Plurimath

Coverage of LaTeX math symbols in dedicated math fonts

Author’s picture Alexander Dyuzhev Author’s picture Ronald Tse on 14 Aug 2023

Math symbols and Unicode

Plurimath supports all math symbols supported in LaTeX, including those in the amsmath package published by the American Mathematical Society.

LaTeX supports a huge collection of symbols, and a subset of them deal with math. The following references provide a listing of commonly used LaTeX math symbols:

In total, there are 1,814 math symbols useable via predefined TeX commands. Plurimath supports usage of all these symbols, with the full list shown in its source code.

Note
 The Comprehensive LaTeX Symbols List provides a full list of symbols supported in LaTeX 2e.

Rendering of math symbols depend on availability of corresponding glyphs from fonts, and fortunately, most of these math symbols have been standardized in Unicode.

Math symbols are mostly provided in the following Unicode planes:

Note
 There are certain math symbols not (yet) available via Unicode, which is a topic for another post.

Dedicated math fonts

Introduction

In text rendering, or computer typesetting, math symbols are shown using font glyphs. There are a number of fonts today that are dedicated for rendering math symbols, these are appropriately called the "dedicated math fonts".

There are a few popular dedicated math fonts that contain the big set of mathematical symbols:

That said, the math symbol space is large. Not all math fonts provide sufficient glyph coverage for all these defined Unicode points.

When people / SDOs choose one of these fonts, they need to know what math symbols are available and which ones are not.

Cambria Math

Cambria Math is the dedicated math font designed to accompany Cambria, the default document typesetting font from Microsoft for Windows and Office. Cambria itself was meant as a replacement for the rather universal font Times New Roman.

Cambria Math is part of the Microsoft ClearType Font Collection and the first font to implement the OpenType math extension, and was released in 2007.

The design philosophy and process of Cambria Math is elaborated in the Mathematical Typesetting: Mathematical and Scientific Typesetting Solutions from Microsoft document edited by Ross Mills and John Hudson, with contributions by Richard Lawrence and Murray Sargent.

The issue with Cambria Math is its licensing and availability. As the Unicode character sets grows, newer versions of fonts are extended to handle more glyphs. However, the more recent versions of Cambria Math are not independently available and are only offered bundled inside Microsoft products, which means the usage of the font can only occur on Microsoft Windows or require some form of extraction of them.

For open source publishing or for use in non-Windows-based continuous integration systems, Cambria Math may not be the best choice.

Note
 Availability and licensing concerns of Cambria Math can be found at the Licensing and availability of math fonts article.

Official link: https://learn.microsoft.com/en-us/typography/font-list/cambria-math

STIX Two Math

The STIX Two Math font is part of the STIX fonts project.

From its website:

The mission of the Scientific and Technical Information Exchange (STIX) font creation project is the preparation of a comprehensive set of fonts that serve the scientific and engineering community in the process from manuscript creation through final publication, both in electronic and print formats.

STIX dates back to 1995 to the proposal from Arie de Ruiter of Elsevier, and is joined by the American Mathematical Society in 1997. STIX Fonts 1.0 was released in May 2010, with STIX Fonts 2.0 ("STIX Two Fonts") released in December 2016.

The STIX Two Math fonts are made available open-source and in an openly licensed manner, making it suitable for open-source publishing, re-distribution and for non-interactive continuous integration systems.

Official link: https://www.stixfonts.org

Noto Sans Math

Noto Sans Math is a dedicated math font produced by Google as part of the Noto Sans family which belongs to the Noto collection.

The Noto collection is best described by Google as:

Noto is a global font collection for writing in all modern and ancient languages.

Noto Sans Math provides 2,655 glyphs and is offered open source, available under the Open Font License, allowing anyone to use or modify the font. This makes Noto Sans Math suitable for open-source publishing, re-distribution and for non-interactive continuous integration systems.

Official link: https://fonts.google.com/noto/specimen/Noto+Sans+Math

Libertinus Math

The Libertinus Math font was originally developed as the OpenType companion for the Linux Libertine fonts.

Libertinus Math was forked from version 5.3.0 of Linux Libertine fonts, and was first released as 6.0.0 in 2016.

Libertinus Math is offered under the Open Font License which makes it suitable for open-source publishing, re-distribution and for non-interactive continuous integration systems.

Link: https://github.com/alerque/libertinus

Support of LaTeX math symbols

General

Here we compare these dedicated math fonts to visualize their coverage gaps against the list of LaTeX math symbols suppored by Plurimath.

