Helvetica-matching math-version

Question

I have the strong conviction that I have only understood 1% of how LaTeX selects (math) fonts, so I guess that most of my problems come from that, apart from the lack of a proper math font matching Helvetica.

My goal is to have sans serif math in surroundings where text is sans serif, and serif math where the text is serif. To that end I define mathversions sans and sansbold (I have heard about this 16-font limitation, so I guess I shouldn't be doing this, but now I'm curious). I have tried to copy at least some stuff from newtxsf.sty (I think) I understand, ending with

\documentclass{scrartcl}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb}
\usepackage{newtxtext,newtxmath}
\usepackage[scaled=0.87]{helvet}

\DeclareMathVersion{sans}
\DeclareMathVersion{boldsans}

\DeclareFontEncoding{LMS}{}{}
\DeclareFontSubstitution{LMS}{ntxsy}{m}{n}
\DeclareFontSubstitution{U}{ntxsfmia}{m}{it}

\SetSymbolFont{operators}       {sans}{\encodingdefault}{\sfdefault}{m}{n}
\SetSymbolFont{letters}         {sans}{OML}{ntxsfmi}{m}{it}
\SetSymbolFont{lettersA}        {sans}{U}{ntxsfmia}{m}{it}
\SetSymbolFont{largesymbolsTXA} {sans}{U}{ntxexa}{m}{n}
\SetMathAlphabet{\mathbf}       {sans}{T1}{phv}{b}{n}
\SetMathAlphabet{\mathit}       {sans}{OML}{ntxsfmi}{m}{it}

\SetSymbolFont{operators}       {boldsans}{\encodingdefault}{\sfdefault}{b}{n}
\SetSymbolFont{letters}         {boldsans}{OML}{ntxsfmi}{b}{n}
\SetSymbolFont{symbols}         {boldsans}{LMS}{ntxsy}{b}{n}
\SetSymbolFont{AMSm}            {boldsans}{U}{ntxsym}{b}{n}
\SetSymbolFont{symbolsC}        {boldsans}{U}{ntxsyc}{b}{n}
\SetSymbolFont{largesymbols}    {boldsans}{LMX}{ntxexx}{b}{n}
\SetSymbolFont{largesymbolsTXA} {boldsans}{U}{ntxexa}{b}{n}
\SetSymbolFont{lettersA}        {boldsans}{U}{ntxsfmia}{b}{it}
\SetMathAlphabet{\mathbf}       {boldsans}{T1}{phv}{b}{n}
\SetMathAlphabet{\mathit}       {boldsans}{OML}{ntxsfmi}{b}{it}

\newcommand\test{
    \emph{h}$h \sum_i \bigl[\bigr]  \to \lim_{\alpha} \Xi\ \mathbf{aB\Xi}\mathrm{aB}\mathit{aB\Xi}\mathfrak{aB}\mathcal{A}$
}
\begin{document}
        \test
        
        \bfseries\mathversion{bold}\test
        
        \mdseries\sffamily\mathversion{sans}\test

        \bfseries\mathversion{boldsans}\test
\end{document}

The obvious issues are

• The \bigl[\bigr] don't match. Other brackets and sizes seem to work.
• The $\mathbf{\Xi}$ does not work (should it even?), which is because \mathrm is done using phv as there seems to be no upright version of ntxsfmi. I'm not sure if I should care.
• The Fraktur letters look different in mathversion{normal} and \mathversion{sans}. Although it does not hurt so much, I wonder where it comes from.

Apart from that, should I be doing this? Did I miss something really important? You'll have noticed that I used scaled=.87 for helvet instead of the common 0.95, which I chose to be somewhere between Times and newtxsf.

Answer 1

What you have looks fine actually (akthough you probably want to use OT1 not T1 in math as campa noted in comments).

The 16 math group limit is 16 fonts per math version so adding two new math versions is exactly the right approach.

The issue with the mis-aligned [] is not your fault, it appears to be an error in the txfonts setup that you should perhaps report:

\documentclass{scrartcl}
\usepackage[T1]{fontenc}

\usepackage{newtxtext,newtxmath}

\begin{document}
        
\boldmath

$[], \bigl[\bigr], \Bigl[\Bigr]$
        
\end{document}

Answer 2

For completeness, here is how you might do the same thing in the modern toolchain. The \versionsymbol code should work in any engine.

\documentclass{article}
\usepackage{unicode-math}

\defaultfontfeatures{ Scale=MatchLowercase,
                      Ligatures = TeX }
\setmainfont{TeX Gyre Pagella}[Scale=1.0]
\setmathfont{KpMath-Regular}
\setmathfont[version=bold]{KpMath-Bold}
\setmathfont[version=sans]{KpMath-Sans}
\setmathfont[version=sansbold, FakeBold=1.2]{KpMath-Sans}

% A higher-order version of \boldsymbol from amsbsy.sty:
\makeatletter
\DeclareRobustCommand{\versionsymbol}[2]{%
  \begingroup
  \let\@nomath\@gobble \mathversion{#1}%
  \math@atom{#2}{%
  \mathchoice%
    {\hbox{\(\m@th\displaystyle#2\)}}%
    {\hbox{\(\m@th\textstyle#2\)}}%
    {\hbox{\(\m@th\scriptstyle#2\)}}%
    {\hbox{\(\m@th\scriptscriptstyle#2\)}}}%
  \endgroup}
\makeatother

\newcommand\sansmath{\mathversion{sans}}
\newcommand\sansboldmath{\mathversion{sansbold}}
\newcommand\sanssymbol[1]{\versionsymbol{sans}{#1}}
\newcommand\sansboldsymbol[1]{\versionsymbol{sansbold}{#1}}

\begin{document}

\( [x] \, \boldsymbol{[x]} \, \sanssymbol{[x]} \, \sansboldsymbol{[x]} \)

Default \( (r, \theta, \phi ) \)

{\bfseries\boldmath Bold \( (r, \theta, \phi ) \) }

{\sffamily\sansmath Sans-serif \( (r, \theta, \phi ) \) }

{\sffamily\bfseries\sansboldmath Sans-serif bold \( (r, \theta, \phi ) \)}

\end{document}