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+%D \module
+%D   [       file=x-asciimath,
+%D        version=2014.06.01, % 2006.04.24, % 1999.11.06,
+%D          title=\CONTEXT\ Modules,
+%D       subtitle=AsciiMath,
+%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.
+
+\registerctxluafile{x-asciimath}{}
+
+%D When the Math4All project started, we immediately started using content \MATHML.
+%D Because in school math there is often a reference to calculator input, we also
+%D provided what we called \quote {calcmath}: a predictable expression based way
+%D entering math. At some point \OPENMATH\ was also used but that was later
+%D abandoned because editing is more cumbersome.
+%D
+%D Due to limitations in the web variant (which is independent of rendering for
+%D paper but often determines the coding of document, not seldom for the worse) the
+%D switch was made to presentational \MATHML. But even that proved to be too complex
+%D for rendering on the web, so it got converted to so called \ASCIIMATH\ which
+%D can be rendered using some \JAVASCRIPT\ magic. However, all the formulas (and
+%D we're talking of tens of thousands of them) were very precisely coded by the main
+%D author. Because in intermediate stages of the editing (by additional authors) a
+%D mixture of \MATHML\ and \ASCIIMATH\ was used, we wrote the first version of this
+%D module. As reference we took \url
+%D {http://www1.chapman.edu/~jipsen/mathml/asciimath.html} and. The idea was to
+%D stick to \MATHML\ as reference and if needed use \ASCIIMATH\ as annotation.
+%D
+%D Eventually we ended up with supporting several math encodings in \CONTEXT\ that
+%D could be used mixed: content \MATHML\ (preferred), presentation \MATHML\ (often
+%D messy), \OPENMATH\ (somewhat minimalistic) calcmath (handy for students who are
+%D accustomed to calculators), \ASCIIMATH\ (to make web support easier) and of
+%D course \TEX.
+%D
+%D The first version had some limitations as we didn't want to support all quirks of
+%D \ASCIIMATH\ and also because I was not really in the mood to write a complex parser
+%D when a bit of sane coding can work equally well. Some comments from that version:
+%D
+%D \startnarrower
+%D \startitemize
+%D \item We support only the syntactically clear variants and as long as lpeg does
+%D       not support left recursion this is as far as we want to go.
+%D \item The parser is rather insensitive for spaces but yet the advice is to avoid
+%D       weird coding like \type {d/dxf(x)} but use \type {d/dx f(x)} instead. After
+%D       all we're not in a compact coding cq.\ parser challenge.
+%D \item We also don't support the somewhat confusing \type {sqrt sqrt 2} nor \type
+%D       {root3x} (although the second one kind of works). A bit of defensive coding
+%D       does not hurt.
+%D \item We can process \type {a/b/c/d} but it's not compatible with the default
+%D       behaviour of \ASCIIMATH. Use grouping instead. Yes, we do support the somewhat
+%D       nonstandard grouping token mix.
+%D \item You should use explicit \type {text(..)} directives as one can never be sure
+%D       what is a reserved word and  not.
+%D \stopitemize
+%D
+%D Actually, as the only parsing sensitive elements of \TEX\ are fractions (\type {\over}
+%D and friends, a restricted use of \TEX\ coding is probably as comprehensive and
+%D parsable. The webpage with examples served as starting point so anything beyond
+%D what can be found there isn't supported.
+%D \stopnarrower
+%D
+%D Then in 2014 something bad happened. Following the fashion of minimal encoding
+%D (which of course means messy encoding of complex cases and which can make authors
+%D sloppy too) the web based support workflow of the mentioned project ran into some
+%D limitations and magically one day all carefully coded \MATHML\ was converted into
+%D \ASCIIMATH. As there was no way to recover the original thousands of files and
+%D tens of thousands of formulas we were suddenly stuck with \ASCIIMATH. Because the
+%D conversion had be done automagically, we also saw numerous errors and were forced
+%D to come up with some methods to check formulas. Because \MATHML\ poses some
+%D restrictions it has predictable rendering; \ASCIIMATH\ on the other hand enforces
+%D no structure. Also, because \MATHML\ has to be valid \XML\ it always processes.
+%D Of course, during the decade that the project had run we also had to built in
+%D some catches for abuse but at least we had a relatively stable and configurable
+%D subsystem. So, in order to deal with less predictable cases as well as extensive
+%D checking, a new \ASCIIMATH\ parser was written, one that could also be used to
+%D trace bad coding.
