAOp_{#2}{#3}}% bvars,condition, scope -\newcommand{\CCartesianproductCond}[4][]{\CMathML@CartesianproductCond{#2}{#3}{#4}} -%</sty> -%<*ltxml> -DefConstructor('\CUnionDAOp []', - "<ltx:XMTok meaning='union' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CUnionDA [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='union' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CUnionCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='union' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CIntersectDaOp []', - "<ltx:XMTok meaning='intersect' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CIntersectDa [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='intersect' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CIntersectCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='intersect' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CCartesianproductDaOp []', - "<ltx:XMTok meaning='cartesianproduct' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CCartesianproductDa [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='cartesianproduct' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CCartesianproductCond [] {}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='BIGOP' meaning='cartesianproduct' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Sequences and Series}\label{impl:sequences} -% -% \begin{macrocode} -%<*sty> - \def\CMathML@sumOp{\sum} - \newcommand{\CsumOp}{\CMathML@sumOp} -\def\CMathML@sumLimits#1#2#3#4{\CMathML@sumOp_{#1=#2}^{#3}#4}% bvar, llimit, ulimit, body -\newcommand{\CsumLimits}[5][]{\CMathML@sumLimits{#2}{#3}{#4}{#5}} -\def\CMathML@sumCond#1#2#3{\CMathML@sumOp_{#1\in{#2}}#3} % bvar, condition, body -\newcommand{\CsumCond}[4][]{\CMathML@sumCond{#2}{#3}{#4}} -\def\CMathML@sumDA#1#2{\CMathML@sumOp_{#1}#2} % set, body -\newcommand{\CsumDA}[3][]{\CMathML@sumDA{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\CsumOp []', - "<ltx:XMTok meaning='sum' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CsumLimits [] {}{}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='sum' role='SUMOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "#5</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% \ednote{complete the other cases}\ednote{add a keyword argument to all newcommands} -% \begin{macrocode} -%<*sty> - \def\CMathML@prodOp{\prod} - \newcommand{\CprodOp}{\CMathML@prodOp} -\def\CMathML@prodLimits#1#2#3#4{\CMathML@prodOp_{#1=#32^{#3}#4}}% bvar, llimit, ulimit, body -\newcommand{\CprodLimits}[5][]{\CMathML@prodLimits{#2}{#3}{#4}{#5}} -\def\CMathML@prodCond#1#2#3{\CMathML@prodOp_{#1\in{#2}}#3} % bvar, condition, body -\newcommand{\CprodCond}[4][]{\CMathML@prodCond{#2}{#3}{#4}} -\def\CMathML@prodDA#1#2{\CMathML@prodOp_{#1}#2} % set, body -\newcommand{\CprodDA}[3]{\CMathML@prodDA{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\CprodOp []', - "<ltx:XMTok meaning='prod' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\CprodLimits [] {}{}{}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='prod' role='SUMOP' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg><ci>#2</ci></ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "<ltx:XMArg>#4</ltx:XMArg>" - . "#5</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% \ednote{complete the other cases} -% \subsection{Elementary Classical Functions}\label{impl:specfun} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@sin#1{\sin(#1)} -\newcommand{\Csin}[2][]{\CMathML@sin{#2}} -\def\CMathML@cos#1{\cos(#1)} -\newcommand{\Ccos}[2][]{\CMathML@cos{#2}} -\def\CMathML@tan#1{\tan(#1)} -\newcommand{\Ctan}[2][]{\CMathML@tan{#2}} -\def\CMathML@sec#1{\sec(#1)} -\newcommand{\Csec}[2][]{\CMathML@sec{#2}} -\def\CMathML@csc#1{\csc(#1)} -\newcommand{\Ccsc}[2][]{\CMathML@csc{#2}} -\def\CMathML@cot#1{\cot(#1)} -\newcommand{\Ccot}[2][]{\CMathML@cot{#2}} -\def\CMathML@sinh#1{\sinh(#1)} -\newcommand{\Csinh}[2][]{\CMathML@sinh{#2}} -\def\CMathML@cosh#1{\cosh(#1)} -\newcommand{\Ccosh}[2][]{\CMathML@cosh{#2}} -\def\CMathML@tanh#1{\tanh(#1)} -\newcommand{\Ctanh}[2][]{\CMathML@tanh{#2}} -\def\CMathML@sech#1{\mbox{sech}(#1)} -\newcommand{\Csech}[2][]{\CMathML@sech{#2}} -\def\CMathML@csch#1{\mbox{csch}(#1)} -\newcommand{\Ccsch}[2][]{\CMathML@csch{#2}} -\def\CMathML@coth#1{\mbox{coth}(#