%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

% quite old ... still needed?

%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\math_fractions_forced#1#2#3{\relax\mathematics{\Ustack{{#1{#2}}\normalover{#1{#3}}}}}
% \def\math_fractions_auto    #1#2{\relax\mathematics{\Ustack{{#1}\normalover{#2}}}}

\def\math_fractions_forced#1#2#3%
  {\normalexpanded{\vcenter\bgroup\hbox\bgroup\startimath\triggermathstyle\normalmathstyle}%
     \Ustack{{#1{#2}}\normalover{#1{#3}}}%
   \stopimath\egroup\egroup}

\def\math_fractions_auto#1#2%
  {\normalexpanded{\vcenter\bgroup\hbox\bgroup\startimath\triggermathstyle\normalmathstyle}%
     \Ustack{{#1}\normalover{#2}}%
   \stopimath\egroup\egroup}

% \def\math_fractions_auto{\math_fractions_forced\firstofoneargument}

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

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

\setnewconstant\mathfracmode\zerocount

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

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

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

%D Something low level for scientific calculator notation:

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

% I have no clue what \mthfrac and \mthsqrt are supposed to do but
% I guess that it can be done with tweaking luatex's math parameters.
% Otherwise I'll write something from scratch.

% \def\math_stylebuilders_frac#1#2#3#4#5#6#7%
%   {\begingroup
%    \mathsurround\zeropoint
%    \setbox0\hbox{$#1 #6$}%
%    \setbox2\hbox{$#1 #7$}%
%    \dimen0\wd\ifdim\wd2>\wd0 2\else 0\fi
%    \setbox4\hbox to \dimen0{\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\math_stylebuilders_sqrt#1#2#3#4#5%
%   {\begingroup
%    \mathsurround\zeropoint
%    \setbox0\hbox{$#1 #5$}%
%    \ht0\dimexpr1.05\ht0+\onepoint\relax
%    \dp0\dimexpr1.05\dp0+\onepoint\relax
%    \setbox4\hbox to \wd0{\mr#2\leaders\hbox{#3}\hfill#4}%
%    \delimitershortfall\zeropoint
%    \nulldelimiterspace\zeropoint
%    \setbox2\hbox{$\left\delimiter"0270370 \vrule \s!height\ht0 \s!depth \dp0 \s!width\zeropoint\right.$}% is this the right code point?
%    \mathord{\vcenter{\hbox{\copy2\rlap{\raise\dimexpr\ht2-\ht4\relax\copy4}\copy0}}}%
%    \endgroup}
%
% \def\mthfrac#1#2#3#4#5{\mathchoice
%   {\math_stylebuilders_frac\displaystyle     \textface        {#1}{#2}{#3}{#4}{#5}}%
%   {\math_stylebuilders_frac\textstyle        \textface        {#1}{#2}{#3}{#4}{#5}}%
%   {\math_stylebuilders_frac\scriptstyle      \scriptface      {#1}{#2}{#3}{#4}{#5}}%
%   {\math_stylebuilders_frac\scriptscriptstyle\scriptscriptface{#1}{#2}{#3}{#4}{#5}}}
%
% \def\mthsqrt#1#2#3{\mathchoice
%   {\math_stylebuilders_sqrt\displaystyle     \textface{#1}{#2}{#3}}%
%   {\math_stylebuilders_sqrt\textstyle        \textface{#1}{#2}{#3}}%
%   {\math_stylebuilders_sqrt\scriptstyle      \textface{#1}{#2}{#3}}%
%   {\math_stylebuilders_sqrt\scriptscriptstyle\textface{#1}{#2}{#3}}}

\unexpanded\def\mthfrac#1#2#3{[mthfrac: #1 #2 #3]}
\unexpanded\def\mthsqrt#1#2#3{[mthsqrt: #1 #2 #3]}

%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 \getbuffer

% extra {} after displaystyle etc are needed

%unexpanded\def\frac  #1#2{{                  {{#1}\normalover                       {#2}}}}
%unexpanded\def\xfrac #1#2{{\scriptstyle      {{#1}\normalover                       {#2}}}}
%unexpanded\def\xxfrac#1#2{{\scriptscriptstyle{{#1}\normalover                       {#2}}}}
\unexpanded\def\dfrac #1#2{{\displaystyle     {{#1}\normalover                       {#2}}}}
\unexpanded\def\tfrac #1#2{{\textstyle        {{#1}\normalover                       {#2}}}}

%unexpanded\def\binom #1#2{{                  {{#1}\normalabovewithdelims()\zeropoint{#2}}}}
\unexpanded\def\dbinom#1#2{{\displaystyle     {{#1}\normalabovewithdelims()\zeropoint{#2}}}}
\unexpanded\def\tbinom#1#2{{\textstyle        {{#1}\normalabovewithdelims()\zeropoint{#2}}}}

\unexpanded\def\binom #1#2{{\Ustack{{#1}\normalabovewithdelims()\zeropoint{#2}}}}

% \let\frac\math_fractions_auto

%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

\unexpanded\def\cfrac
  {\doifnextoptionalelse\math_cfrac_yes\math_cfrac_nop}

\def\math_cfrac_nop    {\math_cfrac_indeed[cc]}
\def\math_cfrac_yes[#1]{\math_cfrac_indeed[#1cc]}

\def\math_cfrac_indeed[#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 but adapted a bit.

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

\unexpanded\def\splitdfrac#1#2%
  {{\displaystyle{{          #1\quad\hfill}\normalabove\zeropoint{          \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\nobreakspace\hfill#1\par
   \else\ifmmode
     #1\relax % leading \eqno removed
   \else
     \dontleavehmode\emptyhbox\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   {boxed}
%D
%D [HH] Another macro that users might expect (slightly adapted):

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

\protect \endinput