+%D
+%D Because the formal description is incomplete, and because some links to resources
+%D are broken, and because some testing on the web showed that sequences of characters
+%D are interpreted that were not mentioned anywhere (visible), and because we noticed
+%D that the parser was dangerously tolerant, the new code is quite different from the
+%D old code.
+%D
+%D One need to keep in mind that because spaces are optional, the only robust way to
+%D edit \ASCIIMATH\ is to use a \WYSIWYG\ editor and hope that the parser doesn't
+%D change ever. Keys are picked up from spaceless sequences and when not recognized
+%D a (sequence) of characters is considered to be variables. So, \type {xsqrtx} is
+%D valid and renders as \type {$x\sqrt{x}$}, \type {xx} becomes \type {×} (times)
+%D but \type {ac} becomes \type {$a c$} (a times c). We're lucky that \type {AC} is
+%D not turned into Alternating Current, but who knows what happens a few years from
+%D now. So, we do support this spaceless mess, but users are warned: best use a
+%D spacy sequence. The extra amount of spaces (at one byte each) an author has to
+%D include in his|/|her active writing time probably stays below the size of one
+%D holiday picture. Another complication is that numbers (in Dutch) use commas instead
+%D of periods, but vectors use commas as well. We also hav esome different names for
+%D functions which then can conflict with the expectations about collapsed variables.
+%D
+%D It must be noted that simplified encodings (that seem to be the fashion today)
+%D can demand from applications to apply fuzzy logic to make something work out
+%D well. Because we have sequential data that gets rendered, sometimes wrong input
+%D gets obscured simply by the rendering: like the comma's in numbers as well as
+%D for separators (depending on space usage), or plain wrong symbols that somehow
+%D get a representation anyway. This in itself is more a side effect of trying to
+%D use the simplified encoding without applying rules (in the input) or to use it
+%D beyong its intended usage, which then of course can lead to adapted parsers and
+%D catches that themselves trigger further abuse. Imagine that instead of developing
+%D new cars, planes, space ships, mobile phones, computers we would have adapted
+%D horse cars, kites, firework, old fashioned phones and mechanical calculators in a
+%D similar way: patch upon patch of traditional means for sure would not have
+%D worked. So, when you use \ASCIIMATH\ best check immediately how it gets rendered
+%D in the browser as well as on paper. And be prepared to check the more complex
+%D code in the future again. We don't offer any guarantees but of course will try to
+%D keep up.
+%D
+%D In retrospect I sometimes wonder if the energy put into constantly adapting to
+%D the fashion of the day pays off. Probably not. It definitely doesn't pay of.
+%D
+%D More complex crap:
+%D
+%D 1: $x + \stackrel{comment}{\stackrel{\utfchar{"23DE}}{yyyyyyyy}} = y$ \blank
+%D 2: \asciimath{x + stackrel{\utfchar{"23DE}}{yyyyyyyy} = y} \blank
+%D 3: \asciimath{x + stackrel{yyyyyyyy}{\utfchar{"23DE}} = y} \blank
+%D 4: \asciimath{x + stackrel{"comment"}{stackrel{\utfchar{"23DE}}{yyyyyyyy}} = y} \blank
+
+\usemodule[mathml-basics]
+
+\startmodule[asciimath]
+
+\unprotect
+
+\writestatus{asciimath}{beware, this is an experimental (m4all only) module}
+
+%D Hacks:
+
+\unexpanded\def\asciimathoptext        #1{\ifmmode\mathoptext{#1}\else#1\fi}
+\unexpanded\def\asciimathoptexttraced  #1{\ifmmode\mathoptext{\color[darkgreen]{#1}}\else\color[darkgreen]{#1}\fi}
+\unexpanded\def\asciimathstackrel    #1#2{\mathematics{\mathop{\let\limits\relax\mover{#2}{#1}}}}
+\unexpanded\def\asciimathroot        #1#2{\sqrt[#1]{#2}}
+\unexpanded\def\asciimathsqrt          #1{\sqrt{#1}}
+
+%D The core commands:
+
+% if we need to set
+
+\installsetuponlycommandhandler {asciimath} {asciimath}
+
+\appendtoks
+    \ctxlua{moduledata.asciimath.setup {
+        splitmethod = "\asciimathparameter\c!splitmethod",
+        separator   = "\asciimathparameter\c!separator",
+        symbol      = "\asciimathparameter\c!symbol",
+    }}%
+\to \everysetupasciimath
+
+\newtoks\everyasciimath
+
+% \appendtoks
+%     \ignorediscretionaries
+% \to \everyasciimath
+
+\appendtoks
+    \enableautofences
+\to \everyasciimath
+
+\unexpanded\def\asciimath
+  {\doifnextoptionalelse\asciimath_yes\asciimath_nop}
+
+\def\asciimath_yes[#1]#2%
+  {\mathematics
+    [#1]%
+    {\the\everyasciimath%
+     \clf_justasciimath{\detokenize\expandafter{\normalexpanded{#2}}}}}
+
+\def\asciimath_nop#1%
+  {\mathematics
+    {\the\everyasciimath
+     \clf_justasciimath{\detokenize\expandafter{\normalexpanded{#1}}}}}
+
+\unexpanded\def\ctxmoduleasciimath#1%
+  {\ctxlua{moduledata.asciimath.#1}}
+
+%D Some tracing commands. Using tex commands is 10\% slower that directly piping
+%D from \LUA, but this is non|-|critical code.
