Published 20240131.
Last modified 20240208.
Time to read: 4 minutes.
llm
collection.
Most math markup systems have some kind of relationship with TeX and LaTeX. These are my LaTeX notes for the MathLive flavor of LaTeX.
While TeX is a programming language in the sense that it is Turing complete, its main job is to serve as a markup language for describing how your document should look. The fine control TeX offers over document structure and formatting makes it a powerful and formidable tool.
TeX is renowned for being extremely stable, for running on many different kinds of computers, and for being virtually bug free. The version numbers of TeX are converging toward the mathematical constant π, with the current version number being 3.1415926.
LaTeX (pronounced either "Lahtech" or "Laytech") is a set of macros for TeX created by Leslie Lamport. Its purpose is to simplify the TeX typesetting, especially for documents containing mathematical formulae. Within the typesetting system, its name is formatted as LATEX.
TeX is both a typographical and logical markup language, and one has to take account of both issues when writing a TeX document. In creating LaTeX, Lamport's aim was to split those two aspects. A typesetter can make a template and the writers can focus on LaTeX logical markup despite perhaps not know anything about typesetting.
In addition to the commands and options LaTeX offers, many other authors have contributed extensions, called packages or styles, which you can use for your documents. Many of these are bundled with most TeX/LaTeX software distributions; more can be found in the Comprehensive TeX Archive Network (CTAN).
Terms
Many terms can be entered just as they are.
However, you can group terms by enclosing them within {
curly braces }
.
For example, x_t
and x_{t}
both render the t
as a subscript:
x_t.
You need to group terms in order to modify them as a unit.
For example,
x_t1
renders as x_t1, which is fine, unless you meant
x_{t1}, which would be written as x_{t1}
.
Symbols
Greek
Greek symbols can be upper and lower case. Each font displays greek and other LaTeX symbols differently, and some fonts do not display them at all. You can specify them several ways; in decreasing order of preference:

