%D \module
%D   [       file=meta-imp-newmath,
%D        version=2023.04.01,
%D          title=\METAPOST\ Graphics,
%D       subtitle=New Math Symbols,
%D         author=Mikael Sundqvist & 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.

%D In this file we will collect solutions for special math symbols. When such symbols
%D are used in publications the CMS will contact the Unicode Consortium to suggest that
%D they get a slot, because then we have proof of usage. We also consider old obsolete
%D symbols because they can be treated like some ancient out|-|of|-|use script and fit
%D into the \type {ancient math script}.

\startMPextensions
    vardef math_ornament_hat(expr w,h,d,o,l) =
        image ( path p ; p :=
            (w/2,h + 10l) --
            (o + w,h + o) --
            (w/2,h + 7l) --
            (-o,h + o) --
            cycle ;
            fill p randomized o ;
            setbounds currentpicture to (-o,0) -- (w+o,0) -- (w+o,h+2o) -- (-o,h+2o) -- cycle ;
        )
    enddef ;
\stopMPextensions

\startuniqueMPgraphic{math:ornament:hat}
    draw
        math_ornament_hat(
            OverlayWidth,
            OverlayHeight,
            OverlayDepth,
            OverlayOffset,
            OverlayLineWidth
        )
    withpen
        pencircle
            xscaled (2OverlayLineWidth)
            yscaled (3OverlayLineWidth/4)
            rotated 30
    withcolor
        OverlayLineColor ;
%         draw boundingbox currentpicture;
\stopuniqueMPgraphic

\definemathornament [widerandomhat] [mp=math:ornament:hat]

\continueifinputfile{meta-imp-newmath.mkxl}

\starttext

This symbol was designed for one of Mikaels students working on a thesis on
probability. This student needed to typeset the characteristic function of a
random variable \im {X} with density function \im {f_{X}}, and it was insisted to
use another notation than the (wide) hat, that was already used for something
else. For this reason the \tex {widerandomhat} was introduced,

\startformula
    E[\ee^{\ii tX}] = \widerandomhat{f_{X}}(t)\mtp{,}
    E[\ee^{\ii t(X_1+X_2)}] = \widerandomhat{f_{X_1} \ast f_{X_2}}(t)\mtp{.}
\stopformula

Naturally, it is automatically scaled, just like the ordinary wide hat

\startformula
    \widehat{a+b+c+d+e+f} \neq \widerandomhat{a+b+c+d+e+f}
\stopformula

\stoptext