The fonts compared are:

  • STIX Two Math (v2.13 b171, 2021-05-26)

  • Cambria Math (v5.24, 2009-04-23)

  • Cambria Math (v6.99, 2019-07-07), from Windows 10

  • Noto Sans Math (v2.0001, 2020-11-19)

  • Libertinus Math (v7.040, 2021-02-26)

Math symbols supported by dedicated math fonts

The rendered PDF with glyphs for each font can be found here.

Note
 the character # means that 'the glyph is not available in font' (except the number sign U+0023 code).

Refer to Annex A: Supported LaTeX math symbols for dedicated math fonts for the full comparison table.

Conclusion

The order of coverage concludes in this order:

  • STIX Two Math — 3 missing glyphs

  • Cambria Math v6.99 — 176 missing glyphs

  • Cambria Math v5.24 — 288 missing glyphs

  • Noto Sans Math — 321 missing glyphs

  • Libertinus Math — 792 missing glyphs

Interestingly, there are some missing glyphs in all fonts, namely:

  • arrowbullet 0x27a2

  • ballotx 0x2717

  • pencil 0x270e

STIX Two Math is the clear winner where it provides most of the math glyphs supported in LaTeX, while Cambria Math comes as a second.

Since Noto Sans and Libertinus Math are both open source projects, perhaps this is call that someone could contribute these missing glyphs to them!

Certainly, those who work with Microsoft Word which uses Cambria might want to stay with Cambria Math for stylistic alignment and pretty good coverage.

In conclusion, considering math glyph coverage with font licensing, STIX Two Math is the clear winner.

Note
 That’s why Metanorma, the open source standards publication suite, currently defaults to STIX Two Math for rendering math.

Annex A: Supported LaTeX math symbols for dedicated math fonts

Table 1. Supported LaTeX math symbols for dedicated math fonts
LaTeX symbol name Unicode character code STIX Two Math [1] Cambria Math (open) [2] Cambria Math (Windows) [3] Noto Sans Math [4] Libertinus Math [5]

