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As titled.

I've been creating a few personal OpenType math fonts (by combining existing fonts, like Minion, with existing math fonts); one strange thing that I've observed along the way is that it seems like almost every OpenType math font defines the Latin-1 Supplement, Latin Extended A, and Latin Extended B character sets. For example, see this specimen table for Fira Math (Fira Math even defines Cyrillic, which I don't quite understand either, for reasons below)

However, as far as I can tell (for LuaLaTeX use at least), unicode-math doesn't map any of these glyphs to characters in math mode. Accented characters in math mode seem to always be created from combining the original characters with marks defined in U+00300 onwards (the "Combining Diacritical Marks" section in Fira Math's specimen).

Also, personally, I always setup my fonts to pull the regular upright glyphs (used in mathrm, etc.) from the regular document font - which I can always trust to be properly configured for good typesetting.*

(* If anyone finds this point confusing, I'll admit that I'm not entirely sure where mathrm is sourced from - the regular font from fontspec or the math font specified by unicode-math?)

In other words, if I was using Latin Modern Math as my math font, I would ask LaTeX to pull all the upright glyphs from Latin Modern. (This use case might not make much sense for Latin Modern, but for my own custom fonts - and as I'm not a professional typographer - I obviously choose to pull the upright fonts from the original file as they were created by a professional typographer. And I don't see why one would bother to duplicate the same glyphs, without changes, into the math font). I don't see why they need to be defined if they are either never used or are simply duplicates from the regular non-math font (as why not simply source the original font?)

Even stranger are the unicode fraction character sets (which Fira Math also defines, according to its specimen table), which I don't think are ever used in mathmode, let alone being commonplace in math typesetting. TeX fractions seem to be always preferred and used in my experience.

In summary, I don't quite see why these character sets are defined in OpenType Math fonts, at least for LaTeX use. They seem redundant to me, as they are either unused or seem to be simply duplicated (with no adjustments) from the regular non-math font:

  • Latin-1 Supplement
  • Latin Extended A
  • Latin Extended B
  • unicode fractions (in both the Latin-1 Supplement set and Ux2150 onwards - "Number Forms" section in the Fira specimen)
  • (Cyrillic)
  • (the upright alphabet in Basic Latin)

There are only a few explanations that I can see why they were defined:

  • So that the OpenType Math font can also used as the regular document font. This seems like a very odd use case (and doesn't seem functional either - as you would need to source in the italic glyphs with unmodified spacing from the regular non-math font to have properly typeset italic)
  • They were defined for non-LaTeX use cases (like in Microsoft Word). I'm not sure if Word even uses these character sets, but it seems like a possible explanation.
  • XeLaTeX or mathspec use. No clue if this is true, but it doesn't seem to me that they are used in LuaLaTeX + unicode-math.

Am I correct in thinking that these glyphs are actually never used (and/or can be supplemented by asking LaTeX to source the glyphs from the regular non-math font), in a LuaLaTeX, unicode-math context?

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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 correct that no math font seems to take advantage of this to use different alphabets for upright math letters, with \symup, than for words in math mode, with \mathrm—you must load a second font for that) and some math papers do use Cyrillic letters as math symbols, so those are not totally useless in math mode.

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  • This makes sense - I never considered OpenType Math fonts using all of the original font's glyphs as a base (the "good coding practice" side of me is half-questioning why the unused glyphs weren't simply deleted. But I suppose the 'bloat' isn't doing any harm to the font by remaining + it does have some redundancy functionality in case someone really wants to use the glyphs from the math font.) – Longjing Nov 11 '20 at 5:01
  • "some math papers do use Cyrillic letters as math symbols, so those are not totally useless in math mode" - Do you mean upright Cyrillic letters, or italicized Cyrillic? I've never seen the latter defined in the math fonts I've looked over somewhat thoroughly (Latin Modern, Garamond Math, Fira Math). I agree with you in that I can see the former being used - though, I still question why anyone would want to get the Cyrillic glyphs from the math font instead of the regular font. Also, how would one even access them in LuaLatex? – Longjing Nov 11 '20 at 5:05
  • Cyrillic math symbols is a fairly common question: tex.stackexchange.com/questions/218159/… Defining new symbols (and operators) is possible with Latex. – Cicada Nov 11 '20 at 8:36
  • @Longjing Unicode does not define italic Cyrillic mathematical alphanumeric characters. – Davislor Nov 11 '20 at 15:46

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