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+%D \module
+%D [ file=xtag-mmc,
+%D version=2000.12.20,
+%D title=\CONTEXT\ XML Support,
+%D subtitle=Math ML,
+%D author=Hans Hagen,
+%D date=\currentdate,
+%D copyright={PRAGMA / Hans Hagen \& Ton Otten}]
+%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 math ml)}
+
+% 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
+
+\unprotect
+
+\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!variant=\v!a] % a|b|c
+
+\def\MMLcpolar#1%
+ {\doifdefinedelse{MMLcdopolar\@@MMLpolarvariant}
+ {\getvalue{MMLcdopolar\@@MMLpolarvariant}{#1}}
+ {#1}}
+
+\def\MMLcdopolara#1%
+ {\def\MMLcsep{,}\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!symbool=\v!nee] % \v!ja|dot
+
+\def\MMLcfloat#1%
+ {\doifelse{\@@MMLfloatsymbool}{\v!nee}
+ {{\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{\@@MMLfloatsymbool}{dot}{\cdot}{\times}%
+ 10^{\last}%
+ \fi\fi}}
+
+% we now have:
+
+\setupMMLappearance[enotation][\c!symbool=\v!nee] % \v!ja|dot
+
+\def\MMLcenotation#1%
+ {\doifelse{\@@MMLenotationsymbool}{\v!nee}
+ {\def\MMLcsep%
+ {\unskip{\rm e}\ignorespaces}}
+ {\def\MMLcsep##1\empty
+ {\doifelse{\@@MMLenotationsymbool}{dot}{\cdot}{\times}10^{##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%
+ {{\blackboard#1}}
+
+\def\widevec#1%
+ {\vbox{\m@th\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}
+ {\let\next\MMLcCIdefault}
+ {\let\next\MMLcFNdefault}%
+ \next{}{#1}}
+
+\def\MMLcCIdefault#1#2% #1=dummy
+ {#2\!% \getXMLentity{NegThinSpace}%
+ \doifnextcharelse\xmlr
+ {\encapsulatenextXMLRelements{\left(}{,}{\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!symbool=\v!cijfers] % cijfers|letters|tekst|nee
+
+\def\MMLcCNinteger#1%
+ {\doifXMLparelse{cn}{base}
+ {\def\MMLcCNbase{\XMLpar{cn}{base}{}}%
+ \doifelse{\@@MMLbasesymbool}{\v!nee}
+ {\MMLcCNbasedata{#1}}
+ {\MMLcCNbasedata{#1}_{\hbox{$\rm\scriptscriptstyle
+ \processaction
+ [\@@MMLbasesymbool]
+ [\v!letters=>\MMLcCNbasestring BODH,
+ \v!tekst=>\MMLcCNbasestring{BIN}{OCT}{DEC}{HEX},
+ \s!unknown=>\MMLcCNbase]$}}}}
+ {#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/,
+ 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/,apply}
+
+% better: no () here but explicitly when needed, which is in
+% less cases
+
+\def\MMLcAPPLY#1#2%
+ {\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}
+
+\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}
+ {\let\next\MMLcFNoperator}
+ {\let\next\MMLcFNdefault}}
+ {\let\next\MMLcFNdefault}%
+ \next{#1}{#2}}
+
+\def\MMLcFNdefault#1#2% neg space needed because of \left
+ {#2\!% \getXMLentity{NegThinSpace}%
+ \MMLcreset\encapsulatenextXMLRelements{\left(}{,}{\right)}}
+
+% special function handlers
+
+\def\MMLcFNoperator
+ {\getvalue{doMMLcFN\mmloperator}}
+
+\def\doMMLcFNplusminus#1#2#3\empty
+ {\countXMLRchildren{#3}%
+ \ifcase\nofXMLRchildren\or
+ #2#3%
+ \else
+ \encapsulateXMLR{\left(}{#2}{\right)}{\MMLcreset#3}%
+ \fi}
+
+\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!status=\v!start]
+
+\def\MMLcDECLARE#1#2%
+ {\doif{\@@MMLdeclarestatus}{\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!variant=b]
+
+\def\MMLcLAMBDA#1#2%
+ {\doifelse{\@@MMLlambdavariant}{a}
+ {\encapsulateXMLR{\getXMLentity{lambda}(}{,}{)}{#2}}
+ {\countXMLRchild{bvar}{#2}%
+ \ifnum\nofXMLRchildren>1
+ \collectXMLRchild{bvar}{#2}%
+ \encapsulateXMLR{\left(}{,}{\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
+
+\def\MMLcPIECEWISE#1#2%
+ {\cases{#2}}
+
+\def\MMLcPIECE#1#2%
+ {\withnexttwoXMLRelements
+ {\@EA\XMLRtoks\@EA{\firstXMLRelement\@col@amp@}%
+ \@EA\appendtoks\@EA\mathematics\@EA{\secondXMLRelement}\to\XMLRtoks
+ \the\XMLRtoks\crcr}%
+ #2}%
+
+\def\MMLcOTHERWISE#1#2%
+ {#2\@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!niveau=\!!maxcard]
+
+\def\MMLcDIVIDE#1#2%
+ {\withnexttwoXMLRelements
+ {\increment\MMLcDIVIDElevel
+ \ifnum\MMLcDIVIDElevel>\@@MMLdivideniveau\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\{}
+ {,}{\right\}}{#3}}
+
+\def\MMLcMAX#1#2#3\empty
+ {\encapsulateXMLR
+ {\max\doifXMLRchild{bvar}{#3}{_{\processXMLRchild{bvar}{#3}}}\left\{}
