%D \module
%D   [       file=math-frc,
%D        version=2007.07.19,
%D          title=\CONTEXT\ Math Macros,
%D       subtitle=Fractions,
%D         author={Hans Hagen \& Taco Hoekwater},
%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 Math Macros / Fractions}

\unprotect

%D \macros
%D   {frac, xfrac, xxfrac}
%D
%D This is another one Tobias asked for. It replaces the
%D primitive \type {\over}. We also take the opportunity to
%D handle math style restoring, which makes sure units and
%D chemicals come out ok.
%D The \type {\frac} macro kind of replaces the awkward \type
%D {\over} primitive. Say that we have the following formulas:
%D
%D \startbuffer[sample]
%D test $\frac  {1}{2}$ test $$1 + \frac  {1}{2} = 1.5$$
%D test $\xfrac {1}{2}$ test $$1 + \xfrac {1}{2} = 1.5$$
%D test $\xxfrac{1}{2}$ test $$1 + \xxfrac{1}{2} = 1.5$$
%D \stopbuffer
%D
%D \typebuffer[sample]
%D
%D With the most straightforward definitions, we get:
%D
%D \startbuffer[code]
%D \def\dofrac#1#2#3{\relax\mathematics{{{#1{#2}}\over{#1{#3}}}}}
%D
%D \def\frac  {\dofrac\mathstyle}
%D \def\xfrac {\dofrac\scriptstyle}
%D \def\xxfrac{\dofrac\scriptscriptstyle}
%D \stopbuffer
%D
%D \typebuffer[code] \getbuffer[code,sample]
%D
%D Since this does not work well, we can try:
%D
%D \startbuffer[code]
%D \def\xfrac #1#2{\hbox{$\dofrac\scriptstyle      {#1}{#2}$}}
%D \def\xxfrac#1#2{\hbox{$\dofrac\scriptscriptstyle{#1}{#2}$}}
%D \stopbuffer
%D
%D \typebuffer[code] \getbuffer[code,sample]
%D
%D This for sure looks better than:
%D
%D \startbuffer[code]
%D \def\xfrac #1#2{{\scriptstyle      \dofrac\relax{#1}{#2}}}
%D \def\xxfrac#1#2{{\scriptscriptstyle\dofrac\relax{#1}{#2}}}
%D \stopbuffer
%D
%D \typebuffer[code] \getbuffer[code,sample]
%D
%D So we stick to the next definitions (watch the local
%D overloading of \type {\xfrac}).

% \def\dofrac#1#2#3{\relax\mathematics{{{#1{#2}}\over{#1{#3}}}}}

\def\dofrac#1#2#3{\relax\mathematics{\Ustack{{#1{#2}}\normalover{#1{#3}}}}}
\def\nofrac  #1#2{\relax\mathematics{\Ustack{{#1}\normalover{#2}}}}

% $\mathfracmode0 \frac{1}{2}$
% $\mathfracmode1 \frac{1}{2}$
% $\mathfracmode2 \frac{1}{2}$
% $\mathfracmode3 \frac{1}{2}$
% $\mathfracmode4 \frac{1}{2}$
% $\mathfracmode5 \frac{1}{2}$

% 0=auto, 1=displaystyle, 2=textstyle, 3=scriptstyle, 4=scriptscriptstyle, 5=mathstyle

\setnewconstant\mathfracmode\zerocount

\unexpanded\def\frac
  {\ifcase\mathfracmode
     \expandafter\nofrac
   \or
     \expandafter\dofrac\expandafter\displaystyle
   \or
     \expandafter\dofrac\expandafter\textstyle
   \or
     \expandafter\dofrac\expandafter\scriptstyle
   \or
     \expandafter\dofrac\expandafter\scriptscriptstyle
   \else
     \expandafter\dofrac\expandafter\mathstyle
   \fi}

\unexpanded\def\xfrac#1#2%
  {\begingroup
   \let\xfrac\xxfrac
   \dofrac\scriptstyle{#1}{#2}%
   \endgroup}

\unexpanded\def\xxfrac#1#2%
  {\begingroup
   \dofrac\scriptscriptstyle{#1}{#2}%
   \endgroup}

%D The \type {xx} variant looks still ugly, so maybe it's
%D best to say:

\unexpanded\def\xxfrac#1#2%
  {\begingroup
   \dofrac\scriptscriptstyle{#1}{\raise.25ex\hbox{$\scriptscriptstyle#2$}}%
   \endgroup}

%D Something low level for scientific calculator notation:

\unexpanded\def\scinot#1#2%
  {#1\times10^{#2}}

%D The next macro, \type {\ch}, is \PPCHTEX\ aware. In
%D formulas one can therefore best use \type {\ch} instead of
%D \type {\chemical}, especially in fractions.

