Mathematics

texish has a TeX math mode set in Latin Modern Math through an OpenType MATH table. Math is delimited by dollar signs: a single $…$ for inline math, a doubled $$…$$ for a display centered on its own line.

Inline, like $a^2 + b^2 = c^2$, or displayed:
$$ e^{i\pi} + 1 = 0. $$

To render math on a web page (KaTeX-style, in the browser), see Rendering in the Browser.

Scripts

^ and _ attach a superscript and subscript to the preceding atom. Braces group a multi-token script.

$x^2$    $a_i$    $x_i^2$    $e^{-x^2}$    $\sum_{i=1}^{n}$

Style

A formula is set in one of four styles — display, text, script and scriptscript. Which one you are in decides the type size and how scripts are placed: a display \sum stacks its bounds above and below, while the same sum inline sets them beside it and at a smaller size. $…$ opens in text style and $$…$$ in display style.

The four declarations switch style for the rest of the enclosing sub-formula, the way \bfseries switches weight for the rest of its group. Braces bound the switch, because a {…} in math is a sub-formula of its own:

The sum $\displaystyle \sum_{i=1}^{n} x_i$ sets its bounds above and below,
even here in running text.

$$ \sum_{i=1}^{n} {\textstyle \frac{1}{2}} x_i $$   % one small fraction in a big display

The declaration has to be inside the math, not around it: the braces that bound it are a sub-formula’s braces, so {\displaystyle …} is written within a $…$, never outside one.

A switch keeps the crampedness of where it sits, so one made under a radical or in a denominator still sets its superscripts at the lowered, cramped height.

Fractions and radicals

$\frac{a}{b}$            % a fraction
$a \over b$              % the infix form
$\sqrt{2}$               $\sqrt[3]{x}$        % square and higher roots

\frac takes parameters that between them cover every fraction-like stack: the bar thickness, a pair of fences around the stack, and the style to set it at.

$\frac rule:0 {n}{k}$                        % a bare stack
$\frac left:( right:) rule:0 {n}{k}$         % which is what \binom is
$\frac rule:1.2pt {a}{b}$                    % a heavier bar
$\frac style:display {1}{2}$                 % a big fraction in running text

\dfrac, \tfrac, \binom, \dbinom and \tbinom are the combinations common enough to have names of their own.

Big operators and limits

$\sum_{i=1}^{n} i$       $\int_0^\infty f$
$\sum\limits_{i=1}^{n}$  % force stacked limits in inline style

In display style, the limits of \sum, \prod, and the like stack above and below by default.

Delimiters

\left and \right grow a delimiter to the height of the material between them.

$\left( \frac{a}{b} \right)$
$\left[ \sum_{i} x_i \right]$

That is the right rule whenever there is a formula between the two fences. A fence that stands on its own has nothing to be sized from — an opening bracket whose partner is a line away, the bar of a set-builder, a divider in a piecewise definition — and \fence sets one at a size you choose instead:

$\{\, x \fence{|} x > 0 \,\}$              % a divider at the ordinary size
$\fence size:2 {(} \frac{a}{b} \fence size:2 {)}$

size:0 is the plain glyph and each step up climbs to the font’s next larger variant, stopping at the largest it has; the default is size:1. The space around the fence follows from the delimiter — an opener keeps none from what follows it, a symmetric fence like | keeps a relation’s space on both sides — and class:open, class:close, class:rel or class:ord overrides that for a fence used against its usual sense.

Accents

$\hat{x}$    $\vec{v}$    $\widehat{abc}$

Braces over and under

\overbrace and \underbrace grow a brace to span whatever they cover. A script attached to one rides centred over (or under) the brace rather than beside it, which is how the brace gets its label:

$\overbrace{a + b + c}^{n \text{ terms}}$
$\underbrace{x_1 + x_2 + x_3}_{\text{the sum}}$

Boxes on the math axis

The math axis is the invisible line a fraction bar sits on and a fence centres about. \vcenter sets a box centred there rather than standing on the baseline, so a stack of lines beside a formula reads level with it:

$x = \vcenter{\hbox{first}\hbox{second}}$

Roman text and the math alphabets

\text sets upright words inside a formula, through the normal text path:

$V = \text{volume}$        $x \text{ for } x > 0$

The math alphabets remap their letters into the corresponding Unicode Mathematical Alphanumeric block, so the same letter can be set in any of the standard math typefaces:

$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{R} \subset \mathbb{C}$
$\mathcal{F} : \mathfrak{A} \to \mathfrak{B}$        $\mathbf{x} \in \mathbb{R}^n$

A character an alphabet has no shape for — a digit in italic or fraktur, say — falls back to its ordinary form.

Phantoms and smash

A phantom reserves the size of its argument without printing it; \smash does the opposite, printing the argument but reporting zero height and depth. They line things up that would not otherwise align.

$a \phantom{=} b$           % a gap exactly as wide as "="
$\smash{\frac{p}{q}} + r$   % a fraction that no longer spreads the line's spacing

Matrices

$\matrix{ a & b \cr c & d }$       % unbracketed
$\pmatrix{ a & b \cr c & d }$      % parentheses
$\bmatrix{ a & b \cr c & d }$      % brackets
$\cases{ x & if positive \cr -x & otherwise }$

Arrows and relations

Alongside \to / \rightarrow and the basic arrows, the long arrows and the equilibrium harpoon are available as relations:

$\longrightarrow$   $\longleftarrow$   $\longleftrightarrow$   $\longmapsto$
$\rightharpoonup$   $\rightleftharpoons$

Spacing

The TeX math-space commands insert a rigid space scaled to the font (a mu is 1/18 em):

$f(x)\,dx$        $a\;b$        $\int\!f$

mu is also a unit in its own right, so a space that is not one of the four named ones is written with the ordinary spacing commands — there is no separate math-skip command to learn:

$x \hskip 3mu y$              % the same space \, gives
\set g {0mu plus 6mu}          % and it works in a glue spec too

Displayed equations with numbers

\eqno sets an equation number flush right on a display line, and \leqno flushes it left. The formula stays centred on the measure either way. Which side a document numbers on is a house style, so it is normally set once, in the macro that wraps the display, rather than chosen equation by equation.

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \eqno(1) $$
$$ e^{i\pi} + 1 = 0 \leqno(2) $$