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%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-newnmath.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
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