Test

Posted 2020-11-12 alessandro

(Deutsch: MathJax: LaTeX Basic Tutorial und Referenz)

To see how any formula was written in any question or answer, including this one, right-click on the expression it and choose "Show Math As > TeX Commands". (When you do this, the ‘$‘ will not display. Make sure you add these. See the next point.)

For inline formulas, enclose the formula in $...$. For displayed formulas, use $$...$$.
These render differently. For example, type
$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
to show ∑ni=0i2=(n2+n)(2n+1)6

(which is inline mode) or type
\[\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\]
to show
∑i=0ni2=(n2+n)(2n+1)6

(which is display mode).

For Greek letters, use \alpha, \beta, …, \omega: α,β,…ω
. For uppercase, use \Gamma, \Delta, …, \Omega: Γ,Δ,…,Ω

.

For superscripts and subscripts, use ^ and _. For example, x_i^2: x2i
, \log_2 x: log2x

.

Groups. Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}. If you do 10^10, you will get a surprise: 1010
. But 10^{10} gives what you probably wanted: 1010. Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is xyz, and x^{y^z} is xyz. Observe the difference between x_i^2 x2i and x_{i^2} xi2

.

Parentheses Ordinary symbols ()[] make parentheses and brackets (2+3)[4+4]
. Use { and } for curly braces {}

.

These do not scale with the formula in between, so if you write (\frac{\sqrt x}{y^3}) the parentheses will be too small: (x√y3)
. Using \left(…\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is (x√y3)

.

\left and\right apply to all the following sorts of parentheses: ( and ) (x)
, [ and ] [x], { and } {x}, | |x|, \vert |x|, \Vert ∥x∥, \langle and \rangle ?x?, \lceil and \rceil ?x?, and \lfloor and \rfloor ?x?. \middle can be used to add additional dividers. There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is 12}

.

If manual size adjustments are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives (((((x)))))

.

Sums and integrals \sum and \int; the subscript is the lower limit and the superscript is the upper limit, so for example \sum_1^n ∑n1
. Don‘t forget {…} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is ∑∞i=0i2. Similarly, \prod ∏, \int ∫, \bigcup ?, \bigcap ?, \iint ?, \iiint ?

.

Fractions There are two ways to make these. \frac ab applies to the next two groups, and produces ab
; for more complicated numerators and denominators use {…}: \frac{a+1}{b+1} is a+1b+1. If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1} is a+1b+1

.

Fonts

Use \mathbb or \Bbb for "blackboard bold": CHNQRZ

.
Use \mathbf for boldface: ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz
.
Use \mathtt for "typewriter" font: ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz
.
Use \mathrm for roman font: ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz
.
Use \mathsf for sans-serif font: ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz
.
Use \mathcal for "calligraphic" letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Use \mathscr for script letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Use \mathfrak for "Fraktur" (old German style) letters: ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz

.

Radical signs Use sqrt, which adjusts to the size of its argument: \sqrt{x^3} x3??√
; \sqrt[3]{\frac xy} xy??√3

. For complicated expressions, consider using {...}^{1/2} instead.

Some special functions such as "lim", "sin", "max", "ln", and so on are normally set in roman font instead of italic font. Use \lim, \sin, etc. to make these: \sin x sinx
, not sin x sinx. Use subscripts to attach a notation to \lim: \lim_{x\to 0}
limx→0

There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:

\lt \gt \le \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq <>≤≤≦?≥≥≧?≠

. You can use \not to put a slash through almost anything: \not\lt ≮
but it often looks bad.
\times \div \pm \mp ×÷±?
. \cdot is a centered dot: x?y
\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing ∪∩?????∈???
{n+1 \choose 2k} or \binom{n+1}{2k} (n+12k)
\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto →→←???
\land \lor \lnot \forall \exists \top \bot \vdash \vDash ∧∨????⊥??
\star \ast \oplus \circ \bullet ??⊕°?
\approx \sim \simeq \cong \equiv \prec \lhd ≈～??≡?,?
.
\infty \aleph_0 ∞?0
\nabla \partial ?? \Im \Re IR
For modular equivalence, use \pmod like this: a\equiv b\pmod n a≡b(modn)
.
\ldots is the dots in a1,a2,…,an
\cdots is the dots in a1+a2+?+an
Some Greek letters have variant forms: \epsilon \varepsilon ?ε
, \phi \varphi ?φ, and others. Script lowercase l is \ell ?

.

Detexify lets you draw a symbol on a web page and then lists the TEX
symbols that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supported LATEX commands, and one can also check Dr. Carol JVF Burns‘s page of TEX

Commands Available in MathJax.

Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in: a?b and a????b are both ab
. To add more space, use , for a thin space ab; ; for a wider space ab. \quad and \qquad are large spaces: ab, ab

.

To set plain text, use \text{…}: {x∈s∣x is extra large}

. You can nest \(…\) inside of \text{…}.

Accents and diacritical marks Use \hat for a single symbol x^
, \widehat for a larger formula xy?. If you make it too wide, it will look silly. Similarly, there are \bar xˉ and \overline xyzˉˉˉˉˉˉˉˉ, and \vec x? and \overrightarrow xy?→ and \overleftrightarrow xy←→. For dots, as in ddxxx˙=x˙2+xx¨

, use \dot and \ddot.

Special characters used for MathJax interpreting can be escaped using the  character: $ $
, { {, _ _, etc. If you want  itself, you should use \backslash ?

, because \\ is for a new line.

(Tutorial ends here.)