1)} -\newcommand{\Ccoth}[2][]{\CMathML@coth{#2}} -\def\CMathML@arcsin#1{\arcsin(#1)} -\newcommand{\Carcsin}[2][]{\CMathML@arcsin{#2}} -\def\CMathML@arccos#1{\arccos(#1)} -\newcommand{\Carccos}[2][]{\CMathML@arccos{#2}} -\def\CMathML@arctan#1{\arctan(#1)} -\newcommand{\Carctan}[2][]{\CMathML@arctan{#2}} -\def\CMathML@arccosh#1{\mbox{arccosh}(#1)} -\newcommand{\Carccosh}[2][]{\CMathML@arccosh{#2}} -\def\CMathML@arccot#1{\mbox{arccot}(#1)} -\newcommand{\Carccot}[2][]{\CMathML@arccot{#2}} -\def\CMathML@arccoth#1{\mbox{arccoth}(#1)} -\newcommand{\Carccoth}[2][]{\CMathML@arccoth{#2}} -\def\CMathML@arccsc#1{\mbox{arccsc}(#1)} -\newcommand{\Carccsc}[2][]{\CMathML@arccsc{#2}} -\def\CMathML@arcsinh#1{\mbox{arcsinh}(#1)} -\newcommand{\Carcsinh}[2][]{\CMathML@arcsinh{#2}} -\def\CMathML@arctanh#1{\mbox{arctanh}(#1)} -\newcommand{\Carctanh}[2][]{\CMathML@arctanh{#2}} - -\def\CMathML@exp#1{\exp(#1)} -\newcommand{\Cexp}[2][]{\CMathML@exp{#2}} -\def\CMathML@ln#1{\ln(#1)} -\newcommand{\Cln}[2][]{\CMathML@ln{#2}} -\def\CMathML@log#1#2{\log_{#1}(#2)} -\newcommand{\Clog}[3][]{\CMathML@log{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\Csin [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='sin' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccos [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='cos' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ctan [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='tan' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Csec [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='sec' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccsc [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='csc' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccot [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='cot' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Csinh [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='sinh' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccosh [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='cosh' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ctanh [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='tanh' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Csech [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='sech' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccsch [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='csch' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ccoth [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='coth' role='TRIGFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carcsin [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arcsin' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carccos [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arccos' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carctan [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arctan' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carcsec [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arcsec' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carccsc [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arccsc' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carccot [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arccot' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carcsinh [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arcsinh' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carccosh [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arccosh' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carctanh [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arctanh' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carcsech [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arcsech' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carccsch [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arccsch' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Carccoth [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='arccoth' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cexp [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='exp' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cln [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='ln' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Clog [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='log' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Statistics}\label{impl:statistics} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@mean#1{\mbox{mean}(#1)} -\newcommand{\Cmean}[2][]{\CMathML@mean{#2}} -\def\CMathML@sdev#1{\mbox{std}(#1)} -\newcommand{\Csdev}[2][]{\CMathML@sdev{#2}} -\def\CMathML@var#1{\mbox{var}(#1)} -\newcommand{\Cvar}[2][]{\CMathML@var{#2}} -\def\CMathML@median#1{\mbox{median}(#1)} -\newcommand{\Cmedian}[2][]{\CMathML@median{#2}} -\def\CMathML@mode#1{\mbox{mode}(#1)} -\newcommand{\Cmode}[2][]{\CMathML@mode{#2}} -\def\CMathML@moment#1#2{\langle{#2}^{#1}\rangle}% degree, momentabout, scope -\newcommand{\Cmoment}[3][]{\CMathML@moment{#2}{#3}} -\def\CMathML@momentA#1#2{\langle{#2}^{#1}\rangle}% degree, momentabout, scope -\newcommand{\CmomentA}[4][]{\CMathML@momentA{#2}{#3}{#4}} -%</sty> -%<*ltxml> -DefConstructor('\Cmean [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='mean' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Csdev [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='sdev' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cvar [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='var' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cmedian [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='median' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cmode [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='mode' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cmoment [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='moment' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% \ednote{we do not seem to need the momentabout.}\ednote{moment and momentA have funny -% elided arguments} -% -% \subsection{Linear Algebra}\label{impl:linalg} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@vector#1{(#1)} -\newcommand{\Cvector}[2][]{\CMathML@vector{#2}} -\def\CMathML@matrix#1#2{\left(\begin{array}{#1}#2\end{array}\right)}% row pattern, body -\newcommand{\Cmatrix}[3][]{\CMathML@matrix{#2}{#3}} -\def\CMathML@determinant#1{\left|#1\right|} -\newcommand{\Cdeterminant}[2][]{\CMathML@determinant{#2}} -\def\CMathML@transpose#1{#1^\top} -\newcommand{\Ctranspose}[2][]{\CMathML@transpose{#2}} -\def\CMathML@selector#1#2{#1_{#2}} -\newcommand{\Cselector}[3][]{\CMathML@selector{#2}{#3}} - \def\CMathML@vectproductOp{\cdot} - \newcommand{\CvectproductOp}{\CMathML@vectproductOp} -\def\CMathML@vectproduct#1#2{#1\CMathML@vectproductOp{#2}} -\newcommand{\Cvectproduct}[3][]{\CMathML@vectproduct{#2}{#3}} -\def\CMathML@scalarproduct#1#2{{#1}#2} -\newcommand{\Cscalarproduct}[3][]{\CMathML@scalarproduct{#2}{#3}} - \def\CMathML@outerproductOp{\times} - \newcommand{\CouterproductOp}{\CMathML@outerproductOp} -\def\CMathML@outerproduct#1#2{#1\CMathML@outerproductOp{#2}} -\newcommand{\Couterproduct}[3][]{\CMathML@outerproduct{#2}{#3}} -%</sty> -%<*ltxml> -DefConstructor('\Cvector [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONSTRUCTOR' meaning='vector' ?#1(definitionURL='#1')()/>" - . "#2" - . "</ltx:XMApp>", - afterDigest=>sub { remove_math_commas($_[1], 2); }); -DefConstructor('\Cmatrix [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok role='CONSTRUCTOR' meaning='matrix' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cdeterminant [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='determinant' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Ctranspose [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='transpose' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cselector [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='selector' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CvectorproductOp []', - "<ltx:XMTok meaning='vectorproduct' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cvectorproduct [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='vectorproduct' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\Cscalarproduct [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='scalarproduct' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -DefConstructor('\CouterproductOp []', - "<ltx:XMTok meaning='outerproduct' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Couterproduct [] {}{}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='outerproduct' role='OPFUNCTION' ?