+
+\unexpanded\def\ShowAsciiMathLoad  [#1]{\ctxlua{moduledata.asciimath.show.load("#1")}}
+\unexpanded\def\ShowAsciiMathIgnore[#1]{\ctxlua{moduledata.asciimath.show.ignore("#1")}}
+\unexpanded\def\ShowAsciiMathXML   #1#2{\ctxlua{moduledata.asciimath.show.filter("#1","#2")}}
+\unexpanded\def\ShowAsciiMathStats     {\ctxlua{moduledata.asciimath.show.statistics()}}
+\unexpanded\def\ShowAsciiMathMax       {\ctxlua{moduledata.asciimath.show.max()}}
+
+\unexpanded\def\ShowAsciiMathResult#1%
+  {\begingroup
+     \blank
+     % if we are in vmode, we don't get positions i.e. a smaller tuc file
+     \inleft{\ttbf#1\hfill\ctxlua{moduledata.asciimath.show.count(#1,true)}}%
+     \dontleavehmode
+     \begingroup
+       \ttbf
+       \ctxlua{moduledata.asciimath.show.files(#1)}
+     \endgroup
+     \blank[medium,samepage]
+     \startcolor[darkblue]
+     \ctxlua{moduledata.asciimath.show.input(#1,true)}
+     \stopcolor
+     \blank[medium,samepage]
+     \doifmode{asciimath:show:dirty} {
+        \dorecurse{\ctxlua{moduledata.asciimath.show.nofdirty(#1)}} {
+          \ctxlua{moduledata.asciimath.show.dirty(\recurselevel,true)}
+          \blank[medium,samepage]
+        }
+     }
+     \ctxlua{moduledata.asciimath.show.result(#1)}
+     \blank
+   \endgroup}
+
+\unexpanded\def\ShowAsciiMathStart
+  {\begingroup
+   \let\asciimathoptext\asciimathoptexttraced
+   \setuptyping[\v!buffer][\c!before=,\c!after=]
+   \setupmargindata[\v!left][\c!style=]}
+
+\unexpanded\def\ShowAsciiMathStop
+  {\endgroup}
+
+\unexpanded\def\ShowAsciiMath
+  {\dodoubleempty\doShowAsciiMath}
+
+\unexpanded\def\doShowAsciiMath[#1][#2]%
+  {\iffirstargument
+     \ShowAsciiMathStart
+     \ShowAsciiMathLoad[#1]
+     \ifsecondargument
+       \ShowAsciiMathIgnore[#2]
+     \fi
+     \dorecurse{\ShowAsciiMathMax}{\ShowAsciiMathResult\recurselevel}
+     \page
+     \ShowAsciiMathStats
+     \ShowAsciiMathStop
+  \fi}
+
+\unexpanded\def\xmlShowAsciiMath#1#2%
+  {\iffirstargument
+     \ShowAsciiMathStart
+     \ShowAsciiMathXML{#1}{#2}%
+     \dorecurse{\ShowAsciiMathMax}{\ShowAsciiMathResult\recurselevel}
+     \page
+     \ShowAsciiMathStats
+     \ShowAsciiMathStop
+  \fi}
+
+\unexpanded\def\ShowAsciiMathSave
+  {\dosingleempty\doShowAsciiMathSave}
+
+\unexpanded\def\doShowAsciiMathSave[#1]%
+  {\ctxlua{moduledata.asciimath.show.save("#1")}}
+
+\protect
+
+\startsetups asciimath:layout
+
+    \setupbodyfont
+    % [pagella,10pt]
+      [dejavu,10pt]
+
+    \setuplayout
+      [backspace=35mm,
+       leftmargin=20mm,
+       rightmargindistance=0pt,
+       leftmargindistance=5mm,
+       cutspace=1cm,
+       topspace=1cm,
+       bottomspace=1cm,
+       width=middle,
+       height=middle,
+       header=0cm,
+       footer=1cm]
+
+    \setupheadertexts
+      []
+
+    \setupfootertexts
+      [\currentdate][\pagenumber]
+
+    \setupalign
+      [flushleft,verytolerant,stretch]
+
+    \dontcomplain
+
+\stopsetups
+
+\stopmodule
+
+\continueifinputfile{x-asciimath.mkiv}
+
+%D This will become an extra.