barleftarrowrightarrowba

↹

✅

✅

✅

✅

✅

rightarrowshortleftarrow

⥂

✅

✅

✅

✅

❌

leftarrowshortrightarrow

⥃

✅

✅

✅

✅

❌

shortrightarrowleftarrow

⥄

✅

✅

✅

✅

❌

leftrightharpoondowndown

⥐

✅

✅

✅

✅

❌

smallblacktriangleright

▸

✅

❌

✅

❌

❌

invwhiteupperhalfcircle

◚

✅

❌

✅

❌

❌

invwhitelowerhalfcircle

◛

✅

❌

✅

❌

❌

concavediamondtickright

⟣

✅

✅

✅

✅

❌

nvtwoheadrightarrowtail

⤗

✅

✅

✅

✅

❌

nVtwoheadrightarrowtail

⤘

✅

✅

✅

✅

❌

updownharpoonrightright

⥏

✅

✅

✅

✅

❌

updownharpoonsleftright

⥮

✅

✅

✅

✅

❌

downupharpoonsleftright

⥯

✅

✅

✅

✅

❌

leftrightarrowtriangle

⇿

✅

✅

✅

✅

✅

smallblacktriangleleft

◂

✅

❌

✅

❌

❌

blackcircleulquadwhite

◕

✅

❌

✅

❌

✅

concavediamondtickleft

⟢

✅

✅

✅

✅

❌

leftrightharpoonupdown

⥊

✅

✅

✅

✅

❌

leftrightharpoondownup

⥋

✅

✅

✅

✅

❌

updownharpoonrightleft

⥌

✅

✅

✅

✅

❌

updownharpoonleftright

⥍

✅

✅

✅

✅

❌

downtrianglerightblack

⧩

✅

✅

✅

✅

❌

partialmeetcontraction

⪣

✅

✅

✅

✅

❌

nvtwoheadleftarrowtail

⬼

✅

❌

❌

✅

❌

nVtwoheadleftarrowtail

⬽

✅

❌

❌

✅

❌

underrightharpoondown

⃬

✅

❌

❌

✅

❌

barovernorthwestarrow

↸

✅

✅

✅

✅

✅

rangledownzigzagarrow

⍼

✅

✅

✅

✅

❌

circlebottomhalfblack

◒

✅

❌

✅

❌

✅

twoheadrightarrowtail

⤖

✅

✅

✅

✅

❌

updownharpoonleftleft

⥑

✅

✅

✅

✅

❌

downharpoonsleftright

⥥

✅

✅

✅

✅

❌

leftrightharpoonsdown

⥧

✅

✅

✅

✅

❌

rightleftharpoonsdown

⥩

✅

✅

✅

✅

❌

downtriangleleftblack

⧨

✅

✅

✅

✅

❌

blackdiamonddownarrow

⧪

✅

✅

✅

✅

❌

closedvarcupsmashprod

⩐

✅

✅

✅

✅

❌

underleftharpoondown

⃭

✅

❌

❌

✅

❌

CapitalDifferentialD

ⅅ

✅

✅

✅

✅

❌

bigblacktriangledown

▼

✅

❌

✅

❌

✅

circlerighthalfblack

◑

✅

❌

✅

❌

✅

blackrighthalfcircle

◗

✅

❌

✅

❌

✅

blackcircledrightdot

⚈

✅

❌

❌

❌

❌

whiteinwhitetriangle

⟁

✅

❌

✅

✅

❌

whitesquaretickright

⟥

✅

✅

✅

✅

❌

barrightarrowdiamond

⤠

✅

✅

✅

✅

❌

downrightcurvedarrow

⤵

✅

✅

✅

✅

❌

rightdowncurvedarrow

⤷

✅

✅

✅

✅

❌

curvearrowrightminus

⤼

✅

✅

✅

✅

❌

leftrightarrowcircle

⥈

✅

✅

✅

✅

❌

twoheaduparrowcircle

⥉

✅

✅

✅

✅

❌

leftrightharpoonupup

⥎

✅

✅

✅

✅

❌

leftrightharpoondown

⥐

✅

✅

✅

✅

❌

dashrightharpoondown

⥭

✅

✅

✅

✅

❌

blackcircledownarrow

⧭

✅

✅

✅

✅

❌

NestedGreaterGreater

⪢

✅

✅

✅

✅

❌

twoheadleftarrowtail

⬻

✅

❌

❌

✅

❌

rightarrowbackapprox

⭈

✅

❌

❌

✅

❌

leftrightsquigarrow

↭

✅

✅

✅

✅

✅

whitearrowupfrombar

⇪

✅

✅

✅

❌

✅

blockthreeqtrshaded

▓

✅

❌

❌

❌

❌

blackinwhitediamond

◈

✅

❌

✅

❌

❌

circlelefthalfblack

◐

✅

❌

✅

❌

✅

blacklefthalfcircle

◖

✅

❌

✅

❌

✅

blackcircledtwodots

⚉

✅

❌

❌

❌

❌

whitesquaretickleft

⟤

✅

✅

✅

✅

❌

longrightsquigarrow

⟿

✅

✅

✅

✅

✅

nvtwoheadrightarrow

⤀

✅

✅

✅

✅

❌

nVtwoheadrightarrow

⤁

✅

✅

✅

✅

❌

diamondleftarrowbar

⤟

✅

✅

✅

✅

❌

leftdowncurvedarrow

⤶

✅

✅

✅

✅

❌

downharpoonrightbar

⥕

✅

✅

✅

✅

❌

rightharpoondownbar

⥗

✅

✅

✅

✅

❌

bardownharpoonright

⥝

✅

✅

✅

✅

❌

barrightharpoondown

⥟

✅

✅

✅

✅

❌

upharpoonsleftright

⥣

✅

✅

✅

✅

❌

rightharpoonsupdown

⥤

✅

✅

✅

✅

❌

leftrightharpoonsup

⥦

✅

✅

✅

✅

❌

rightleftharpoonsup

⥨

✅

✅

✅

✅

❌

dashleftharpoondown

⥫

✅

✅

✅

✅

❌

twoheadleftdbkarrow

⬷

✅

❌

❌

✅

❌

leftarrowbackapprox

⭂

✅

❌

❌

✅

❌

rightharpoonaccent

⃑

✅

✅

✅

✅

✅

overleftrightarrow

⃡

✅

✅

✅

✅

✅

acwopencirclearrow

↺

✅

✅

✅

✅

✅

upharpoonrightdown

⇂

✅

✅

✅

✅

✅

circleonrightarrow

⇴

✅

✅

✅

✅

✅

rightarrowtriangle

⇾

✅

✅

✅

✅

✅

PrecedesSlantEqual

≼

✅

✅

✅

✅

✅

SucceedsSlantEqual

≽

✅

✅

✅

✅

✅

measuredrightangle

⊾

✅

✅

✅

✅

❌

blackinwhitesquare

▣

✅

❌

✅

❌

❌

parallelogramblack

▰

✅

❌

✅

❌

❌

bigblacktriangleup

▲

✅

❌

✅

❌

✅

blacktriangleright

▶

✅

❌

✅

❌

✅

smalltriangleright

▹

✅

❌

✅

❌

❌

circletophalfblack

◓

✅

❌

✅

❌

✅

inversewhitecircle

◙

✅

❌

✅

❌

❌

trianglerightblack

◮

✅

❌

✅

❌

❌

longleftrightarrow

⟷

✅

✅

✅

✅

✅

Longleftrightarrow

⟺

✅

✅

✅

✅

✅

curvearrowleftplus

⤽

✅

✅

✅

✅

❌

ccwundercurvearrow

⤿

✅

✅

✅

✅

❌

leftrightharpoonup

⥎

✅

✅

✅

✅

❌

rightupdownharpoon

⥏

✅

✅

✅

✅

❌

RightDownVectorBar

⥕

✅

✅

✅

✅

❌

barleftharpoondown

⥖

✅

✅

✅

✅

❌

DownRightVectorBar

⥗

✅

✅

✅

✅

❌

downharpoonleftbar

⥙

✅

✅

✅

✅

❌

RightDownTeeVector

⥝

✅

✅

✅

✅

❌

leftharpoondownbar

⥞

✅

✅

✅

✅

❌

DownRightTeeVector

⥟

✅

✅

✅

✅

❌

bardownharpoonleft

⥡

✅

✅

✅

✅

❌

leftharpoonsupdown

⥢

✅

✅

✅

✅

❌

rightrightharpoons

⥤

✅

✅

✅

✅

❌

rightharpoonupdash

⥬

✅

✅

✅

✅

❌

circledwhitebullet

⦾

✅

✅

✅

✅

❌

errbarblackdiamond

⧱

✅

✅

✅

✅

❌

longleftsquigarrow

⬳

✅

❌

❌

✅

❌

nvtwoheadleftarrow

⬴

✅

❌

❌

✅

❌

nVtwoheadleftarrow

⬵

✅

❌

❌

✅

❌

bsimilarrightarrow

⭇

✅

❌

❌

✅

❌

rightarrowbsimilar

⭌

✅

❌

❌

✅

❌

rightpentagonblack

⭓

✅

❌

❌

❌

❌

leftharpoonaccent

⃐

✅

✅

✅

✅

✅

twoheadrightarrow

↠

✅

✅

✅

✅

✅

cwopencirclearrow

↻

✅

✅

✅

✅

✅

upharpoonleftdown

⇃

✅

✅

✅

✅

✅

leftrightharpoons

⇋

✅

✅

✅

✅

✅

rightleftharpoons

⇌

✅

✅

✅

✅

✅

leftarrowtriangle

⇽

✅

✅

✅

✅

✅

kernelcontraction

∻

✅

✅

✅

✅

✅

vardoublebarwedge

⌆

