How do I use a math symbol from the private use area with unicode-math?

Question

There are many math symbols which are not, unfortunately, in Unicode. One such symbol is the sequent relational operator that looks something like this ">-" and is found in the literature. I have a custom font, where this symbol is in the private use area. Using both LuaLaTeX and XeLaTeX, I can load the font and display it in text mode. The symbol is only defined in a normal weight, non-italic form. However, I cannot successfully define it as a math operator. This is the result of compiling the file...

Here is a minimal, commented .tex file that compiles to .pdf with both LuaLaTeX and XeLaTeX, but gives the wrong result for the math operator.

% Build .pdf using lualatex or xelatex

\documentclass{amsart}

% Load fontspec, unicode-math.

   \usepackage{fontspec}
   \usepackage{unicode-math}

% Load MyFont font

   \newfontface \MyFont {MyFont.ttf}

% Define Sequent operator in math mode.

   \DeclareSymbolFont{MyFont}{U}{cmr}{m}{n}

   \DeclareMathSymbol{\mathSequent}{\mathrel}{MyFont}{"E8A8}               

% Define Sequent operator in text mode.

   \newcommand \textSequent {{\MyFont{\char"E8A8}}}                        

\begin{document}
   \begin{flushleft}

      This is what the sequent operator looks like in text mode: \textSequent.\\
      This is what the sequent operator looks like in math mode: $\mathSequent$.

      \end{flushleft}
   \end{document}

Answer 1

I almost had it right. Instead of "cmr", it was necessary to declare the family and then use it. Instead of U, TU was required. \DeclareMathSymbol works if a) the declared family was used and b) the character was FF or less. Because of the latter problem with \DeclareMathSymbol it was necessary to instead use \Umathchardef. The modified code is shown below, with the replaced lines commented out. There is an extra commented out line for \DeclareMathSymbol showing how it should be used for those cases where it works.

The updated version has been tested with both LuaLaTeX and XeLaTeX. Where I have used MyFontB and MyFontC I wanted to make it clear where the same value has to be used. MyFontB represents an arbitrary font family name. MyFontC represents an arbitrary symbol font name. Notice that the fontface name is never used, except when defining the symbol in text mode. The family name can be the same as the fontface name, but still has to be defined.

I also found that the type of math symbol (mathbin, mathrel, etc.) doesn't make any practical difference, unless I remove the sidebearings (white space to the left and right of the glyph, used for minimum spacing in text) in the font itself. Then, the type of math symbol works as expected. Apparently when the font is loaded, the sidebearings are not stripped out. That would be ok if those symbols are never directly used in text. Since they could be wrapped in math mode, that shouldn't be a problem. I can create a custom variant of the font with zero width sidebearings. There may be some arcane way to have TeX remove the sidebearings, but I haven't found it.

% Build .pdf using lualatex or xelatex

\documentclass{amsart}

% Load fontspec, unicode-math.

\usepackage{fontspec}

\usepackage{unicode-math}

% Load MyFont font

%  \newfontface \MyFont {MyFont.ttf}

\newfontface \MyFont {MyFont.ttf}[NFSSFamily=MyFontB]

% Define Sequent operator in math mode.

%  \DeclareSymbolFont{MyFont}{U}{cmr}{m}{n}

\DeclareSymbolFont{MyFontC}{TU}{MyFontB}{m}{n}

%  \DeclareMathSymbol{\mathSequent}{\mathrel}{MyFont}{"E8A8}               
%  \DeclareMathSymbol{\mathSequent}{\mathrel}{MyFontC}{"E8A8}               
\Umathchardef\mathSequent="3 \symMyFontC "E8A8

% Define Sequent operator in text mode.

\newcommand \textSequent {{\MyFont{\char"E8A8}}}                        

\begin{document}
\begin{flushleft}
   This is what the sequent operator looks like in text mode: \textSequent.\\
      This is what the sequent operator looks like in math mode: $\mathSequent$.
\end{flushleft}
\end{document}

Answer 2

While not directly an answer in terms of using the font (which was previously answered, in two different ways). For this specific symbol, I have found two ways to create it directly in LaTex. The first is almost indistinguishable from the original (with slight differences depending on the math font). The second is fairly close, but is clearly different. Both would be close enough to use in practice, with the first being preferable.

This uses the scalerel package.

{\vstretch{0.90}{\hstretch{0.50}{{\mkern5mu}{>}{\mkern-3mu}{-}{\mkern5mu}}}}

This uses the graphicx package.

{\mkern3mu{\rotatebox[origin=c]{270}{\raisebox{-1pt}{\Yup}}}\mkern3mu}

Answer 3

In unicode-math 0.81, \setmathfont[range="E8A8] unfortunately fails when the requested character is in the Private Use Area. Here is a workaround.

\documentclass[varwidth, preview]{standalone}

\usepackage{amsmath}
\usepackage{unicode-math}

% \setmainfont goes here.
\defaultfontfeatures{Scale=MatchUppercase}
% \setsansfont, \setmonofont, etc. go here.

\newfontface\mathsymbolfont{MyFont.ttf}
\DeclareRobustCommand\textsequent{{\mathsymbolfont\symbol{"E8A8}}\relax}
\DeclareRobustCommand\sequent{\mathrel{\text{\textsequent}}}

\begin{document}
In text mode, the sequent symbol is \textsequent.

In math mode, \(A \sequent B\).

Compare \(A \succ B\).
\end{document}

The symbol is, according to the Comprehensive LaTeX Symbols List, also in two packages on CTAN, of which stmaryrd got an update early this century and is still usable:

\documentclass[varwidth, preview]{standalone}

\usepackage{amssymb} % Used by stmaryrd
\usepackage{stmaryrd} % For \Yright
\usepackage{unicode-math} % Or font packages of choice.
\DeclareRobustCommand\sequent{\mathrel{\Yright}}

\begin{document}
In math mode, \(A \sequent B\).

Contrast \(A \succ B\).
\end{document}

ETA:

There is a similar symbol in Unicode, available in unicode-math as \righttail, although you might need to load it from another font.

\documentclass[varwidth, preview]{standalone}

\usepackage{stmaryrd} % \Yright
\usepackage{unicode-math}

\setmathfont{Latin Modern Math}
\setmathfont[Scale=MatchUppercase, range={\righttail}]{STIX Two Math}

\newcommand\sequent{\mathrel\righttail}

\begin{document}
Compare \(A \sequent B\) to \(A \mathrel\Yright B\).
\end{document}