+
+\showframe
+
+\setups[asciimath:layout]
+
+% \enabletrackers[modules.asciimath.mapping]
+% \enabletrackers[modules.asciimath.detail]
+
+% \starttext
+%     \enablemode[asciimath:show:dirty]
+%     \ShowAsciiMath[e:/temporary/asciimath/*.xml]
+%   % \ShowAsciiMathSave[e:/temporary/asciimath/asciimath.lua]
+% \stoptext
+
+\starttext
+\unexpanded\def\MyAsciiMath#1{\startformula\asciimath{#1}\stopformula}
+\startlines
+\MyAsciiMath{x^2 / 10 // z_12^34 / 20}
+% \MyAsciiMath{{:{:x^2:} / 10:} // {:{:z_12^34 :} / 20:}}
+% \MyAsciiMath{x^2+y_1+z_12^34}
+% \MyAsciiMath{sin^-1(x)}
+% \MyAsciiMath{d/dx f(x)=lim_(h->0) (f(x+h)-f(x))/h}
+% \MyAsciiMath{f(x)=sum_(n=0)^oo(f^((n))(a))/(n!)(x-a)^n}
+% \MyAsciiMath{int_0^1 f(x)dx}
+% \MyAsciiMath{int^1_0 f(x)dx}
+% \MyAsciiMath{a//b}
+% \MyAsciiMath{a//\alpha}
+% \MyAsciiMath{(a/b)/(d/c)}
+% \MyAsciiMath{((a*b))/(d/c)}
+% \MyAsciiMath{[[a,b],[c,d]]((n),(k))}
+% \MyAsciiMath{1/x={(1,text{if } x!=0),(text{undefined},if x=0):}}
+% \MyAsciiMath{{ (1,2), (x,(x + text(x))) }}
+% \MyAsciiMath{{(1,2),(x,(x+text(x))),(x,text(x))}}
+% \MyAsciiMath{{(1,2),(x,(x+text(x))),(x,x text(x))}}
+% \MyAsciiMath{{(1,2/2),(x,(x+x^22+sqrt(xx))),(x,x text(xyz))}}
+% \MyAsciiMath{{(1,2/2),(x,(x+x^22+sqrt(xx))),(x,text(xyz)+1+text(hans))}}
+% \MyAsciiMath{<<a,b>> text{and} {:(x,y),(u,v):}}
+% \MyAsciiMath{(a,b] = {x text(in) RR | a < x <= b}}
+% \MyAsciiMath{a/b / c/d = (a * d) / (b * d) / (b * c) / (b * d) = (a * d) / (b * c)}
+% \MyAsciiMath{ (a/b) // (c/d) =  ( (a * d) / (b * d) ) // ( (b * c) / (b * d) ) = (a * d) / (b * c)}
+% \MyAsciiMath{sin(x+1)_3^2/b / c/d}
+% \MyAsciiMath{{:{:sin(x+1)_3^2:}/b:} / {:c/d:}}
+% \MyAsciiMath{cos(a) + sin(x+1)_3^2/b / c/d = (a * d) / (b * d) / (b * c) / (b * d) = (a * d) / (b * c)}
+% \MyAsciiMath{S_(11)}
+% \MyAsciiMath{f(x)}
+% \MyAsciiMath{sin(x)}
+% \MyAsciiMath{sin(x+1)}
+% \MyAsciiMath{sin^-1(x)}
+% \MyAsciiMath{sin(2x)}
+% \MyAsciiMath{a_2^2}
+% \MyAsciiMath{( (S_(11),S_(12),S_(1n)),(vdots,ddots,vdots),(S_(m1),S_(m2),S_(mn)) ]}
+% \MyAsciiMath{frac a b}
+% \MyAsciiMath{sin(x)/2 // cos(x)/pi}
+% \MyAsciiMath{a/13 // c/d}
+% \MyAsciiMath{a/b // c/d}
+% \MyAsciiMath{x}
+% \MyAsciiMath{x^2}
+% \MyAsciiMath{sqrt x}
+% \MyAsciiMath{sqrt (x)}
+% \MyAsciiMath{root 2 x}
+% \MyAsciiMath{x+x}
+% \MyAsciiMath{x/3}
+% \MyAsciiMath{x^2 / 10}
