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Diffstat (limited to 'tex/context/base/mkii/xtag-mmc.mkii')
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diff --git a/tex/context/base/mkii/xtag-mmc.mkii b/tex/context/base/mkii/xtag-mmc.mkii new file mode 100644 index 000000000..9da7fef84 --- /dev/null +++ b/tex/context/base/mkii/xtag-mmc.mkii @@ -0,0 +1,1265 @@ +%D \module +%D [ file=xtag-mmc, +%D version=2000.12.20, +%D title=\CONTEXT\ XML Macros, +%D subtitle=Content MathML, +%D author=Hans Hagen, +%D date=\currentdate, +%D copyright={PRAGMA ADE \& \CONTEXT\ Development Team}] +%C +%C This module is part of the \CONTEXT\ macro||package and is +%C therefore copyrighted by \PRAGMA. See mreadme.pdf for +%C details. + +\writestatus{loading}{ConTeXt XML Macros / Content MathML} + +% this is the first, experimental, shabby implementation, as +% always, the third will do -) + +% okay, now this is the second one, with a more kid based +% approach, which we needed for proper nesting, but the +% code is still too ugly + +\startXMLmapping[mml] + +\unprotect + +\def\MMLccomma{{,}} + +\def\getmmlarguments#1#2#3#4#5#6% {class} {defaults} mmlargs + {\getXMLarguments{#1}{#2 #5}}% + +\def\doifMMLoperatorelse#1#2#3% temp hack + {\pushmacro\xmlrent + \let\xmlrent\firstofoneargument + \edef\mmloperator{#1}% + \@EA\unspaceargument\mmloperator\to\mmloperator + \popmacro\xmlrent + \doifXMLentityelse\mmloperator + {\doifdefinedelse{doMMLcFN\mmloperator}{#2}{#3}} + {#3}} + +\remapXMLsequence [ci] [CPA] \MMLcCI +\remapXMLsequence [cn] [CPA] \MMLcCN +\remapXMLsequence [csymbol] [CPA] \MMLcCSYMBOL + +\setupMMLappearance[polar][\c!alternative=\v!a] % a|b|c + +\def\MMLcpolar#1% + {\doifdefinedelse{MMLcdopolar\@@MMLpolaralternative} + {\getvalue{MMLcdopolar\@@MMLpolaralternative}{#1}} + {#1}} + +\def\MMLcdopolara#1% + {\def\MMLcsep{\MMLccomma}\getXMLentity{polar}\left(#1\right)} + +\def\MMLcdopolarb#1% + {\def\MMLcsep##1\empty% + {\getXMLentity{exponentiale}^{##1\mskip2mu\getXMLentity{imaginaryi}}}#1} + +\def\MMLcdopolarc#1% + {\def\MMLcsep##1\empty% + {\getXMLentity{exp}\left(##1\mskip2mu\getXMLentity{imaginaryi}\right)}#1} + +\def\MMLccartesian#1% + {\def\MMLcsep{+}#1\getXMLentity{imaginaryi}} + +% float will be obsolete, an is replace by e-notation + +\setupMMLappearance[float][\c!symbol=\v!no] % \v!yes|dot + +\def\MMLcfloat#1% + {\doifelse\@@MMLfloatsymbol\v!no + {{\rm#1}} % make sure that e shows up ok + {% we should ignore \entities ! + \beforesplitstring#1\at e\to\first + \aftersplitstring #1\at e\to\last + \ifx\first\empty #1\else + \ifx\last \empty #1\else + \first + \doifelse\@@MMLfloatsymbol{dot}\cdot\times + 10^{\last}% + \fi\fi}} + +% we now have: + +\setupMMLappearance[enotation][\c!symbol=\v!no] % \v!yes|dot + +\def\MMLcenotation#1% + {\doifelse\@@MMLenotationsymbol\v!no + {\def\MMLcsep {\unskip{\rm e}\ignorespaces}} + {\def\MMLcsep##1\empty{\doifelse\@@MMLenotationsymbol{dot}\cdot\times10^{##1}}}% + #1\empty} + +\def\MMLcCI#1% #2% can be sped up with \doifundefined ... + {\getXMLarguments{ci}{type="" #1}% + \doifXMLparelse{ci}{type} + {\processaction + [\XMLpar{ci}{type}{}] + [ set=>\let\next\MMLcCIset, + vector=>\let\next\MMLcCIvector, + matrix=>\let\next\MMLcCImatrix, + function=>\let\next\MMLcCIfunction, +complex-cartesian=>\let\next\MMLccartesian, + complex=>\let\next\MMLccartesian, + complex-polar=>\let\next\MMLcpolar, + polar=>\let\next\MMLcpolar, + fn=>\let\next\MMLcCIfunction, + unknown=>\let\next\firstofoneargument]} % integer constant real float + {\let\next\firstofoneargument}% + \next} + +\def\MMLcCIset#1% + {{\bbd#1}} + +\def\widevec#1% + {\vbox{\mathsurround\zeropoint\ialign{##\crcr + \rightarrowfill\crcr\noalign{\nointerlineskip}% + $\hfil\displaystyle{#1}\hfil$\crcr}}} + +\def\MMLcCIvector#1% + {\widevec{#1}} + +\def\MMLcCImatrix#1% + {{\bi#1}} + +\def\MMLcCIfunction#1% + {\doifMMLoperatorelse{#1}\MMLcCIdefault\MMLcFNdefault{}{#1}} + +\def\MMLcCIdefault#1#2% #1=dummy + {#2%\!% \getXMLentity{NegThinSpace}% looks bad in A(x) + \doifnextcharelse\xmlr + {\encapsulatenextXMLRelements{\left(}{\MMLccomma}{\right)}} + {}} + +% \def\MMLcFNdefault#1#2% neg space needed because of \left +% {#2\!