+ {,}{\right\}}{#3}}
+
+\remapXMLsingular [minus] [CPA] \MMLcMINUS
+\remapXMLsingular [plus] [CPA] \MMLcPLUS
+
+\setupMMLappearance[sign][\c!reductie=\v!ja]
+
+\def\MMLcMINUS
+ {\doifelse{\@@MMLsignreductie}{\v!ja}
+ {\expandafter\MMLcMINUSyes}{\expandafter\MMLcMINUSno}}
+
+\def\MMLcPLUS
+ {\doifelse{\@@MMLsignreductie}{\v!ja}
+ {\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!reductie=\v!ja]
+
+\let\MMLpowerelement\empty
+
+\def\MMLcPOWER#1#2%
+ {\withnexttwoXMLRelements
+ {\doifXMLRchildelse{apply}{\firstXMLRelement}
+ {\doifelse{\@@MMLpowerreductie}{\v!ja}
+ {\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!symbool=\v!nee]
+
+\def\MMLcTIMES#1#2#3\empty
+ {\setMMLcreset{\MMLcfunctionlist,\MMLcconstructlist}%
+ \doifelse{\@@MMLtimessymbool}{\v!ja}
+ {\encapsulateXMLR{}{\times}{}{#3\empty}}
+ {\doifelse{\@@MMLtimessymbool}{dot}
+ {\encapsulateXMLR{}{\cdot}{}{#3\empty}}
+ {#3\empty}}}
+
+\remapXMLsingular [root] [CPA] \MMLcROOT
+
+\def\MMLcROOT#1#2#3\empty%
+ {\doifXMLRchildelse{degree}{#3}
+ {\root\processXMLRchild{degree}{#3}\of
+ {\let\MMLcDEGREE\ignoreXMLRelement
+ \MMLcreset\processXMLRchildren{#3}}}
+ {\sqrt{\MMLcreset\processXMLRchildren{#3}}}}
+
+\remapXMLsingular [gcd] [CPA] \MMLcGCD
+
+\def\MMLcGCD#1#2#3\empty{\encapsulateXMLR{\gcd(}{,}{)}{#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}{}{,}{}{#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}(}{,}{)}{#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!uitlijnen=\v!nee]
+
+\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
+ [\@@MMLrelationuitlijnen]
+ [\v!laatste=>\let\next\lastMMLcrelation ,
+ \v!eerste=>\let\next\firstMMLcrelation,
+ \v!ja=>\let\next\leftMMLcrelation ,
+ \v!links=>\let\next\leftMMLcrelation ,
+ \v!rechts=>\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}
+
+%%% calculus and vector calculus
+
+\setupMMLappearance[int][\c!plaats=\v!boven]
+
+\remapXMLsingular [int] [CPA] \MMLcINT
+
+\def\doMMLlimits#1%
+ {\doifelsevalue{@@MML#1\c!plaats}{\v!boven}{\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!plaats=\v!boven]
+
+\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{\@@MMLdiffplaats}{\v!boven}
+ {\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{\@@MMLdiffplaats}{\v!boven}
+ {\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}{}{,}{}{#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{\{}{,}{\}}{#2}}}
+
+\remapXMLsequence [list] [CPA] \MMLcLIST
+
+\def\MMLcLIST#1#2{\encapsulateXMLR{[} {,}{]} {#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!plaats=\v!boven]
+\setupMMLappearance[product][\c!plaats=\v!boven]
+
+\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!plaats=\v!boven]
+
+\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!plaats=\v!rechts]
+
+\def\MMLcLOG#1#2#3\empty
+ {\pushmacro\MMLcLOGBASE
+ \let\MMLcLOGBASE\secondoftwoarguments
+ \doifXMLRchildelse{logbase}{#3}
+ {\doifelse{\@@MMLlogplaats}{\v!links}
+ {\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!reductie=\v!ja]
+
+\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{\@@MMLfunctionreductie}{\v!ja}
+ {\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!richting=\v!horizontaal] % \v!vertikaal
+
+\def\MMLcVECTOR#1#2%
+ {\countXMLRchildren{#2}%
+ \ifnum\nofXMLRchildren>1
+ \doifelse{\@@MMLvectorrichting}{\v!horizontaal}
+ {\encapsulateXMLR{\left(}{,}{\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
+ {_{\encapsulateXMLR{}{,}{}{#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%
+ {\getXMLarguments{annotation}{encoding="" #1}%
+ \doif{\XMLpar{annotation}{encoding}{}}{TeX}%
+ {\begingroup
+ \setnormalXMLentities
+ \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
+
+\ifx\blackboard\undefined \let\blackboard\empty \fi
+
+\def\MMLcINTEGERS #1#2{{\blackboard Z}}
+\def\MMLcREALS #1#2{{\blackboard R}}
+\def\MMLcRATIONALS #1#2{{\blackboard Q}}
+\def\MMLcNATURALNUMBERS#1#2{{\blackboard N}}
+\def\MMLcCOMPLEXES #1#2{{\blackboard C}}
+\def\MMLcPRIMES #1#2{{\blackboard P}}
+\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}
+
+\protect \endinput