% let's see who complains ... \mathstyle is now a primitive
%
% \unexpanded\def\ch#1%
%   {\ifdefined\@@chemicalletter
%      \dosetsubscripts
%      \mathstyle{\@@chemicalletter{#1}}%
%      \doresetsubscripts
%    \else
%      \mathstyle{\rm#1}%
%    \fi}

% \unexpanded\def\ch#1%
%   {\ifdefined\@@chemicalletter
%      \dosetsubscripts
%      \mathematics{\@@chemicalletter{#1}}%
%      \doresetsubscripts
%    \else
%      \mathematics{\rm#1}%
%    \fi}

%D \macros
%D   {/}
%D
%D Just to be sure, we restore the behavior of some typical
%D math characters.

\bgroup

\catcode`\/=\othercatcode    \global           \let\normalforwardslash/
\catcode`\/=\activecatcode \doglobal\appendtoks\let/\normalforwardslash\to\everymathematics

\egroup

% to be checked:

\unexpanded\def\exmthfont#1%
  {\symbolicsizedfont#1\plusone{MathExtension}}

\def\domthfrac#1#2#3#4#5#6#7%
  {\begingroup
   \mathsurround\zeropoint
   \setbox0\hbox{$#1 #6$}%
   \setbox2\hbox{$#1 #7$}%
   \dimen0\wd0
   \ifdim\wd2>\dimen0 \dimen0\wd2 \fi
   \setbox4\hbox to \dimen0{\exmthfont#2#3\leaders\hbox{#4}\hss#5}%
   \mathord{\vcenter{{\offinterlineskip
     \hbox to \dimen0{\hss\box0\hss}%
     \kern \ht4%
     \hbox to \dimen0{\hss\copy4\hss}%
     \kern \ht4%
     \hbox to \dimen0{\hss\box2\hss}}}}%
   \endgroup}

\def\domthsqrt#1#2#3#4#5%
  {\begingroup
   \mathsurround\zeropoint
   \setbox0\hbox{$#1 #5$}%
   \dimen0=1.05\ht0 \advance\dimen0 1pt  \ht0 \dimen0
   \dimen0=1.05\dp0 \advance\dimen0 1pt  \dp0 \dimen0
   \dimen0\wd0
   \setbox4\hbox to \dimen0{\exmthfont#2\leaders\hbox{#3}\hfill#4}%
   \delimitershortfall=0pt
   \nulldelimiterspace=0pt
   \setbox2\hbox{$\left\delimiter"0270370 \vrule height\ht0 depth \dp0 width0pt
                  \right.$}%
   \mathord{\vcenter{\hbox{\copy2
                           \rlap{\raise\dimexpr\ht2-\ht4\relax\copy4}\copy0}}}%
   \endgroup}

\unexpanded\def\mthfrac#1#2#3#4#5{\mathchoice
  {\domthfrac\displaystyle     \textface        {#1}{#2}{#3}{#4}{#5}}
  {\domthfrac\textstyle        \textface        {#1}{#2}{#3}{#4}{#5}}
  {\domthfrac\scriptstyle      \scriptface      {#1}{#2}{#3}{#4}{#5}}
  {\domthfrac\scriptscriptstyle\scriptscriptface{#1}{#2}{#3}{#4}{#5}}}

\unexpanded\def\mthsqrt#1#2#3{\mathchoice
  {\domthsqrt\displaystyle     \textface    {#1}{#2}{#3}}
  {\domthsqrt\textstyle        \textface    {#1}{#2}{#3}}
  {\domthsqrt\scriptstyle      \textface    {#1}{#2}{#3}}
  {\domthsqrt\scriptscriptstyle\textface    {#1}{#2}{#3}}}

%D Moved from math-new.tex (not that new anyway):

%D \macros
%D   {genfrac}
%D
%D [TH] The definition of \type {\genfrac} \& co. is not
%D trivial, because it allows some flexibility. This is
%D supposed to be a user||level command, but will fail quite
%D desparately if called outside math mode (\CONTEXT\ redefines
%D \type {\over})
%D
%D [HH] We clean up this macro a bit and (try) to make it
%D understandable. The expansion is needed for generating
%D the second argument to \type {\dogenfrac}, which is to
%D be a control sequence like \type {\over}.

\unexpanded\def\genfrac#1#2#3#4%
  {\edef\!!stringa
     {#1#2}%
   \expanded
     {\dogenfrac{#4}%
      \csname
        \ifx @#3@%
          \ifx\!!stringa\empty
            \strippedcsname\normalover
          \else
            \strippedcsname\normaloverwithdelims
          \fi
        \else
          \ifx\!!stringa\empty
            \strippedcsname\normalabove
          \else
            \strippedcsname\normalabovewithdelims
          \fi
        \fi
      \endcsname}%
     {#1#2#3}}

\def\dogenfrac#1#2#3#4#5%
  {{#1{\begingroup#4\endgroup#2#3\relax#5}}}

%D \macros
%D   {dfrac, tfrac, frac, dbinom, tbinom, binom}
%D
%D \startbuffer
%D $\dfrac {1}{2} \tfrac {1}{2} \frac {1}{2}$
%D $\dbinom{1}{2} \tbinom{1}{2} \binom{1}{2}$
%D \stopbuffer
%D
%D \typebuffer
%D
%D \getbuffer