✅

✅

✅

❌

❌

varhexagonlrbonds

⌬

✅

❌

❌

❌

❌

varcarriagereturn

⏎

✅

✅

✅

❌

❌

blackpointerright

►

✅

❌

✅

❌

❌

whitepointerright

▻

✅

❌

✅

❌

❌

blacktriangledown

▾

✅

❌

✅

❌

❌

smalltriangledown

▿

✅

❌

✅

❌

❌

blacktriangleleft

◀

✅

❌

✅

❌

✅

smalltriangleleft

◃

✅

❌

✅

❌

❌

circleurquadblack

◔

✅

❌

✅

❌

✅

triangleleftblack

◭

✅

❌

✅

❌

❌

acwgapcirclearrow

⟲

✅

✅

✅

✅

✅

rightarrowonoplus

⟴

✅

✅

✅

✅

❌

rightarrowdiamond

⤞

✅

✅

✅

✅

❌

uprightcurvearrow

⤴

✅

✅

✅

✅

❌

cwundercurvearrow

⤾

✅

✅

✅

✅

❌

leftupdownharpoon

⥑

✅

✅

✅

✅

❌

rightharpoonupbar

⥓

✅

✅

✅

✅

❌

barupharpoonright

⥔

✅

✅

✅

✅

❌

DownLeftVectorBar

⥖

✅

✅

✅

✅

❌

LeftDownVectorBar

⥙

✅

✅

✅

✅

❌

barrightharpoonup

⥛

✅

✅

✅

✅

❌

upharpoonrightbar

⥜

✅

✅

✅

✅

❌

DownLeftTeeVector

⥞

✅

✅

✅

✅

❌

LeftDownTeeVector

⥡

✅

✅

✅

✅

❌

leftharpoonupdash

⥪

✅

✅

✅

✅

❌

similarrightarrow

⥲

✅

✅

✅

✅

✅

rightarrowsimilar

⥴

✅

✅

✅

✅

✅

measuredangleleft

⦛

✅

✅

✅

✅

❌

errbarblacksquare

⧯

✅

✅

✅

✅

❌

errbarblackcircle

⧳

✅

✅

✅

✅

❌

diamondrightblack

⬗

✅

❌

❌

❌

❌

circleonleftarrow

⬰

✅

❌

❌

✅

✅

bsimilarleftarrow

⭁

✅

❌

❌

✅

❌

leftarrowbsimilar

⭋

✅

❌

❌

✅

❌

twoheadleftarrow

↞

✅

✅

✅

✅

✅

twoheaddownarrow

↡

✅

✅

✅

✅

✅

circlearrowright

↻

✅

✅

✅

✅

✅

rightharpoondown

⇁

✅

✅

✅

✅

✅

downharpoonright

⇂

✅

✅

✅

✅

✅

uparrowdownarrow

⇅

✅

✅

✅

✅

✅

rightrightarrows

⇉

✅

✅

✅

✅

✅

downarrowuparrow

⇵

✅

✅

✅

✅

✅

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thermod

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rsolbar

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bigodot

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varprod

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npolint

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project

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plushat

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simplus

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plusdot

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plussim

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intprod

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twocaps

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veeodot

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congdot

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eqqplus

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ddotseq

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equivDD

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ltquest

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gtquest

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lesdoto

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✅

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gesdoto

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eqqless

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simless

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bumpeqq

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precneq

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✅

✅

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succneq

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✅

✅

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preceqq

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✅

✅

✅

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succeqq

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✅

✅

✅

✅

✅

llcurly

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✅

✅

✅

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ggcurly

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submult

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supmult

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subedot

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supedot

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lsqhook

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rsqhook

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suphsub

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supdsub

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✅

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topfork

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revnmid

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✅

✅

❌

nhVvert

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✅

✅

✅

✅

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lllnest

⫷

✅

✅

✅

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❌

gggnest

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✅

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trslash

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hzigzag

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overbar

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upGamma

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upDelta

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upTheta

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upKappa

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✅

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upSigma

