Math alphabets

Math alphabets are a counterpart to the mathematical alphanumeric symbols block in Unicode. Both are “to be used for mathematical variables where style variations are important semantically”. The font guide [fntguide] defines in section 3:

Some math fonts are selected explicitly by one-argument commands such as \mathsf{max} or \mathbf{vec}; such fonts are called math alphabets.

Math fonts [...] have the same five attributes as text fonts: encoding, family, series, shape and size. However, there are no commands that allow the attributes to be individually changed. Instead, the conversion from math fonts to these five attributes is controlled by the math version.

The predefined math alphabets are:

\mathnormal	default1
\mathrm	roman2
\mathbf	bold roman
\mathsf	sans serif
\mathit	text italic
\mathtt	typewriter
\mathcal	calligraphic

1

\mathnormal is used by default for alphanumeric characters in math mode. It sets the letter shape according to character class and math style. (Table 1 shows the default letter shapes for common math styles).

2

The specifier “roman” is ambiguous: roman shape stands for upright, while roman type stands for serif (as opposed to sans serif).

Many packages define additional math alphabets (cf. Table 5).

In contrast to the similar named text commands, math alphabets are not orthogonal, e. g., the code $\mathit{\mathbf{a}}$ sets the letter a in upright bold type.

Math versions

The number of mathematical symbols exceeds the maximal number of characters in a TeX font file by an order of magnitude.³ Grouping math fonts with common characteristics in math versions simplifies the setting of font attributes for mathematical expressions.

Math versions set up “math symbol fonts” for non-alphanumeric symbols and bind the math alphabet commands to fonts using default values for non-specified font attributes. TeX limits the number of (symbol + alphanumeric) fonts per math version to 16.

The predefined math versions are normal and bold with the defaults:

	normal	bold
type	serif	serif
weight	medium	bold
shape	upright	upright

Packages can define additional math versions, e. g., the wrisym package defines a mono math version. A sans math version example is available from a comp.text.tex post

Math versions are intended for mathematical content in a special context, e. g., a bold section heading. Setting a math version resembles the individual selection of text font attributes (bold, sans-serif, monospaced).

Math versions can only be changed outside of math mode. The commands \boldsymbol (amsmath) and \bm (bm) behave like “in-line math versions”: they typeset their argument using the fonts of the bold math version but can be used inside math mode.

Example: four ways to set the letter a in a bold sans-serif font:

% Text                 Math:
\textbf{\textsf{a}}    $\bm{\mathsf{a}}$
\bfseries \textsf{a}   \mathversion{bold} $\mathsf{a}$

3

Unicode provides about 2500 math characters. Font files used by 8-bit TeX engines can hold up to 256 characters. The standard math fonts adhere to the original limit of 128 characters.

Math styles

A math style is a document-level feature that determines the default letter shape in math mode (i. e. the shape attribute of letters in the \mathnormal math alphabet).

LaTeX defaults to the “TeX” math style (without naming it such). Alternative math styles are introduced by extension packages (Table 2).

OML font encoding

The LaTeX font encodings guide [encguide] names the OML encoding TeX math italic and defines:

The OML encoding contains italic Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols.

The reference to italic shape is odd:

• No other font encoding is specific to the font shape.

• The different font selection and the semantic of font features in math do not interfere with the font encoding: Both, \DeclareSymbolFont and \DeclareMathAlphabet require a shape argument. Thus it is possible to set up OML encoded math alphabets in roman {n} as well as italic {it} shape without conflicts.

This seems to be more a remnant of pre-NFSS times than a necessary restriction – there is only one OML encoded font in Knuth's Computer Modern fonts: Computer Modern Math Italic (cmmi).

Proposals:

• Drop the italic from the definition. Optionally add an explanation:

  The OML encoding contains Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols. It first appeared in the Computer Modern Math Italic (cmmi) font.

• The name TeX math italic can be interpreted as “the encoding of Computer Modern Math Italic” rather than “an encoding for math italic” fonts.

  A less confusing name would be TeX math letters or Original/Old Math Letters. The latter would also explain the acronym OML.

OML Support

Unfortunately, support for the OML encoding is missing for many font families even if the text font defines Greek letters. Supported font families can be found searching for oml*.fd files and grepping for DeclareFont.*OML in *.sty files.

Table 3 lists the findings for a selection of TeXLive 2009 + some additionally installed font packages.

• If there is an alias (substitution) from the text font to a math-variant, only the text font is listed.

• Many text fonts define substitutions also for upright shape, however mapping to an italic variant of the OML encoded font. These are not listed as supporting m/n or bx/n here.

Unicode math alphabets

Chapter 2 Mathematical Character Repertoire of [tr25] lists 14 Mathematical Alphabets in Table 2.1. These mathematical alphabets are a superset of the predefined math alphabets in the LaTeX core.

Unicode assignes code points to most letters of the mathematical alphabets in the mathematical alphanumeric symbols Unicode block. The plain (upright, serifed) letters have been unified with the existing characters in the Basic Latin and Greek blocks.

Table 4 maps the 14 Unicode mathematical alphabets to LaTeX commands according to the naming scheme below. Table 5 lists the status of LaTeX support for the mathematical alphanumeric symbols. Full support is provided by the unicode-math package.

4

(1, 2)

plain standard characters outside the mathematical alphanumeric symbols Unicode block.

\mathbf{d}     % MATHEMATICAL BOLD SMALL D
\mathsfbfit{d} % MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL D.