% \getXMLentity{NegThinSpace}% +% \MMLcreset\encapsulatenextXMLRelements{\left(}{\MMLccomma}{\right)}} + +\def\MMLcCN#1% #2% can be sped up with \doifundefined ... + {\getXMLarguments{cn}{type="" #1}% + \doifXMLparelse{cn}{type} + {\processaction + [\XMLpar{cn}{type}{}] + [ integer=>\let\next\MMLcCNinteger, + logical=>\let\next\MMLcCNlogical, + rational=>\let\next\MMLcCNrational, +complex-cartesian=>\let\next\MMLccartesian, + complex=>\let\next\MMLccartesian, + complex-polar=>\let\next\MMLcpolar, + polar=>\let\next\MMLcpolar, + e-notation=>\let\next\MMLcenotation, % new + float=>\let\next\MMLcfloat, % obsolete + real=>\let\next\MMLcfloat, % ? + unknown=>\let\next\firstofoneargument]} + {\let\next\firstofoneargument} + \next} + +\setupMMLappearance[base][\c!symbol=\v!numbers] % cijfers|letters|tekst|nee + +\def\MMLcCNinteger#1% + {\doifXMLparelse{cn}{base} + {\def\MMLcCNbase{\XMLpar{cn}{base}{}}% + \doifelse\@@MMLbasesymbol\v!no + {\MMLcCNbasedata{#1}} + {\MMLcCNbasedata{#1}_{\hbox{$\rm\scriptscriptstyle + \processaction + [\@@MMLbasesymbol] + [\v!characters=>\MMLcCNbasestring BODH, + \v!text=>\MMLcCNbasestring{BIN}{OCT}{DEC}{HEX}, + \s!unknown=>\MMLcCNbase]$}}}} + {#1}} + +\def\MMLcCNbasedata#1% + {\ifnum\MMLcCNbase>10{\rm#1}\else#1\fi} + +\def\MMLcCNbasestring#1#2#3#4% + {\ifnum\MMLcCNbase= 2 #1\else + \ifnum\MMLcCNbase= 8 #2\else + \ifnum\MMLcCNbase=10 #3\else + \ifnum\MMLcCNbase=16 #4\else + \MMLcCNbase \fi\fi\fi\fi} + +\def\MMLcCNlogical#1% + {{\rm#1}} + +\def\MMLcCNrational#1% + {\ConvertConstantAfter\doifinstringelse{sep}{#1} + {\doMMLcCNrational#1\empty} + {#1}} + +\def\doMMLcCNrational#1\xmlr#2#3#4#5\empty + {\hbox{$\frac{#1}{#5}$}} + +\def\MMLcCSYMBOL#1#2% TO DO + {\getXMLarguments{csymbol}{encoding="text" #1}% + \doifelse{\XMLpar{csymbol}{encoding}{}}{text} + {{\rm#2}}{#2}} + +%%% basic content elements + +\remapXMLsequence [apply] [CPA] \MMLcAPPLY + +\newcount\@MMLlevel \def\MMLcreset{\@MMLlevel=0 } + +\let\MMLctempresetlist\empty \def\setMMLcreset{\edef\MMLctempresetlist} + +\def\MMLcmainresetlist% + {times/,divide/,power/,% + lt/,gt/,eq/,leq/,geq/,% + in/,inverse/,% + fn,% + floor/,ceiling/,% + mean/,% + selector/,% + abs/,int/,limit/,sum/,product/,% + outerproduct/,innerproduct/,scalarproduct/} + +\def\MMLcfunctionlist + {sin/,arcsin/,sinh/,arcsinh/,% + cos/,arccos/,cosh/,arccosh/,% + tan/,arctan/,tanh/,arctanh/,% + cot/,arccot/,coth/,arccoth/,% + csc/,arccsc/,csch/,arccsch/,% + sec/,arcsec/,sech/,arcsech/,% + ln/,exp/,log/,% + abs/,int/,limit/,sum/,product/,% + fn} % ? + +\def\MMLcconstructlist + {diff/,partialdiff/,root/} % apply goes wrong on 1/2 * (a_2 + b_3) + +% better: no () here but explicitly when needed, which is in +% less cases + +\def\MMLcAPPLY#1#2% + {\mathinner{\begingroup % new, else 1/2(1+2) problem / inner: ask taco + \pushmacro\xmlr + \@EA\@EA\@EA\doifXMLRchild\@EA\@EA\@EA{\@EA\MMLcmainresetlist\@EA,\MMLctempresetlist}{#2} + {\MMLcreset}% + \ifcase\@MMLlevel + \getXMLarguments{apply}{open="" close="" #1}% + \else + \getXMLarguments{apply}{open="(" close=")" #1}% + \fi + \doifXMLparelse{apply}{open}{\left\XMLpar{apply}{open}{}}{}% + \advance\@MMLlevel+1 + \begingroup + \let\MMLctempresetlist\empty + \let\xmlr\naturalxmlr % beter een \pushmacro\xmlr + #2\empty + \endgroup % ook level push + \advance\@MMLlevel-1 + \doifXMLparelse{apply}{close}{\right\XMLpar{apply}{close}{}}{}% + \popmacro\xmlr + \endgroup}} + +\remapXMLsequence [reln] [CPA] \MMLcRELN + +\def\MMLcRELN% + {\writestatus{XML}{MathML element "reln" is obsolete}\MMLcAPPLY} + +\remapXMLsequence [fn] [CPA] \MMLcFN + +\def\MMLcFN#1#2% neg space needed because of \left + {\doifXMLRchildelse{ci}{#2} + {\collectXMLRchild{ci}{#2}% + \@EA\doifMMLoperatorelse\@EA{\the\XMLRtoks} + \MMLcFNoperator\MMLcFNdefault} + {\MMLcFNdefault}% + {#1}{#2}} + +\def\MMLcFNdefault#1#2% neg space needed because of \left + {#2\!% \getXMLentity{NegThinSpace}% + \MMLcreset\encapsulatenextXMLRelements{\left(}{\MMLccomma}{\right)}} + +% special function handlers + +\def\MMLcFNoperator + {\getvalue{doMMLcFN\mmloperator}} + +% \def\doMMLcFNplusminus#1#2#3\empty +% {\countXMLRchildren{#3}% +% \ifcase\nofXMLRchildren\or +% #2#3% +% \else % suboptimal for instance under root +% \encapsulateXMLR{\left(}{#2}{\right)}{\MMLcreset#3}% +% \fi} + +\def\doMMLcFNplusminus#1#2#3\empty + {\countXMLRchildren{#3}% + \ifcase\nofXMLRchildren\or + \def\next{#2#3}% + \else + \def\next + {\doifnextcharelse\xmlr + {\encapsulateXMLR{\left(}{#2}{\right)}{\MMLcreset#3}}% + {\encapsulateXMLR{}{#2}{}{\MMLcreset#3}}}% + \fi + \next} + +\let\doMMLcFNminusplus\doMMLcFNplusminus + +\def\doMMLcFNcontinued#1#2#3\empty + {#3\getXMLentity{continued}} + +% so far for the special handlers + +\remapXMLsequence [interval] [CPA] \MMLcINTERVAL + +\def\MMLcINTERVAL#1#2% + {\withnexttwoXMLRelements + {\getXMLarguments{interval}{closure="closed" #1}% + \processaction + [\XMLpar{interval}{closure}{closed}] + [ closed=>{[\firstXMLRelement,\secondXMLRelement]}, + open-closed=>{(\firstXMLRelement,\secondXMLRelement]}, + closed-open=>{[\firstXMLRelement,\secondXMLRelement)}, + open=>{(\firstXMLRelement,\secondXMLRelement)}, + \s!unknown=>{[\firstXMLRelement,\secondXMLRelement]}]}% + #2\empty} + +\remapXMLsingular [inverse] [CPA] \MMLcINVERSE + +\def\MMLcINVERSE#1#2% + {\withnextXMLRelement + {\nextXMLRelement\empty^{-1}% \empty kills MMLcfunction lookahead + \withnextXMLRelement + {\ifx\nextXMLRelement\empty \else + \left[\nextXMLRelement\right]% + \fi}}} + +\remapXMLsingular [sep] [CPA] \MMLcSEP + +\def\MMLcSEP#1#2{\MMLcsep} \def\MMLcsep{\,} + +\remapXMLsequence [condition] [CPA] \MMLcCONDITION + +\def\MMLcCONDITION#1#2% + {\pushmacro\MMLcBVAR + \doifXMLRchild{bvar}{#2}{\processXMLRchild{bvar}{#2}\mid}% + \let\MMLcBVAR\ignoreXMLRelement + \processXMLRchildren{#2}% + \popmacro\MMLcBVAR} + +\remapXMLsequence [declare] [CPA] \MMLcDECLARE + +\setupMMLappearance[declare][\c!state=\v!start] + +\def\MMLcDECLARE#1#2% + {\doif\@@MMLdeclarestate\v!start + {\withnextXMLRelement + {\getXMLentity{declare}\nextXMLRelement + \countXMLRchildren{#2}% + \ifnum\nofXMLRchildren>1 + \;% \getXMLentity{ThickSpace}% + \getXMLentity{as}% + \;% \getXMLentity{ThickSpace}% + \fi}% + #2\empty}} + +\remapXMLsequence [lambda] [CPA] \MMLcLAMBDA + +\setupMMLappearance[lambda][\c!alternative=b] + +\def\MMLcLAMBDA#1#2% + {\doifelse\@@MMLlambdaalternative\v!a + {\encapsulateXMLR{\getXMLentity{lambda}(}{\MMLccomma}{)}{#2}} + {\countXMLRchild{bvar}{#2}% + \ifnum\nofXMLRchildren>1 + \collectXMLRchild{bvar}{#2}% + \encapsulateXMLR{\left(}{\MMLccomma}{\right)}{\the\XMLRtoks}% + \else + \processXMLRchild{bvar}{#2}% + \fi + \getXMLentity{mapsto}% + \processXMLRchild{apply,reln,ci,cn}{#2}}} + +\remapXMLsingular [compose] [CPA] \MMLcCOMPOSE + +\def\MMLcCOMPOSE#1#2#3\empty + {\doifMMLfunctionelse{#3} + {\encapsulateXMLR{\left(}{\circ}{\right)}{#3}} + {\encapsulateXMLR{}{\circ}{}{#3}}} + +\remapXMLsingular [ident] [CPA] \MMLcIDENT + +\def\MMLcIDENT#1#2{\getXMLentity{identity}} + +\remapXMLsingular [domain] [CPA] \MMLcDOMAIN +\remapXMLsingular [codomain] [CPA] \MMLcCODOMAIN + +\def\MMLcDOMAIN #1#2#3\empty + {\getXMLentity{domain}(\MMLcreset\processXMLRchildren{#3})} + +\def\MMLcCODOMAIN#1#2#3\empty + {\getXMLentity{codomain}(\MMLcreset\processXMLRchildren{#3})} + +\remapXMLsingular [image] [CPA] \MMLcIMAGE + +\def\MMLcIMAGE#1#2% + {\withnextXMLRelement{\getXMLentity{image}(\nextXMLRelement)}} + +\remapXMLsequence [domainofapplication] [CPA] \MMLcDOMAINOFAPPLICATION + +\def\MMLcDOMAINOFAPPLICATION#1#2{#2} + +\remapXMLsequence [piecewise] [CPA] \MMLcPIECEWISE +\remapXMLsequence [piece] [CPA] \MMLcPIECE +\remapXMLsequence [otherwise] [CPA] \MMLcOTHERWISE + +\setupMMLappearance[piece][\c!separator=] + +\def\MMLcPIECEWISE#1#2% + {\cases{#2}} + +\def\MMLcPIECEseparator{\doif\@@MMLpieceseparator\v!yes,} + +\def\MMLcPIECE#1#2% + {\withnexttwoXMLRelements + {\@EA\XMLRtoks\@EA{\firstXMLRelement\MMLcPIECEseparator\@col@amp@}% + \@EA\appendtoks\@EA\mathematics\@EA{\secondXMLRelement}\to\XMLRtoks + \the\XMLRtoks\crcr}% + #2} + +\def\MMLcOTHERWISE#1#2% + {#2\MMLcPIECEseparator\@col@amp@\mathematics{\getXMLentity{otherwise}}\crcr} + +%%% arithmic, algebra and logic + +\remapXMLsingular [quotient] [CPA] \MMLcQUOTIENT + +\def\MMLcQUOTIENT#1#2% + {\withnexttwoXMLRelements{\lfloor\firstXMLRelement/\secondXMLRelement\rfloor}} + +\remapXMLsingular [factorial] [CPA] \MMLcFACTORIAL + +\def\MMLcFACTORIAL#1#2% + {\withnextXMLRelement{\nextXMLRelement !}} + +\remapXMLsingular [divide] [CPA] \MMLcDIVIDE + +\setupMMLappearance [divide] [\c!level=\!!maxcard] + +\def\MMLcDIVIDE#1#2% + {\withnexttwoXMLRelements + {\increment\MMLcDIVIDElevel + \ifnum\MMLcDIVIDElevel>\@@MMLdividelevel\space + \firstXMLRelement/\secondXMLRelement + \else + \frac{\MMLcreset\firstXMLRelement}{\MMLcreset\secondXMLRelement}% + \fi + \decrement\MMLcDIVIDElevel}} + +\remapXMLsingular [min] [CPA] \MMLcMIN +\remapXMLsingular [max] [CPA] \MMLcMAX + +\def\MMLcMIN#1#2#3\empty + {\encapsulateXMLR + {\min\doifXMLRchild{bvar}{#3}{_{\processXMLRchild{bvar}{#3}}}\left\{} + {\MMLccomma}{\right\}}{#3}} + +\def\MMLcMAX#1#2#3\empty + {\encapsulateXMLR + {\max\doifXMLRchild{bvar}{#3}{_{\processXMLRchild{bvar}{#3}}}\left\{} + {\MMLccomma}{\right\}}{#3}} + +\remapXMLsingular [minus] [CPA] \MMLcMINUS +\remapXMLsingular [plus] [CPA] \MMLcPLUS + +\setupMMLappearance[sign][\c!reduction=\v!yes] + +\def\MMLcMINUS % expandafter needed ? + {\doifelse\@@MMLsignreduction\v!yes + {\expandafter\MMLcMINUSyes}{\expandafter\MMLcMINUSno}} + +\def\MMLcPLUS % expandafter needed ? + {\doifelse\@@MMLsignreduction\v!yes + {\expandafter\MMLcPLUSyes}{\expandafter\MMLcPLUSno}} + +\def\MMLcMINUSno#1#2#3\empty + {\countXMLRchildren{#3}% + \encapsulateXMLR{\ifcase\nofXMLRchildren\or-\fi}{-}{}{#3}} + +\def\MMLcPLUSno#1#2#3\empty + {\countXMLRchildren{#3}% + \encapsulateXMLR{\ifcase\nofXMLRchildren\or+\fi}{+}{}{#3}} + +\def\MMLcMINUSyes#1#2#3\empty + {\setMMLcreset{\MMLcfunctionlist}% + \countXMLRchildren{#3}% + \encapsulateXMLR{\ifcase\nofXMLRchildren\or-\fi}{-}{}{#3}} + +\def\MMLcPLUSyes#1#2#3\empty + {\setMMLcreset{plus/,minus/,\MMLcfunctionlist,\MMLcconstructlist}% + \encapsulatenextXMLRelements + {} + {\doifXMLRchildelse{apply}{\nextXMLRelement}% + {\collectXMLRchild{apply}{\nextXMLRelement}% + \doifXMLRchildelse{minus/}{\the\XMLRtoks} + {\countXMLRchildren{\the\XMLRtoks} + \ifnum\nofXMLRchildren>2 +\else\fi}{+}} + {+}} + {} + {#3\empty}} + +\remapXMLsingular [power] [CPA] \MMLcPOWER + +\setupMMLappearance[power][\c!reduction=\v!yes] + +\let\MMLpowerelement\empty + +\def\MMLcPOWER#1#2% + {\withnexttwoXMLRelements + {\doifXMLRchildelse{apply}{\firstXMLRelement} + {\doifelse\@@MMLpowerreduction\v!yes + {\collectXMLRchild{apply}{\firstXMLRelement}% + \@EA\doifXMLRchildelse\@EA{\MMLcfunctionlist}{\the\XMLRtoks} + {\let\MMLpowerelement\secondXMLRelement + \MMLcreset\firstXMLRelement\empty} + {\left(\MMLcreset\firstXMLRelement\empty\right)^{\MMLcreset\secondXMLRelement}}} + {\left(\MMLcreset\firstXMLRelement\empty\right)^{\MMLcreset\secondXMLRelement}}} + {\firstXMLRelement^{\MMLcreset\secondXMLRelement}}}} + +\remapXMLsingular [rem] [CPA] \MMLcREM + +\def\MMLcREM#1#2% + {\withnexttwoXMLRelements + {\firstXMLRelement\getXMLentity{mod}\secondXMLRelement}} + +\remapXMLsingular [times] [CPA] \MMLcTIMES + +\setupMMLappearance[times][\c!symbol=\v!no] % +\setupMMLappearance[times][\c!auto=\v!yes] % new, auto catches cn cn cn + +\def\MMLcTIMES#1#2#3\empty + {\setMMLcreset{\MMLcfunctionlist,\MMLcconstructlist}% + \doifelse\@@MMLtimesauto\v!no + {\let\@@MMLtimes@@symbol\@@MMLtimessymbol} + {\doifelseXMLRneighbors{cn}{#3} + {\let\@@MMLtimes@@symbol\v!yes} + {\let\@@MMLtimes@@symbol\@@MMLtimessymbol}}% + \doifelse\@@MMLtimes@@symbol\v!yes + {\encapsulateXMLR{}{\times}{}{#3\empty}} + {\doifelse\@@MMLtimes@@symbol{dot} + {\encapsulateXMLR{}{\cdot}{}{#3\empty}} + {#3\empty}}} + +\remapXMLsingular [root] [CPA] \MMLcROOT + +\setupMMLappearance[root][\c!symbol=\v!yes] + +\def\MMLcROOT#1#2#3\empty + {\doifXMLRchildelse{degree}{#3}\donetrue\donefalse + \doif\@@MMLrootsymbol\v!no\donefalse + \ifdone + \root\processXMLRchild{degree}{#3}\of + {\let\MMLcDEGREE\ignoreXMLRelement + \MMLcreset\processXMLRchildren{#3}}% + \else + \sqrt + {\MMLcreset\processXMLRchildren{#3}}% + \fi} + +\remapXMLsingular [gcd] [CPA] \MMLcGCD + +\def\MMLcGCD#1#2#3\empty{\encapsulateXMLR{\gcd(}{\MMLccomma}{)}{#3}} + +\remapXMLsingular [and] [CPA] \MMLcAND +\remapXMLsingular [or] [CPA] \MMLcOR +\remapXMLsingular [xor] [CPA] \MMLcXOR +\remapXMLsingular [implies] [CPA] \MMLcIMPLIES + +\def\MMLcAND #1#2#3\empty{\encapsulateXMLR{}{\getXMLentity{and}}{}{#3}} +\def\MMLcOR #1#2#3\empty{\encapsulateXMLR{}{\getXMLentity{or}}{}{#3}} +\def\MMLcXOR #1#2#3\empty{\encapsulateXMLR{}{\getXMLentity{xor}}{}{#3}} +\def\MMLcIMPLIES#1#2#3\empty{\encapsulateXMLR{}{\getXMLentity{implies}}{}{#3}} + +\remapXMLsingular [not] [CPA] \MMLcNOT + +\def\MMLcNOT#1#2#3\empty{\getXMLentity{not}\processXMLRchildren{#3}} + +\remapXMLsingular [forall] [CPA] \MMLcFORALL +\remapXMLsingular [exists] [CPA] \MMLcEXISTS + +\def\MMLcFORALL% + {\getXMLentity{forall}% + \!% \getXMLentity{NegThinSpace}% + \MMLcFORALLandEXISTS} + +\def\MMLcEXISTS% + {\getXMLentity{exists}% + \MMLcFORALLandEXISTS} + +\def\MMLcFORALLandEXISTS#1#2#3\empty + {\MMLcreset + _{\encapsulateXMLRchildren{bvar}{}{\MMLccomma}{}{#3}}% + \doifXMLRchildelse{condition}{#3} + {\;% \getXMLentity{ThickSpace}% + \processXMLRchild{condition}{#3} + \doifXMLRchildelse{apply,reln,ci,cn}{#3} + {\countXMLRchild{apply,reln,ci,cn}{#3}% + \ifcase\nofXMLRchildren\or % == snelle volgende + \encapsulateXMLRchildren{apply,reln,ci,cn} + {\left\vert}% + {} + {\right.} + {#3\empty}% + \else % special case + \pushmacro\MMLcCONDITION + \let\MMLcCONDITION\gobbletwoarguments + \collectbetweenXMLRchild{apply,reln,ci,cn}{\hfill\crcr}{#3}% + \left\vert\matrix{\the\XMLRtoks}\right.% + \popmacro\MMLcCONDITION + \fi} + {}} + {:\processXMLRchild{apply,reln,ci,cn}{#3\empty}}} + +\remapXMLsingular [abs] [CPA] \MMLcABS + +\def\MMLcABS#1#2#3\empty + {\left\vert\MMLcreset\processXMLRchildren{#3}\right\vert} + +\remapXMLsingular [conjugate] [CPA] \MMLcCONJUGATE + +\def\MMLcCONJUGATE#1#2#3\empty% + {\overline{\MMLcreset\processXMLRchildren{#3}}} + +\remapXMLsingular [arg] [CPA] \MMLcARG + +\def\MMLcARG#1#2#3\empty + {\getXMLentity{arg}(\MMLcreset\processXMLRchildren{#3})} + +\remapXMLsingular [real] [CPA] \MMLcREAL +\remapXMLsingular [imaginary] [CPA] \MMLcIMAGINARY + +\def\MMLcREAL#1#2#3\empty + {\getXMLentity{real}(\MMLcreset\processXMLRchildren{#3})} + +\def\MMLcIMAGINARY#1#2#3\empty + {\getXMLentity{imaginary}(\MMLcreset\processXMLRchildren{#3})} + +\remapXMLsingular [lcm] [CPA] \MMLcLCM + +\def\MMLcLCM#1#2#3\empty + {\encapsulateXMLR{\getXMLentity{lcm}(}{\MMLccomma}{)}{#3}} + +\remapXMLsingular [floor] [CPA] \MMLcFLOOR +\remapXMLsingular [ceiling] [CPA] \MMLcCEILING + +\def\MMLcFLOOR#1#2#3\empty + {\getXMLentity{lfloor}\processXMLRchildren{#3}\getXMLentity{rfloor}} + +\def\MMLcCEILING#1#2#3\empty + {\getXMLentity{lceiling}\processXMLRchildren{#3}\getXMLentity{rceiling}} + +%%% relations + +\remapXMLsingular [eq] [CPA] \MMLcEQ +\remapXMLsingular [neq] [CPA] \MMLcNEQ +\remapXMLsingular [gt] [CPA] \MMLcGT +\remapXMLsingular [lt] [CPA] \MMLcLT +\remapXMLsingular [geq] [CPA] \MMLcGEQ +\remapXMLsingular [leq] [CPA] \MMLcLEQ +\remapXMLsingular [equivalent] [CPA] \MMLcEQUIVALENT +\remapXMLsingular [approx] [CPA] \MMLcAPPROX +\remapXMLsingular [factorof] [CPA] \MMLcFACTOROF + +\setupMMLappearance[relation][\c!align=\v!no] + +\def\noMMLcrelation#1#2% + {\encapsulatenextXMLRelements{}{#1}{}#2\empty} + +\def\lastMMLcrelation#1#2% + {\countXMLRchildren{#2}% + \rawcollectbetweenXMLR + {\advance\nofXMLRchildren -1 + \ifnum\nofXMLRchildren>1 + \appendtoks\@col@amp@#1\crcr\to\XMLRtoks + \else + \appendtoks\@col@amp@#1\to\XMLRtoks + \fi} + {#2}% + \eqalign{\the\XMLRtoks\crcr}} + +\def\firstMMLcrelation#1#2% + {\nofXMLRchildren=0 + \rawcollectbetweenXMLR + {\advance\nofXMLRchildren 1 + \ifnum\nofXMLRchildren=1 + \appendtoks\@col@amp@#1\to\XMLRtoks + \else + \appendtoks\crcr\@col@amp@#1\to\XMLRtoks + \fi} + {#2}% + \eqalign{\the\XMLRtoks\crcr}} + +\def\leftMMLcrelation#1#2% + {\collectbetweenXMLR{\@col@amp@#1\crcr}{#2}% + \eqalign{\the\XMLRtoks}} + +\def\rightMMLcrelation#1#2% + {\collectbetweenXMLR{\crcr#1{}\@col@amp@}{#2}% watch the {} + \prependtoks\@col@amp@\to\XMLRtoks + \eqalign{\the\XMLRtoks\crcr}} + +\def\MMLcrelation#1#2\empty + {\MMLcreset + \processaction + [\@@MMLrelationalign] + [\v!last=>\let\next\lastMMLcrelation , + \v!first=>\let\next\firstMMLcrelation, + \v!yes=>\let\next\leftMMLcrelation , + \v!left=>\let\next\leftMMLcrelation , + \v!right=>\let\next\rightMMLcrelation, + \s!default=>\let\next\noMMLcrelation , + \s!unknown=>\let\next\noMMLcrelation ] + \next{#1}{#2}} + +\def\MMLcEQ #1#2{\MMLcrelation=} +\def\MMLcNEQ #1#2{\MMLcrelation\neq} +\def\MMLcGT #1#2{\MMLcrelation>} +\def\MMLcLT #1#2{\MMLcrelation<} +\def\MMLcGEQ #1#2{\MMLcrelation\geq} +\def\MMLcLEQ #1#2{\MMLcrelation\leq} +\def\MMLcEQUIVALENT#1#2{\MMLcrelation\equiv} +\def\MMLcAPPROX #1#2{\MMLcrelation\approx} +\def\MMLcFACTOROF #1#2{\MMLcrelation\mid} + +%%% introduced when making an example for Thorsten Bahne: + +\remapXMLsingular [becomes] [CPA] \MMLcBECOMES + +\def\MMLcBECOMES#1#2{\MMLcrelation{:=}} + +\addtocommalist{becomes/}\MMLcmainresetlist + +%%% calculus and vector calculus + +\setupMMLappearance[int][\c!location=\v!top] + +\remapXMLsingular [int] [CPA] \MMLcINT + +\def\doMMLlimits#1% + {\doifelsevalue{@@MML#1\c!location}\v!top\limits\nolimits} + +\def\MMLcINT#1#2#3\empty + {\pushmacro\xmlr + \MMLcreset + \doifXMLRchildelse{domainofapplication}{#3} + {\int\doMMLlimits{int}_{\processXMLRchild{domainofapplication}{#3}}} + {\doifXMLRchildelse{condition}{#3} + {\int\doMMLlimits{int}_{\processXMLRchild{condition}{#3}}} + {\doifXMLRchildelse{lowlimit}{#3} + {\int\doMMLlimits{int} + _{\processXMLRchild{lowlimit}{#3}} + ^{\processXMLRchild {uplimit}{#3}}} + {\int}}}% + \doifXMLRchildelse{apply}{#3} + {\doifMMLfunctionelse{#3}% + {\MMLcreset % TEST + \processXMLRchild{apply}{#3}} + {\left(\MMLcreset % TEST + \processXMLRchild{apply}{#3}\right)}} + {\MMLcreset % TEST + \processXMLRchild{ci}{#3}}% + \doifXMLRchild{bvar}{#3} + {\,% \getXMLentity{ThinSpace}% + {\rm\getXMLentity{mathematicald}}\processXMLRchild{bvar}{#3}}% + \popmacro\xmlr} + +\remapXMLsingular [diff] [CPA] \MMLcDIFF + +\setupMMLappearance[diff][\c!location=\v!top] + +\def\MMLcDIFF#1#2#3\empty + {\pushmacro\xmlr + \MMLcreset + \doifXMLRchildelse{bvar}{#3} + {\frac + {{\rm \getXMLentity{mathematicald}}% + \collectXMLRchild{bvar}{#3}% + \let\MMLcDEGREE\superMMLcelement + \expanded{\processXMLRchild{degree}{\the\XMLRtoks}}% + \doif\@@MMLdifflocation\v!top + {\doifXMLRchildelse{ci}{#3} + {\processXMLRchild{ci}{#3}} + {\doifMMLfunctionelse{#3} + {\MMLcreset\processXMLRchild{apply}{#3}} + {\left(\MMLcreset\processXMLRchild{apply}{#3}\right)}}}} + {\let\MMLcDEGREE\superMMLcelement + \begingroup\rm\getXMLentity{mathematicald}\endgroup + \processXMLRchild{bvar}{#3}}% + \doifnot\@@MMLdifflocation\v!top + {\left(\MMLcreset\processXMLRchild{apply,ci}{#3}\right)}} + {\processXMLRchildren{#3}^\prime}% + \popmacro\xmlr} + +\remapXMLsingular [partialdiff] [CPA] \MMLcPARTIALDIFF + +\def\MMLcBVARpartialdiff#1#2% + {\getXMLentity{differentiald}\processXMLRchild{apply,reln,ci,cn}{#2} + \doifXMLRchild{degree}{#2}{^{\processXMLRchild{degree}{#2}}}} + +\def\MMLcPARTIALDIFF#1#2#3\empty + {\pushmacro\xmlr + \doifXMLRchildelse{list}{#3} + {\getXMLentity{capitaldifferentiald}_{\encapsulateXMLRchild{list}{}{\MMLccomma}{}{#3}}% + \processXMLRchild{apply,reln,ci,cn}{#3}} + {\countXMLRchild{bvar}{#3}% + \ifnum\nofXMLRchildren>0 + \pushmacro\MMLcDEGREE + \pushmacro\MMLcBVAR + \frac + {\doifXMLRchildelse{degree}{#3} + {\collectXMLRchild{degree}{#3}} + {\collectXMLRchild{bvar}{#3}% + \expanded{\collectXMLRchild{degree}{\the\XMLRtoks}}}% + \getXMLentity{differentiald}^{\encapsulateXMLR{}{+}{}{\the\XMLRtoks}}% + \let\MMLcDEGREE\gobbletwoarguments + \doifMMLfunctionelse{#3}{\MMLcreset}{}% + \processXMLRchild{apply,reln,ci,cn}{#3}} + {\let\MMLcBVAR\MMLcBVARpartialdiff + \processXMLRchild{bvar}{#3}}% + \popmacro\MMLcBVAR + \popmacro\MMLcDEGREE + \else + \processXMLRchild{apply,reln,ci,cn}{#3}% + \fi}% + \popmacro\xmlr} + +\def\doifMMLfunctionelse#1#2#3% + {\collectXMLRchild{apply}{#1}% + \doifXMLRchildelse{fn}{\the\XMLRtoks#1} + {#2} + {\doifXMLRchildelse{ci}{\the\XMLRtoks#1} + {\pushmacro\xmlr + \getXMLarguments{dummy}{type=""}% + \def\xmlr{\getmmlarguments{dummy}{}}% + \the\XMLRtoks % what if more than one ? + \popmacro\xmlr + \doif{\XMLpar{dummy}{type}{}}{fn}{#2}{#3}} + {#2}}} + +\def\subMMLcelement #1#2{_{#2}} +\def\superMMLcelement#1#2{^{#2}} + +\remapXMLsequence [lowlimit][CPA] \MMLcLOWLIMIT +\remapXMLsequence [uplimit] [CPA] \MMLcUPLIMIT +\remapXMLsequence [bvar] [CPA] \MMLcBVAR +\remapXMLsequence [degree] [CPA] \MMLcDEGREE + +\def\MMLcLOWLIMIT#1#2{#2} +\def\MMLcUPLIMIT #1#2{#2} +\def\MMLcBVAR #1#2{#2} +\def\MMLcDEGREE #1#2{#2} + +\remapXMLsingular [divergence] [CPA] \MMLcDIVERGENCE +\remapXMLsingular [grad] [CPA] \MMLcGRAD +\remapXMLsingular [curl] [CPA] \MMLcCURL +\remapXMLsingular [laplacian] [CPA] \MMLcLAPLACIAN + +\def\MMLcDIVERGENCE#1#2#3\empty{\getXMLentity{divergence}\processXMLRchildren{#3}} +\def\MMLcGRAD #1#2#3\empty{\getXMLentity{grad}\processXMLRchildren{#3}} +\def\MMLcCURL #1#2#3\empty{\getXMLentity{curl}\processXMLRchildren{#3}} +\def\MMLcLAPLACIAN #1#2#3\empty{\getXMLentity{laplacian}\processXMLRchildren{#3}} + +%%% theory of sets + +\remapXMLsequence [set] [CPA] \MMLcSET + +\def\MMLcSET#1#2% + {\doifXMLRchildelse{condition}{#2} + {\{\processXMLRchild{bvar}{#2}\,\vert\,\processXMLRchild{condition}{#2}\}} + {\encapsulateXMLR{\{}{\MMLccomma}{\}}{#2}}} + +\remapXMLsequence [list] [CPA] \MMLcLIST + +\def\MMLcLIST#1#2{\encapsulateXMLR{[}{\MMLccomma}{]}{#2}} + +\remapXMLsingular [union] [CPA] \MMLcUNION +\remapXMLsingular [intersect] [CPA] \MMLcINTERSECT +\remapXMLsingular [in] [CPA] \MMLcIN +\remapXMLsingular [notin] [CPA] \MMLcNOTIN +\remapXMLsingular [subset] [CPA] \MMLcSUBSET +\remapXMLsingular [prsubset] [CPA] \MMLcPRSUBSET +\remapXMLsingular [notsubset] [CPA] \MMLcNOTSUBSET +\remapXMLsingular [notprsubset] [CPA] \MMLcNOTPRSUBSET +\remapXMLsingular [setdiff] [CPA] \MMLcSETDIFF + +\def\MMLcset#1{\withnexttwoXMLRelements{\firstXMLRelement#1\secondXMLRelement}} + +\def\MMLcUNION #1#2{\MMLcset\cup} +\def\MMLcINTERSECT #1#2{\MMLcset\cap} +\def\MMLcIN #1#2{\MMLcset\in} +\def\MMLcNOTIN #1#2{\MMLcset{\not\in}} +\def\MMLcSUBSET #1#2{\MMLcset\subset} +\def\MMLcPRSUBSET #1#2{\MMLcset\subseteq} +\def\MMLcNOTSUBSET #1#2{\MMLcset{\not\subset}} +\def\MMLcNOTPRSUBSET #1#2{\MMLcset{\not\subseteq}} +\def\MMLcSETDIFF #1#2{\MMLcset\setminus} + +\remapXMLsingular [card] [CPA] \MMLcCARD + +\def\MMLcCARD#1#2#3\empty{\encapsulateXMLR{\vert}{}{\vert}{#3}} + +\remapXMLsingular [cartesianproduct] [CPA] \MMLcCARTESIANPRODUCT + +\def\MMLcCARTESIANPRODUCT#1#2#3\empty{\encapsulateXMLR{}{\times}{}{#3}} + +%%% sequences and series + +\remapXMLsingular [sum] [CPA] \MMLcSUM +\remapXMLsingular [product] [CPA] \MMLcPRODUCT + +\def\MMLcSUM {\MMLcSUMandPRODUCT{sum}\sum} +\def\MMLcPRODUCT{\MMLcSUMandPRODUCT{product}\prod} + +\setupMMLappearance[sum][\c!location=\v!top] +\setupMMLappearance[product][\c!location=\v!top] + +\def\stackMMLsubscripts#1% + {\vbox + {\baselineskip\zeropoint % hack, taco vragen + \halign{$\scriptstyle\hss##\hss$\cr#1\crcr}}} + +\def\MMLcSUMandPRODUCT#1#2#3#4\empty + {\pushmacro\xmlr + \doifXMLRchildelse{condition,bvar,lowlimit}{#4} + {\def\MMLcSUMlow + {_{\doifXMLRchildelse{condition}{#4} + {\collectXMLRchild{condition}{#4}% + \expanded{\collectbetweenXMLR{\crcr}{\the\XMLRtoks}}% + \stackMMLsubscripts{\the\XMLRtoks}} + {\doifXMLRchild{bvar}{#4} + {\processXMLRchild{bvar}{#4}% + \doifXMLRchild{lowlimit}{#4}{=}}% + \processXMLRchild{lowlimit}{#4}}}}} + {\let\MMLcSUMlow\empty}% + \doifXMLRchildelse{uplimit}{#4} + {\def\MMLcSUMup{^{\processXMLRchild{uplimit}{#4}}}} + {\let\MMLcSUMup\empty}% + \MMLcreset#2\doMMLlimits{#1}\MMLcSUMup\MMLcSUMlow + \MMLcreset + \processXMLRchild{apply,ci}{#4}% + \popmacro\xmlr} + +\remapXMLsingular [limit] [CPA] \MMLcLIMIT + +\setupMMLappearance[limit][\c!location=\v!top] + +\def\MMLcLIMIT#1#2#3\empty + {\pushmacro\xmlr + \MMLcreset + \lim\doMMLlimits{limit}_ + {\MMLcreset + \doifXMLRchildelse{condition}{#3} + {\processXMLRchild{condition}{#3}} + {\doifXMLRchild{bvar}{#3} + {\processXMLRchild{bvar}{#3}\rightarrow}% + \processXMLRchild{lowlimit}{#3}}}% + \processXMLRchild{apply}{#3}% + \popmacro\xmlr} + +\remapXMLsingular [tendsto] [CPA] \MMLcTENDSTO + +\def\MMLcTENDSTO#1#2% + {\getXMLarguments{tendsto}{type="default" #1}% + \withnexttwoXMLRelements + {\MMLcreset\firstXMLRelement + \processaction + [\XMLpar{tendsto}{type}{default}] + [ above=>\downarrow, + below=>\uparrow, + unknown=>\rightarrow]% + \MMLcreset\secondXMLRelement}} + +%%% elementary classical functions + +\remapXMLsingular [exp] [CPA] \MMLcEXP + +\def\MMLcEXP#1#2#3\empty + {\getXMLentity{exponentiale}^{\MMLcreset#3}} + +\remapXMLsingular [ln] [CPA] \MMLcLN + +%\def\MMLcLN#1#2#3\empty +% {\ln\left(\MMLcreset#3\right)} + +\def\MMLcLN#1#2% + {\doMMLcfunction{ln}} + +\remapXMLsingular [log] [CPA] \MMLcLOG + +\setupMMLappearance[log][\c!location=\v!right] + +\def\MMLcLOG#1#2#3\empty + {\pushmacro\MMLcLOGBASE + \let\MMLcLOGBASE\secondoftwoarguments + \doifXMLRchildelse{logbase}{#3} + {\doifelse\@@MMLloglocation\v!left + {\mathop{{}^{\processXMLRchild{logbase}{#3}}\!\getXMLentity{log}}} + {\getXMLentity{log}_{\processXMLRchild{logbase}{#3}}}} + {\getXMLentity{log}}% + \let\MMLcLOGBASE\ignoreXMLRelement + \nodoMMLcfunction#3\empty + \popmacro\MMLcLOGBASE} + +\remapXMLsequence [logbase] [CPA] \MMLcLOGBASE + +\def\MMLcLOGBASE#1#2{#2} + +\remapXMLsingular [sin] [CPA] \MMLcSIN +\remapXMLsingular [arcsin] [CPA] \MMLcARCSIN +\remapXMLsingular [sinh] [CPA] \MMLcSINH +\remapXMLsingular [arcsinh] [CPA] \MMLcARCSINH +\remapXMLsingular [cos] [CPA] \MMLcCOS +\remapXMLsingular [arccos] [CPA] \MMLcARCCOS +\remapXMLsingular [cosh] [CPA] \MMLcCOSH +\remapXMLsingular [arccosh] [CPA] \MMLcARCCOSH +\remapXMLsingular [tan] [CPA] \MMLcTAN +\remapXMLsingular [arctan] [CPA] \MMLcARCTAN +\remapXMLsingular [tanh] [CPA] \MMLcTANH +\remapXMLsingular [arctanh] [CPA] \MMLcARCTANH +\remapXMLsingular [cot] [CPA] \MMLcCOT +\remapXMLsingular [arccot] [CPA] \MMLcARCCOT +\remapXMLsingular [coth] [CPA] \MMLcCOTH +\remapXMLsingular [arccoth] [CPA] \MMLcARCCOTH +\remapXMLsingular [csc] [CPA] \MMLcCSC +\remapXMLsingular [arccsc] [CPA] \MMLcARCCSC +\remapXMLsingular [csch] [CPA] \MMLcCSCH +\remapXMLsingular [arccsch] [CPA] \MMLcARCCSCH +\remapXMLsingular [sec] [CPA] \MMLcSEC +\remapXMLsingular [arcsec] [CPA] \MMLcARCSEC +\remapXMLsingular [sech] [CPA] \MMLcSECH +\remapXMLsingular [arcsech] [CPA] \MMLcARCSECH + +\setupMMLappearance[function][\c!reduction=\v!yes] + +\def\doMMLcfunction#1% + {\doifnextcharelse\xmlr{\dodoMMLcfunction{#1}}{\getXMLentity{#1}}} + +\def\dodoMMLcfunction#1% + {\getXMLentity{#1}% + \nodoMMLcfunction} + +\def\nodoMMLcfunction#1\empty + {\ifx\MMLpowerelement\empty\else + ^{\MMLcreset\MMLpowerelement\empty}\!\let\MMLpowerelement\empty + \fi + \doifelse\@@MMLfunctionreduction\v!yes + {\doifXMLRchildelse{apply}{#1} + {\collectXMLRchild{apply}{#1}% + \@EA\doifXMLRchildelse\@EA{\MMLcfunctionlist}{\the\XMLRtoks} + {\MMLcreset#1\empty} + {\left(\MMLcreset#1\empty\right)}} + {\MMLcreset#1\empty}} + {\left(\MMLcreset#1\empty\right)}} + +\def\MMLcSIN #1#2{\doMMLcfunction{sin}} +\def\MMLcARCSIN #1#2{\doMMLcfunction{arcsin}} +\def\MMLcSINH #1#2{\doMMLcfunction{sinh}} +\def\MMLcARCSINH#1#2{\doMMLcfunction{arcsinh}} +\def\MMLcCOS #1#2{\doMMLcfunction{cos}} +\def\MMLcARCCOS #1#2{\doMMLcfunction{arccos}} +\def\MMLcCOSH #1#2{\doMMLcfunction{cosh}} +\def\MMLcARCCOSH#1#2{\doMMLcfunction{arccosh}} +\def\MMLcTAN #1#2{\doMMLcfunction{tan}} +\def\MMLcARCTAN #1#2{\doMMLcfunction{arctan}} +\def\MMLcTANH #1#2{\doMMLcfunction{tanh}} +\def\MMLcARCTANH#1#2{\doMMLcfunction{arctanh}} +\def\MMLcCOT #1#2{\doMMLcfunction{cot}} +\def\MMLcARCCOT #1#2{\doMMLcfunction{arccot}} +\def\MMLcCOTH #1#2{\doMMLcfunction{coth}} +\def\MMLcARCCOTH#1#2{\doMMLcfunction{arccoth}} +\def\MMLcCSC #1#2{\doMMLcfunction{csc}} +\def\MMLcARCCSC #1#2{\doMMLcfunction{arccsc}} +\def\MMLcCSCH #1#2{\doMMLcfunction{csch}} +\def\MMLcARCCSCH#1#2{\doMMLcfunction{arccsch}} +\def\MMLcSEC #1#2{\doMMLcfunction{sec}} +\def\MMLcARCSEC #1#2{\doMMLcfunction{arcsec}} +\def\MMLcSECH #1#2{\doMMLcfunction{sech}} +\def\MMLcARCSECH#1#2{\doMMLcfunction{arcsech}} + +%%% statistics + +\remapXMLsingular [mean] [CPA] \MMLcMEAN +\remapXMLsingular [sdev] [CPA] \MMLcSDEV +\remapXMLsingular [variance] [CPA] \MMLcVARIANCE +\remapXMLsingular [median] [CPA] \MMLcMEDIAN +\remapXMLsingular [mode] [CPA] \MMLcMODE + +\def\MMLcMEAN #1#2{\withnextXMLRelement{\overline{\nextXMLRelement}}} +\def\MMLcSDEV #1#2{\withnextXMLRelement{\sigma(\MMLcreset\nextXMLRelement)}} +\def\MMLcVARIANCE#1#2{\withnextXMLRelement{\sigma(\MMLcreset\nextXMLRelement)^2}} +\def\MMLcMEDIAN #1#2{\withnextXMLRelement{\getXMLentity{median}(\MMLcreset\nextXMLRelement)}} +\def\MMLcMODE #1#2{\withnextXMLRelement{\getXMLentity{mode}(\MMLcreset\nextXMLRelement)}} + +\remapXMLsingular [moment] [CPA] \MMLcMOMENT +\remapXMLsequence [momentabout] [CPA] \MMLcMOMENTABOUT + +\def\MMLcMOMENT#1#2#3\empty + {\left\langle\processXMLRchild{apply,reln,ci,cn}{#3}% + ^{\processXMLRchild{degree}{#3}}\right\rangle} + +\def\MMLcMOMENTABOUT#1#2{} + +%%% linear