+% \MyAsciiMath{x^2 / 10 // z_12^34 / 20}
+% \MyAsciiMath{a^23}
+% \MyAsciiMath{a^{:b^23:}+3x}
+% \MyAsciiMath{a/b / c/d}
+% \MyAsciiMath{sin(x)/b / c/d}
+% \MyAsciiMath{sin(x)/b // c/d}
+% \MyAsciiMath{a/b / c/d = (a * d) / (b * d) / (b * c) / (b * d) = (a * d) / (b * c) }
+% \MyAsciiMath{{:{:x^2:} / 10:} // {:{:z_12^34 :} / 20:}}
+% \MyAsciiMath{x^2+y_1+z_12^34}
+% \MyAsciiMath{sin^-1(x)}
+% \MyAsciiMath{d/dx f(x)=lim_(h->0) (f(x+h)-f(x))/h}
+% \MyAsciiMath{f(x)=sum_(n=0)^oo(f^((n))(a))/(n!)(x-a)^n}
+% \MyAsciiMath{int_0^1 f(x)dx}
+% \MyAsciiMath{int^1_0 f(x)dx}
+% \MyAsciiMath{2x}
+% \MyAsciiMath{a//b}
+% \MyAsciiMath{a//\alpha}
+% \MyAsciiMath{(a/b)/(d/c)}
+% \MyAsciiMath{((a*b))/(d/c)}
+% \MyAsciiMath{[[a,b],[c,d]]((n),(k))}
+% \MyAsciiMath{1/x={(1,text{if } x!=0),(text{undefined},if x=0):}}
+% \MyAsciiMath{{ (1,2), (x,(x + text(x))) }}
+% \MyAsciiMath{{(1,2),(x,(x+text(x))),(x,text(x))}}
+% \MyAsciiMath{{(1,2),(x,(x+text(x))),(x,x text(x))}}
+% \MyAsciiMath{{(1,2/2),(x,(x+x^22+sqrt(xx))),(x,x text(xyz))}}
+% \MyAsciiMath{{(1,2/2),(x,(x+x^22+sqrt(xx))),(x,text(xyz)+1+text(hans))}}
+% \MyAsciiMath{<<a,b>> text{and} {:(x,y),(u,v):}}
+% \MyAsciiMath{(a,b] = {x text(in) RR | a < x <= b}}
+% \MyAsciiMath{x^-2}
+% \MyAsciiMath{x^2(x-1/16)=0}
+% \MyAsciiMath{y= ((1/4)) ^x}
+% \MyAsciiMath{log (0,002) / (log(1/4))}
+% \MyAsciiMath{x=ax+b \ oeps}
+% \MyAsciiMath{x=\ ^ (1/4) log(x)}
+% \MyAsciiMath{x=\ ^ (1/4) log(0 ,002 )= log(0,002) / (log(1/4))}
+% \MyAsciiMath{x^ (-1 1/2) =1/x^ (1 1/2)=1/ (x^1*x^ (1/2)) =1/ (xsqrt(x))}
+% \MyAsciiMath{x^2(10 -x)&gt;2 x^2}
+% \MyAsciiMath{x^4&gt;x}
+\stoplines
+
+\setupasciimath[splitmethod=3,symbol={{,}}]
+
+\startlines
+\asciimath{sqrt 1}
+\asciimath{sqrt 1.2}
+\asciimath{sqrt 1.2}
+\asciimath{1}
+\asciimath{12}
+\asciimath{123}
+\asciimath{1234}
+\asciimath{12345}
+\asciimath{123456}
+\asciimath{1234567}
+\asciimath{12345678}
+\asciimath{123456789}
+\asciimath{1.1}
+\asciimath{12.12}
+\asciimath{1234.123}
+\asciimath{1234.1234}
+\asciimath{12345.1234}
+\asciimath{1234.12345}
+\asciimath{12345.12345}
+\asciimath{123456.123456}
+\asciimath{1234567.1234567}
+\asciimath{12345678.12345678}
+\asciimath{123456789.123456789}
+\asciimath{0.1234}
+\asciimath{1234.0}
+\asciimath{1234.00}
+\asciimath{0.123456789}
+\stoplines
+
+\stoptext