1

The question is as simple as that. This is the kind of thing I want to achieve:

enter image description here

The idea is to make a symbol used for divided differences. It needs to be a true delta letter rather than a triangle, but actually it is not that easy.

3 Answers 3

4

Here is a nice solution finally:

\usepackage{tikz}
\usepackage{amsmath}
\newsavebox{\deltabox}

\newcommand{\divdiff}{
    \mathord{
    \mathpalette\makedivdiff\relax
    }
}

\newcommand{\makedivdiff}[2]{
    \sbox{\deltabox}{$#1\Delta$}
    \begin{tikzpicture}[baseline=(char.base), inner sep=0, outer sep=0]
        \node[anchor=south west,inner sep=0,outer sep=0] (char) {\usebox{\deltabox}};
        \fill[black] ([xshift=0.0\wd\deltabox,yshift=0.05\wd\deltabox]char.south) -- ([yshift=-0.05\wd\deltabox]char.north) -- ([xshift=-0.14\wd\deltabox,yshift=0.04\wd\deltabox]char.south east);
    \end{tikzpicture}
}

You can just call the symbol \divdiff when you need it, that gives this result:

enter image description here

I have to add that depending on the font that you are using, you may need to change very slightly the shifts that are used on the anchors of the triangle in the \makedivdiff command definition.

2

The ◮ symbol is U+25EE in Unicode. You can enable it with code like:

\documentclass{article}
\usepackage{unicode-math} % Or amsmath and fontspec.

\newfontfamily\symbolfont{New Computer Modern Math Regular}[Scale=MatchUppercase]

\newcommand\divdiff{\ifmmode%
    \textup{\symbolfont\symbol{"25EE}}%
\else%
    {\symbolfont\symbol{"25EE}}%
\fi}

\begin{document}
In text mode, {\divdiff}.

In math mode, \(\divdiff\increment\).
\end{document}

New Computer Modern Math sample

1

With pict2e:

\documentclass{article}
\usepackage{pict2e,xcolor}

\makeatletter
\newcommand{\divdiff}{\Delta{\mathpalette\divdiff@\relax}}
\newcommand{\divdiff@}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1\Delta$}%
  \llap{% the black triangle
  \begin{picture}(0.54\wd\z@,\ht\z@)
  \moveto(0,0)
  \lineto(0.45\wd\z@,0)
  \lineto(0,0.95\ht\z@)
  \closepath
  \fillpath
  \end{picture}}%
  \endgroup
}
\makeatother

\begin{document}

$\divdiff\scriptstyle\divdiff\scriptscriptstyle\divdiff$

\end{document}

enter image description here

You see the trick if you paint the inner triangle in red.

enter image description here

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