Math mode in LaTeX

Preliminery

If you are NOT fimilar with catcode, mathcode, delcode etc, please see my blog: TeX Coding or other material to learn it fisrt.

If you are not familar with LaTeX text font and math font, you can see by blog LaTeX font Guide to learn it.

font family

Unlike the font scheme(NFSS) in LaTeX, font familt in plain tex is something different. Details as below:

• math roman fonts (family 0)
• math italic fonts (family 1)
• symbol fonts (family 2)
• the extension fonts (family 3)

math atom

Each character(a,b,c, +/-, etc) or control sequence(\alpha, \sum, etc) in math fomulars has its own type, which control its spaces arround(before, after, top, below, etc) it. The math symbol type(atom type) is as follows:

When you need some new math symbols, you need to specify to which atom type this symbol should belong during declaring it.

math code

All of these commands \mathcode, \mathcahr, \mathchardef are related to mathcode in TeX, which is similar to catcode in text but far more complex that it.

Plain TeX

In plain TeX, the syntax of command \mathcode is:

\mathcode`<single token>[=]
    <class(atom type)(1 digits)>
    <font family(1 digits)>
    <glyph slot(2 digits)>

There is a command \mathchar – \mathchardef similar to \char – \chardef for text font. See below:

XeTeX

XeTeX provides command \Umathcode (similar to the original command \mathcode in plain TeX). It also provides command \Umathcodenum, which use a bit-packed single argument.

Thus the syntax is:

\Umathcode<char slot>[=]
    <atom type>
    <font family>
    <glyph slot>

\Umathcodenum<char slot>[=]
    <atom type/font family/glyph slot>

delimiter code

Beside mathcode, catcode, there is a code called delimiter code, you can use command \delcode to set it. For detailed info, see: TeX Coding.

LaTeX 2e

symbol font

How many math symol font pre-defined in LaTeX 2e ? see example below:

% 1.
\DeclareSymbolFont{sfoperators}{OT1}{cmss}{m}{n}
\DeclareSymbolFontAlphabet{\mathsf}{sfoperators}

% 2.
\DeclareSymbolFont{LMletters}{OML}{lmm}{m}{it}
\DeclareMathSymbol{\lmstar}{\mathbin}{LMletters}{63}

There are infinite many math symbol font, see fntguide Page 14:

\DeclareSymbolFont {⟨sym-font⟩} {⟨encoding⟩} {⟨family⟩} {⟨series⟩} {⟨shape⟩}. If this is the first declaration for ⟨sym-font⟩ then a new symbol font with this name is created (i.e. this identifier is assigned to a new TEX math group)

So math symbol font from 3 sources:

• the predefine 4 types: operators, letters, symbols, largesymbols
• From some package: like AMSa, AMSb in amsfont package; zeur in eulervm package
• The type that your define by command \DeclareSymbolFont

operator font bug ?

Is this a Bug for \operator@font in amsopn.sty or ctex.sty? See definition in latex2e: Page 631

The definition in ctex:

❯ latexdef -p ctex \symoperators
\symoperators:
\char"0

\the\symoperators:
0

The definitions in source 2e:ltmath.dtx - Page 722

\DeclareRobustCommand\log{\mathop{\operator@font log}\nolimits}
\DeclareRobustCommand\lg{\mathop{\operator@font lg}\nolimits}
\DeclareRobustCommand\ln{\mathop{\operator@font ln}\nolimits}
\DeclareRobustCommand\lim{\mathop{\operator@font lim}}
\DeclareRobustCommand\limsup{\mathop{\operator@font lim\,sup}}
\DeclareRobustCommand\liminf{\mathop{\operator@font lim\,inf}}
\DeclareRobustCommand\sin{\mathop{\operator@font sin}\nolimits}
...

miscellany

strut and phantom

Reference from “The TeXbook”:

There’s a way out of this dilemma, using an important idea called a “strut.” Plain TEX defines \strut to be an invisible box of width zero that extends just enough above and below the baseline so that you would need no interline glue at all if every line contained a strut.

• strut related:

  • \mathstrut in math mode:

  \DeclareRobustCommand\mathstrut{\vphantom(}

  • and the \strut in text mode:

  \def\strut{\relax\ifmmode\copy\strutbox\else\unhcopy\strutbox\fi}

• phantom related:

\DeclareRobustCommand\vphantom{\v@true\h@false\ph@nt}
\DeclareRobustCommand\hphantom{\v@false\h@true\ph@nt}
\DeclareRobustCommand\phantom{\v@true\h@true\ph@nt}

math surround

Besides, you can control the space arround math atom by command \mathsurround, a simple example:

abc|{\mathsurround10pt$xyz$}|abc|$xyz$|abc 

% abc| xyz |abc|xyz|abc

Additional Reference:

TEX does, in fact, insert additional space before and after each formula; the amount of such space is called \mathsurround, which is a ⟨dimen⟩-valued parameter.

style in math

There are 2 commands \mathpalette, \mathchoice related to style in math fomulars. Definition of \mathpalette, see:

\def\mathpalette#1#2{%
    \mathchoice
    {#1\displaystyle{#2}}%
    {#1\textstyle{#2}}%
    {#1\scriptstyle{#2}}%
    {#1\scriptscriptstyle{#2}}}

What is \mathchoice doing for us? Use different construction in different math style. Syntax of this command is:

\mathchoice{⟨D/D' math⟩}{⟨T/T' math⟩}{⟨S/S' math⟩}{⟨SS/SS' math⟩}

An example using example for “The TeX book”:

\def\puzzle{{\mathchoice{D}{T}{S}{SS}}}
$$\puzzle{\puzzle\over\puzzle^{\puzzle^\puzzle}}$$

The output look like:

Then you may know what \mathpalette doing .