#1(definitionURL='#1')()/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "<ltx:XMArg>#3</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Constant and Symbol Elements}\label{impl:constants} -% -% \begin{macrocode} -%<*sty> -\def\CMathML@integers{{\mathbb{Z}}} -\newcommand{\Cintegers}[1][]{\CMathML@integers} -\def\CMathML@reals{{\mathbb{R}}} -\newcommand{\Creals}[1][]{\CMathML@reals} -\def\CMathML@rationals{{\mathbb{Q}}} -\newcommand{\Crationals}[1][]{\CMathML@rationals} -\def\CMathML@naturalnumbers{{\mathbb{N}}} -\newcommand{\Cnaturalnumbers}[1][]{\CMathML@naturalnumbers} -\def\CMathML@complexes{{\mathbb{C}}} -\newcommand{\Ccomplexes}[1][]{\CMathML@complexes} -\def\CMathML@primes{{\mathbb{P}}} -\newcommand{\Cprimes}[1][]{\CMathML@primes} -\def\CMathML@exponemtiale{e} -\newcommand{\Cexponemtiale}[1][]{\CMathML@exponemtiale} -\def\CMathML@imaginaryi{i} -\newcommand{\Cimaginaryi}[1][]{\CMathML@imaginaryi} -\def\CMathML@notanumber{{\mathrm{NaN}}} -\newcommand{\Cnotanumber}[1][]{\CMathML@notanumber} -\def\CMathML@true{{\mathrm{true}}} -\newcommand{\Ctrue}[1][]{\CMathML@true} -\def\CMathML@false{{\mathrm{false}}} -\newcommand{\Cfalse}[1][]{\CMathML@false} -\def\CMathML@emptyset{\emptyset} -\newcommand{\Cemptyset}[1][]{\CMathML@emptyset} -\def\CMathML@pi{\pi} -\newcommand{\Cpi}[1][]{\CMathML@pi} -\def\CMathML@eulergamma{\gamma} -\newcommand{\Ceulergamma}[1][]{\CMathML@eulergamma} -\def\CMathML@infinit{\infty} -\newcommand{\Cinfinit}[1][]{\CMathML@infinit} -%</sty> -%<*ltxml> -DefConstructor('\Cintegers []', - "<ltx:XMTok meaning='integers' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Creals []', - "<ltx:XMTok meaning='reals' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Crationals []', - "<ltx:XMTok meaning='rationals' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cnaturalnumbers []', - "<ltx:XMTok meaning='naturalnumbers' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ccomplexes []', - "<ltx:XMTok meaning='complexes' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cprimes []', - "<ltx:XMTok meaning='primes' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cexponentiale []', - "<ltx:XMTok meaning='exponentiale' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cimaginaryi []', - "<ltx:XMTok meaning='imaginaryi' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cnotanumber []', - "<ltx:XMTok meaning='notanumber' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ctrue []', - "<ltx:XMTok meaning='true' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cfalse []', - "<ltx:XMTok meaning='false' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cemptyset []', - "<ltx:XMTok meaning='emptyset' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cpi []', - "<ltx:XMTok meaning='pi' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Ceulergamma []', - "<ltx:XMTok meaning='eulergamma' role='ID' ?#1(definitionURL='#1')()/>"); -DefConstructor('\Cinfinit []', - "<ltx:XMTok meaning='infinit' role='ID' ?#1(definitionURL='#1')()/>"); -%</ltxml> -% \end{macrocode} -% -% \subsection{Extensions}\label{sec:impl:cmathmlx} -% \begin{macro}{\Ccomplement} -% \begin{macrocode} -%<*styx> -\def\CMathML@complement#1{#1^c} -\newcommand{\Ccomplement}[2][]{\CMathML@complement{#2}} -%</styx> -%<*ltxmlx> -DefConstructor('\Ccomplement [] {}', - "<ltx:XMApp>" - . "<ltx:XMTok meaning='complement' role='CSYMBOL'/>" - . "<ltx:XMArg>#2</ltx:XMArg>" - . "</ltx:XMApp>"); -%</ltxmlx> -% \end{macrocode} -% \end{macro} -% -% \subsection{Finale}\label{sec:impl:finale} -% -% Finally, we need to terminate the file with a success mark for perl. -% \begin{macrocode} -%<ltxml>1; -% \end{macrocode} -% \Finale -\endinput - -% \iffalse -%%% Local Variables: -%%% mode: doctex -%%% TeX-master: t -%%% End: -% \fi - -% LocalWords: STeX cmathml symdefs CMathML dom codom Im ll reln fn bvar arith -% LocalWords: alg lcm rels Ceq llimit ulimit bvars lowlimit specfun sech csch -% LocalWords: coth arccosh arccot arccoth arccsc arcsinh arctanh logbase std -% LocalWords: var momentabout linalg matrixrow bruce NaN stex cnxml symdef -% LocalWords: DefinitionURLs domainofapplication CmomentA concl |