LaTeX symbol, e.g.
\alpha
(\alpha),\Alpha
(\Alpha),\overline\alpha}
(\overline\alpha}) 
HTML entity name, e.g.
α
(α
),Α
(Α
)
Special
Tilde (~
) is written as \sim
, which displays as \sim
Operators
 Addition and subtraction:
1+23
renders as 1+23  Multiplication and division:
1*2/3
renders as 1*2/3  Exponentiation:
x^y
renders as x^y 
Subscript:
x_y
renders as x_y. If you need an extralow subscript, use two underbars:x__{T1}
renders as x__{T1}.  Log and natural log:
\log_{2}{42}
renders as \log_{2}{42}  Natural log:
\ln(42)
renders as \ln(42)
Arrows
Many types of arrows are possible, including annotated arrows:
\rightarrow
(\rightarrow)\longrightarrow{x}
(\longrightarrow{x})
Functions
These symbols are like functions in that they require parameters.
Fractions
Use \frac
to write a fraction. It accepts two parameters, the numerator and the denominator.
For example:
g(x) = \frac{1}{x}
renders as g(x) = \frac{1}{x}
Integrals
Write as \int^upperBound_lowerBound
or \int_lowerBound^upperBound
.
For example:
F(x) = \int^a_b \frac{1}{3}x^3
and
F(x) = \int^b_a \frac{1}{3}x^3
both render as:
F(x) = \int^b_a \frac{1}{3}x^3
Parentheses, Brackets, etc.
To cause LaTeX to display a large left parenthesis write \left(
;
for a large right parenthesis, write \right)
.
Every \left
requires a matching \right
, however the type of parenthese or bracket that follows need not match.
This works for all types of parentheses and brackets, including ()
, []
and {}
.
For example, the following are all legal. They usually automatically adjust their height according to the content that follows.
(...)
displays as (...)\left(...\right)
displays as \left(...\right)\left[...\right]
displays as \left[...\right]\left\{...\right\}
displays as \left\{...\right\}\left(...\right]
displays as \left(...\right]\left\{...\right)
displays as \left\{...\right)
Note: left and right squiggly braces must be escaped when used with \left
or \right
, as shown above.
You can also use angled parentheses (<>
or \langle\rangle
)
(\langle\rangle) and a vertical bar (
).
For example:
\langle...\rangle
displays as \langle...\rangle<...>
displays as <...>\left\langle...\right\rangle
displays as \left\langle...\right\rangle\left<...\right>
displays as \left<...\right>...
displays as ...\left...\right
displays as \left...\right
If you do not want a closing parenthesis displayed,
use a period (.
) after \right
.
For example (again, note the squiggly parenthesis must be escaped):
\left(...\right.
displays as \left(...\right.\left\{...\right.
displays as \left\{...\right.\left[...\right.
displays as \left[...\right.\left<...\right.
displays as \left<...\right.\left\langle...\right.
displays as \left\langle...\right.\left...\right.
displays as \left...\right.
The parentheses will usually resize automatically, but you can also manually control the size
of round parentheses only
with \big(
, \Big(
, \bigg(
, and \Bigg(
.
These do not need to be matched.
For example:
\big(...\big)
displays as \big(...\big)\Big(...\Big)
displays as \Big(...\Big)\bigg(...\bigg)
displays as \bigg(...\bigg)\Bigg(...\Bigg)
displays as \Bigg(...\Bigg)
For better spacing, use \bigl(
, \bigr)
, \Bigl(
, \Bigr)
,
\biggl(
, \biggr)
, \Biggr)
\bigl(...\bigr)
displays as \bigl(...\bigr)\Bigl(...\Bigr)
displays as \Big(...\Bigr)\biggl(...\biggr)
displays as \biggl(...\biggr)\Biggl(...\Biggr)
displays as \Biggl(...\Biggr)
The other types of parentheses do not work with big
variants:
\big{\big]
displays as \big{\big]\bigl{\bigr]
displays as \bigl{\bigr]\Big{\Big]
displays as \Big{\Big]\bigg{\bigg]
displays as \bigg{\bigg]\Bigg{\Bigg]
displays as \Bigg{\Bigg]
Complete documentation is here.
Alignment and Line Breaks
Locations within a series of equations can be horizontally aligned by wrapping them within \begin{aligned} ... \end{aligned}
and marking the alignment points with an ampersand (&).
Two backslashes (\\
) causes a line break.
This is useful for a sequence of statements that must be evaluated in order (top to bottom).
\begin{aligned} x & = 1 + 2 \\ longVariableName & = x * 3 \end{aligned}
Renders as:
\begin{aligned} x & = 1 + 2 \\ longVariableName & = x * 3 \end{aligned}
You could also write the ampersands without introducing extra whitespace by using {squiggly parentheses}:
\begin{aligned} x&{=} 1 + 2 \\ longVariableName&{=} x * 3 \end{aligned}
Renders as:
\begin{aligned} x&{=} 1 + 2 \\ longVariableName&{=} x * 3 \end{aligned}
CSS Classes and Rotated Text
CSS Classes can be applied to portions of an equation by using \class{className}
.
Here is a CSS class called rotate270
that rotates text counterclockwise 90 degrees:
.rotate270 { display: inlineblock; fontsize: 12pt; transform: rotate(270deg) translate(0, 130%); transformorigin: 50% 50%; }
In the above CSS style, note that the order of the translation operations is significant:

rotate(270deg)

translate(0, 130%)
# TODO this X,Y displacement vector was fudged for demonstration purposes. Need a more accurate expression.
Use the CSS class to rotate text in front of a large open square bracket like this:
\displaystyle \class{rotate270}{\text{Repeat until t=1}}\left[\begin{aligned} \\ x&{=} 1 + 2 \\ y&{=} x * 3 \\ \end{aligned}
Renders as:
\displaystyle \class{rotate270}{\text{Repeat until t=1}}\left[\begin{aligned} \\ x&{=} 1 + 2 \\ y&{=} x * 3 \\ \end{aligned}