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Common expressions
What follows in this and next sections is but a very concise collection of most common and useful symbols available in LaTeX (and hence Aurora). It is primarily based on the material of:
* (Not so) short introduction to LaTeX ,
* Short Math Guide for LaTeX , and the
* TeX Reference Card .
If you cannot find some symbol here or in the documents above, TheComprehensive LaTeX Symbol List —the reference to over 3300 symbols that can be used in LaTeX (and thus, again, Aurora)—will most definitely have whatever it is you need.
Aurora’s default preamble includes both amsmath and amssymb; therefore, the examples below use symbols and commands from these packages indiscriminately. All these examples should be used in math mode unless noted otherwise.Operations
square root | | \sqrt{x+\sqrt{y}} |
higher order roots | | \sqrt[mn]{x+y} \quad \sqrt[3]{2} |
root sign | | \surd[x+y] |
fractions | | \frac{a+b}{x+\log\frac{Y}{Z}} |
force large (display) fraction | | \frac{a+b}{x+\log\dfrac{Y}{Z}} |
continued fraction | | 1+\cfrac{2}{  3+\cfrac{4}{    5+\cfrac{6}{7+\dotsb}}} =\frac{1}{\sqrt e - 1} |
binomial | | \binom{n+1}{k} |
prime || y'' + y' + y = u |
“mod” | | \begin{array}{l}  a\bmod n=b \  a\equiv b\pmod n \  a\equiv b\mod n \  a\equiv b\pod n\end{array} |
Subscripts and superscripts
subscripts | | x_1, x_2 \quad a_{ij} |
superscripts | | x^y \quad e^{2j\pi t} \quada_{ij}^2 |
multilevel subscripts | | \sum_{\substack{      1 \le m \le N, \      m\text{ odd}}} P(m) |
nested sub/superscripts | | a_{b_j}\quad e^{x^2} |
sub- and superscripts before the symbol | | {}_n C_k |
subscripts and superscripts for large symbols | | \sideset{^a_b}{'_c}\sum |   |
| | | | |
Sums, integrals, and products
sum | | \sum_{i=1}^{+\infty} |
product | | \prod_{\alpha \in U} |
integral | | \int_{x_0}^{x_1} |
contour integral | | \oint_C |
double and triple integrals | | \iint_S \quad\iiint_S |
even more integrals | | \iiiint_S \quad \idotsint_S |
integrals with alternative limit placement | | \int\limits_\alpha^\beta \quad\iint\limits_S |
unions and intersections | | \bigcup_{\alpha\in S} \quad\bigcap_{V\in\mathfrak{V}} |
direct sums, co-products, and so on | | \bigodot \quad \bigoplus |
| | \bigotimes \quad \bigsqcup |
| | \biguplus \quad \coprod |
| |\bigvee \quad \bigwedge |
Brackets
pairing brackets | | ( \; ), [ \; ], \{ \; \} |
| | \lvert\;\rvert, \lVert\;\rVert |
| | \lceil\;\rceil, \lfloor\;\rfloor |
| | \langle\;\rangle |
Aurora also defines the following two commands in its default preamble:
absolute value | | \abs{u(t)} |
norm | | \norm{\hat{G}}_\infty |
To make the brackets scale to the size of the enclosedexpression, use \left and \right commands:
\left
\right | | \left(  \sum_{i=1}^{n} e^{2\pi j i^2}\right) |
plain | | ( \sum_{i=1}^{n} e^{2\pi j i^2} ) |
Alternatively, the bracket size can be specified explicitly using the following commands:
\Biggl(  \biggl(  \Bigl(  \bigl( \quad\Biggr\} \biggr\} \Bigr\} \bigr\} | |
This may be necessary when \left and \right commands create delimitersthat are visually too large:
\left
\right | | \left[ \sum_j      \left|\sum_i x_{ij}\right|^2\right]^{1/2} |
manually-sized | | \biggl[ \sum_j      \Bigl|\sum_i x_{ij}\Bigr|^2\biggr]^{1/2} |
or when \left and \right create brackets of the same size in nested expressions:
\left
\right | | O\left(\left(    m^2+n^2\right)\log n\right) |
manually-sized | | O\bigl((m^2+n^2)\log n\bigr) |Multiline formulas and piecewise functions
piecewise functions/cases | | a_k = \begin{cases}  k & \text{for $k \le n/2$} \  n & \text{for $k=n/2$} \  k-1 & \text{otherwise}\end{cases} |
multiline equations (aligned at &) | | \begin{split}\tan^2 x  &= \sin^2 x/\cos^2 x \  &= 1/\cos^2 x - 1\end{split} |
systems of equations | | \left\{\begin{array}{l}  ax+by=r_1 \ ...
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