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upOmega

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upalpha

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upgamma

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updelta

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uptheta

θ

✅

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upkappa

κ

✅

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upsigma

σ

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upsilon

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upomega

ω

✅

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varbeta

ϐ

✅

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upvarpi

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Digamma

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digamma

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✅

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upKoppa

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✅

upkoppa

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✅

✅

✅

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✅

upSampi

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✅

✅

✅

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✅

upsampi

ϡ

✅

✅

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epsilon

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percent

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greater

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✅

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sptilde

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✅

✅

✅

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✅

matheth

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✅

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dagger

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bullet

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second

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Exclam

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fourth

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qprime

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ddddot

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hslash

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mapsup

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forall

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coprod

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propto

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oiiint

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nsimeq

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✅

✅

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approx

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Bumpeq

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✅

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bumpeq

≏

✅

✅

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eqcirc

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✅

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circeq

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✅

✅

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✅

✅

wedgeq

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✅

✅

✅

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✅

stareq

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✅

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measeq

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nequiv

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nvdash

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✅

✅

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nvDash

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nVdash

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nVDash

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✅

✅

✅

✅

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prurel

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✅

✅

✅

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scurel

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Otimes

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egsdot

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eqqgtr

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simgtr

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preceq

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odot

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dint

⋂

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duni

⋃

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cdot

⋅

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star

⋆

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hash

⋕

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nisd

⋺

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obar

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rres

▷

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dres

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flat

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lang

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1. STIX Two Math v2.13 b171
2. Cambria Math v5.24
3. Cambria Math v6.99
4. Noto Sans Math v2.0001
5. Libertinus Math v7.040