algebra + +\remapXMLsequence [vector] [CPA] \MMLcVECTOR + +\setupMMLappearance[vector][\c!direction=\v!horizontal] % \v!vertical + +\def\MMLcVECTOR#1#2% + {\countXMLRchildren{#2}% + \ifnum\nofXMLRchildren>1 + \doifelse\@@MMLvectordirection\v!horizontal + {\encapsulateXMLR{\left(}{\MMLccomma}{\right)}{#2}} + {\collectbetweenXMLR{\crcr}{#2}% + \MMLcreset\left(\matrix{\the\XMLRtoks}\right)}% + \else + \overrightarrow{#2}% + \fi} + +\remapXMLsequence [matrix] [CPA] \MMLcMATRIX +\remapXMLsequence [matrixrow] [CPA] \MMLcMATRIXROW + +\unexpanded\def\@col@amp@{&} + +\def\doMMLcMATRIX#1#2#3% + {\pushmacro\MMLcMATRIXROW + \let\MMLcMATRIXROW\normalMMLcMATRIXROW + \MMLcreset + \ifcase#1\matrix{#3}\else\left(\matrix{#3}\right)\fi + \popmacro\MMLcMATRIXROW} + +\def\MMLcMATRIX#1#2% + {\doMMLcMATRIX1{#1}{#2}} + +\def\MMLcMATRIXROW#1#2% + {\collectbetweenXMLR{\@col@amp@}{#2}\the\XMLRtoks\crcr} + +\let\normalMMLcMATRIXROW\MMLcMATRIXROW + +\def\MMLcMATRIXROW#1#2% + {\collectbetweenXMLR{\@col@amp@}{#2}% + \left(\matrix{\the\XMLRtoks\crcr}\right)} + +\remapXMLsingular [determinant] [CPA] \MMLcDETERMINANT + +% \def\MMLcDETERMINANT#1#2{\getXMLentity{determinant}} % optie + +\def\MMLcDETERMINANT#1#2\empty + {\pushmacro\MMLcMATRIX + \def\MMLcMATRIX##1##2{\doMMLcMATRIX0{##1}{##2}}% + \left|#2\empty\right|% + \popmacro\MMLcMATRIX} + +\remapXMLsingular [transpose] [CPA] \MMLcTRANSPOSE + +\def\MMLcTRANSPOSE#1#2{\withnextXMLRelement{\nextXMLRelement^{\rm T}}} + +\remapXMLsingular [selector] [CPA] \MMLcSELECTOR + +\def\MMLcSELECTOR#1#2#3\empty + {\pushmacro\xmlr + \withnextXMLRelement + {\mathinner{\nextXMLRelement}% hm, assumes a matrix or so + \doMMLcSELECTOR}% + #3\empty + \popmacro\xmlr} + +\def\doMMLcSELECTOR#1\empty + {_{\MMLcreset\encapsulateXMLR{}{\MMLccomma}{}{#1\empty}}} + +\remapXMLsingular [vectorproduct] [CPA] \MMLcVECTORPRODUCT +\remapXMLsingular [scalarproduct] [CPA] \MMLcSCALARPRODUCT +\remapXMLsingular [outerproduct] [CPA] \MMLcOUTERPRODUCT + +\def\MMLcvector#1% + {\withnexttwoXMLRelements{\firstXMLRelement#1\secondXMLRelement}} + +\def\MMLcVECTORPRODUCT#1#2{\MMLcvector{\getXMLentity{vectorproduct}}#2}% #2?% +\def\MMLcSCALARPRODUCT#1#2{\MMLcvector{\getXMLentity{scalarproduct}}#2} +\def\MMLcOUTERPRODUCT #1#2{\MMLcvector{\getXMLentity{outerproduct}}#2} + +%%% semantic mapping elements + +\remapXMLsequence [semantics] [CPA] \MMLcSEMANTICS + +\def\MMLcSEMANTICS#1#2% + {\doifXMLRchildelse{annotation}{#2} + {\processXMLRchild{annotation}{#2}} + {#2}} + +\remapXMLsequence [annotation] [CPA] \MMLcANNOTATION + +\def\MMLcANNOTATION#1#2% we need a better unmapper + {\getXMLarguments{annotation}{encoding="" #1}% + \doif{\XMLpar{annotation}{encoding}{}}{TeX}% + {\begingroup + \setnormalXMLentities % better: \simplifyXMLentities ; test first + \let\xmlrent\expandedXMLentity + \edef\mmlascii{#2}% + \setnormalcatcodes + \ifx\mmlascii\empty + \donefalse + \else + \def\do##1##2\end % hack + {\edef\!!stringa{\string##1}% + \edef\!!stringb{\letterdollar}% + \ifx\!!stringa\!!stringb + \donetrue + \else + \donefalse + \fi}% + \expandafter\do\mmlascii\end + \fi + \ifdone + \hbox{\scantokens\@EA{\mmlascii}}% + \else + \scantokens\@EA{\mmlascii}% + \fi + \endgroup}} + +\remapXMLsequence [annotation-xml] [CPA] \MMLcANNOTATIONXML + +\def\MMLcANNOTATIONXML#1#2{} + +%%% constant and symbol elements + +\remapXMLsingular [integers] [CPA] \MMLcINTEGERS +\remapXMLsingular [reals] [CPA] \MMLcREALS +\remapXMLsingular [rationals] [CPA] \MMLcRATIONALS +\remapXMLsingular [naturalnumbers] [CPA] \MMLcNATURALNUMBERS +\remapXMLsingular [complexes] [CPA] \MMLcCOMPLEXES +\remapXMLsingular [primes] [CPA] \MMLcPRIMES +\remapXMLsingular [exponentiale] [CPA] \MMLcEXPONENTIALE +\remapXMLsingular [imaginaryi] [CPA] \MMLcIMAGINARYI +\remapXMLsingular [notanumber] [CPA] \MMLcNOTANUMBER +\remapXMLsingular [true] [CPA] \MMLcTRUE +\remapXMLsingular [false] [CPA] \MMLcFALSE +\remapXMLsingular [emptyset] [CPA] \MMLcEMPTYSET +\remapXMLsingular [pi] [CPA] \MMLcPI +\remapXMLsingular [eulergamma] [CPA] \MMLcEULERGAMMA +\remapXMLsingular [infinity] [CPA] \MMLcINFINITY + +\def\MMLcINTEGERS #1#2{\getXMLentity{integers}} +\def\MMLcREALS #1#2{\getXMLentity{reals}} +\def\MMLcRATIONALS #1#2{\getXMLentity{rationals}} +\def\MMLcNATURALNUMBERS#1#2{\getXMLentity{naturalnumbers}} +\def\MMLcCOMPLEXES #1#2{\getXMLentity{complexes}} +\def\MMLcPRIMES #1#2{\getXMLentity{primes}} +\def\MMLcEXPONENTIALE #1#2{\getXMLentity{ExponentialE}} +\def\MMLcIMAGINARYI #1#2{\getXMLentity{ImaginaryI}} +\def\MMLcNOTANUMBER #1#2{\mathop{\rm NaN}} +\def\MMLcTRUE #1#2{\mathop{\rm true}} +\def\MMLcFALSE #1#2{\mathop{\rm false}} +\def\MMLcEMPTYSET #1#2{\mathop{\hbox{\O}}} +\def\MMLcPI #1#2{\pi} +\def\MMLcEULERGAMMA #1#2{\gamma} +\def\MMLcINFINITY #1#2{\infty} + +\stopXMLmapping + +\protect \endinput |