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fontspec sets hundreds of things and unicode-math thousands, but i assume you mean the main user-settable fonts that you might want to change. fontspec defaults to Latin Modrern so more or less th esame as \setmainfont{Latin Modern Regular} which is the same font as used if the package is not loaded (the family name is lmr with the default settings but ...

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The only OpenType sans serif math font I know of is GFS Neohellenic Math. \documentclass{article} \usepackage{amsmath} \usepackage{fontspec} \usepackage[]{unicode-math} \setsansfont{GFSNeohellenic}[ Extension=.otf, UprightFont=*, ItalicFont=*It, BoldFont=*Bold, BoldItalicFont=*BoldIt, ] \setmathfont{Latin Modern Math} \setmathfont{...

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I'm not sure there's an official interface; anyway, this works. \documentclass{article} \usepackage{unicode-math} \setmathfont{XITSMath-Regular.otf} \Umathchardef\circledR="0 \symsymbols "24C7 \begin{document} circleddash: $\circleddash$ circledparallel: $\circledparallel$ circledR: $\circledR$ \end{document}

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Ulrike Fischer already provided an answer for unicode-math, and I’d recommend you use that when you can and PDFTeX when you have to. In case you have to, here is a solution that gives you an upright π (correct according to ISO) with PDFTeX: \documentclass{article} \tracinglostchars=2 \usepackage{fourier} \usepackage[OMLmathrm, rmdefault=mdput]{isomath} \...

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\documentclass{article} \usepackage{siunitx} \usepackage[mathrm=sym]{unicode-math} \begin{document} \num{\pi/3} \end{document}

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They do it because it’s easy. Most OpenType math fonts are extensions of an existing font that already covers those ranges, or have a matching text font that does. Even if one doesn’t, nearly every glyph in those blocks combines accents and letters that the font already needs to have. The basic upright Latin letters are used for \symup (although you’re ...

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bookmarks can contain only rather simple text. This means that hyperref has to translate LaTeX input into something that makes sense there. For this it often drops or replace problematic content. In general hyperref is quite good to at least avoid errors in this process, but it can't handle commands which have been let to a char: https://github.com/latex3/...

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I believe you've encountered a basic shortcoming in the way pdf bookmarks may be specified, not a shortcoming in either unicode-math or hyperref per se. The \texorpdfstring device may be used to work around this shortcoming. E.g., under LuaLaTeX, \section{title \texorpdfstring{$\alpha$}{$\symit{alpha}$}} will result in title alpha (note: not title α) ...

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