% language=us runpath=texruns:manuals/math

\environment math-layout

\startcomponent math-fun

\usemodule[mathfun]

\startchapter[title=Fun stuff] % As is watching the funplex DVD.

% \startsection[title=How it started]

When I decided to add the \type {\uuid} macro (a trivial task because there was
already a \LUA\ function for it in \CONTEXT) I wondered about other functions
that could be added, like those for sine and cosine. There is no real need
for that because we can already do this:

\startbuffer[a]
\luaexpr{math.sin(math.pi/4)}
\stopbuffer

\typebuffer[a]

\startbuffer[b]
\luaexpr[.4N]{math.sin(math.pi/4)}
\stopbuffer

which gives us \inlinebuffer[a]\ as result, but still one can ponder the
usability of additional macros. When seeing this, one of the first things that
probably comes to mind is how to get less digits, and indeed that can be
achieved, as \inlinebuffer[b]\ demonstrates.

\typebuffer[b]

The optional argument between square brackets is a template as we know from other
\CONTEXT\ commands without the leading percentage sign. But what if we don't want
this expression and explicit math function call?

\startbuffer
$ \sin (x) = \the\sin{pi/8} $
\stopbuffer

\typebuffer

This gives us a normal rendered sin function symbol at the left hand and a
numeric result at the right hand: \inlinebuffer. The nice thing about it is that
we don't need to come up with new macro names. \footnote {At some point \CONTEXT\
might introduce a namespace mechanism to deal with possible conflicts between
environments.} In a similar fashion we can do this:

\startbuffer
$ \sind(x) = \luaexpr[.4N]{math.sind(120)} = \the\sind[.4N]{120} $
\stopbuffer

\typebuffer

Both calls give the same result: \inlinebuffer\ and in case you wonder why we
have only three digits: the \type {N} formatter removes trailing zeros. However,
the \type {\the} prefix is still not that nice, apart from the fact that we abuse
a feature of the \LUA\ interface meant for other purposes (read: we cheat). So,
in a next step in exploring this I cooked up:

\startbuffer
$ \sqrt(x) = \the\sqrt[.3N]     {2} $
$ \sqrt(x) = \compute\sqrt[.3N] {2} $
\stopbuffer

\typebuffer

There is still a prefix but \type {\compute} looks more natural. It is not an
alias for \type {\the} but a shortcut for a prefix feature that can drive all
kind of interpretations of in this case \type {\sin}, and that is probably where
the real fun will start. Instead of functions we can also have constants:

\startbuffer
$ \pi = \compute\pi[.4N] $
\stopbuffer

In case you wonder how extensible this mechanism is, here is what happens in the
\type {mathfun} module that needs to be loaded in the usual way. There you find:

\pushoverloadmode
    \ifdefined\normalpi \else\let\normalpi\pi \fi

    \registermathfunction[sind,cosd,tand,sin,cos,tan]
    \registermathfunction[sqrt]
    \registermathfunction[pi][constant]
\popoverloadmode

The module also provides a few more expression variants (these can end up in the
core if really needed much):

\startbuffer
$ \pi = \mathexpr[.40N]{pi}            $
$ \pi = \mathexpr[.80N]{sqrt(11)}      $
$ \pi = \decimalexpr[.80N]{sqrt(11)}   $
$ \pi = \decimalexpr{sqrt(11)}         $
$ c = \complexexpr{123 + new(456,789)} $
\stopbuffer

\typebuffer

This gives:

\startlines
    \getbuffer
\stoplines

The question is: do we need this and if so, what more do we need? Feel free to
bing it up on the \CONTEXT\ mailing list. It anyway is a nice demonstration of
what can be done with the mix of languages.

% \stopsection

\stopchapter

\stopcomponent