\unexpanded\def\dfrac {\genfrac\empty\empty{}\displaystyle}
\unexpanded\def\tfrac {\genfrac\empty\empty{}\textstyle}
\unexpanded\def\frac  {\genfrac\empty\empty{}\donothing}

\unexpanded\def\dbinom{\genfrac()\zeropoint\displaystyle}
\unexpanded\def\tbinom{\genfrac()\zeropoint\textstyle}
\unexpanded\def\binom {\genfrac()\zeropoint\donothing}

\unexpanded\def\xfrac {\genfrac\empty\empty{}\scriptstyle}
\unexpanded\def\xxfrac{\genfrac\empty\empty{}\scriptscriptstyle}

\unexpanded\def\frac#1#2{\mathematics{\genfrac\empty\empty{}\donothing{#1}{#2}}}

%D \macros
%D   {cfrac}
%D
%D \startbuffer
%D $\cfrac{12}{3} \cfrac[l]{12}{3} \cfrac[c]{12}{3} \cfrac[r]{12}{3}$
%D $\cfrac{1}{23} \cfrac[l]{1}{23} \cfrac[c]{1}{23} \cfrac[r]{1}{23}$
%D \stopbuffer
%D
%D \typebuffer
%D
%D \getbuffer
%D
%D Now we can align every combination we want:
%D
%D \startbuffer
%D $\cfrac{12}{3} \cfrac[l]{12}{3} \cfrac[c]{12}{3} \cfrac[r]{12}{3}$
%D $\cfrac{1}{23} \cfrac[l]{1}{23} \cfrac[c]{1}{23} \cfrac[r]{1}{23}$
%D $\cfrac[cl]{12}{3} \cfrac[cc]{12}{3} \cfrac[cr]{12}{3}$
%D $\cfrac[lc]{1}{23} \cfrac[cc]{1}{23} \cfrac[rc]{1}{23}$
%D \stopbuffer
%D
%D \typebuffer
%D
%D \getbuffer

\definecomplexorsimple\cfrac

\def\simplecfrac     {\docfrac[cc]}
\def\complexcfrac[#1]{\docfrac[#1cc]}

\def\docfrac[#1#2#3]#4#5%
  {{\displaystyle
    \frac
      {\strut
       \ifx r#1\hfill\fi#4\ifx l#1\hfill\fi}%
      {\ifx r#2\hfill\fi#5\ifx l#2\hfill\fi}%
    \kern-\nulldelimiterspace}}

%D \macros
%D   {splitfrac, splitdfrac}
%D
%D Occasionally one needs to typeset multi||line fractions.
%D These commands use \tex{genfrac} to create such fractions.
%D
%D \startbuffer
%D \startformula
%D      a=\frac{
%D          \splitfrac{xy + xy + xy + xy + xy}
%D                    {+ xy + xy + xy + xy}
%D        }
%D        {z}
%D      =\frac{
%D          \splitdfrac{xy + xy + xy + xy + xy}
%D                    {+ xy + xy + xy + xy}
%D        }
%D        {z}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D These macros are based on Michael J.~Downes posting on
%D comp.text.tex on 2001/12/06

\unexpanded\def\splitfrac#1#2%
  {\genfrac\empty\empty\zeropoint\textstyle%
     {\textstyle#1\quad\hfill}%
     {\textstyle\hfill\quad\mathstrut#2}}

\unexpanded\def\splitdfrac#1#2%
  {\genfrac\empty\empty\zeropoint\displaystyle%
     {#1\quad\hfill}
     {\hfill\quad\mathstrut #2}}

%D For thee moment here, but it might move:

%D \macros
%D   {qedsymbol}
%D
%D [HH] The general Quod Erat Domonstrandum symbol is defined
%D in such a way that we can configure it. Because this symbol
%D is also used in text mode, we make it a normal text symbol
%D with special behavior.

\unexpanded\def\qedsymbol#1%
  {\ifhmode
     \unskip~\hfill#1\par
   \else\ifmmode
     \eqno#1\relax % Do we really need the \eqno here?
   \else
     \leavevmode\hbox{}\hfill#1\par
   \fi\fi}

\definesymbol [qed] [\qedsymbol{\mathematics{\square}}]

%D \macros
%D   {QED}
%D
%D [HH] For compatbility reasons we also provide the \type
%D {\QED} command. In case this command is overloaded, we still
%D have the symbol available. \symbol[qed]

\unexpanded\def\QED{\symbol[qed]}

%D \macros
%D  {mathhexbox}
%D
%D [TH] \type {\mathhexbox} is also user||level (already
%D defined in Plain \TEX). It allows to get a math character
%D inserted as if it was a text character.

\unexpanded\def\mathhexbox#1#2#3%
  {\mathtext{$\mathsurround\zeropoint\mathchar"#1#2#3$}}

%D \macros
%D   {boxed}
%D
%D [HH] Another macro that users expect (slightly adapted):

\unexpanded\def\boxed
  {\ifmmode\expandafter\mframed\else\expandafter\framed\fi}

\protect \endinput