This is for practice, the content is basicly from MathJax basic tutorial and quick reference
- 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 $sum_{i=0}^n i^2 = frac{(n^2+n)(2n+1)}{6}$ (which is inline mode) or type$$sum_{i=0}^n i^2 = frac{(n^2+n)(2n+1)}{6}$$
to show:
- For Greek letters, use
alpha
,beta
,…,omega
: $alpha, beta, … omega$. For uppercase, useGamma
,Delta
,…,Omega
: $Gamma, Delta, …, Omega$. - For superscripts and subscripts, use ^ and _. For example,
x_i^2
: $x_i^2$,log_2 x
: $log_2 x$. - 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 do10^10
, you will get a surprise: $10^10$. But10^{10}
gives what you probably wanted: $10^{10}$.
Use curly braces to delimit a formula to which a superscript or subscript applies:x^5^6
is an error;{x^y}^z
is ${x^y}^z$, andx^{y^z}
is $x^{y^z}$. Observe the difference betweenx_i^2
: $x_i^2$ andx_{i^2}
: $x_{i^2}$. - 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: $(frac{sqrt x}{y^3})$. Usingleft(…right)
will make the sizes adjust automatically to the formula they enclose:left(frac{sqrt x}{y^3}right)
is $left(frac{sqrt x}{y^3}right)$.
left
andright
apply to all the following sorts of parentheses:(
and)
$(x)$,[
and]
$[x]$,{
and}
${x}$,|
$|x|$,vert
$vert x vert$,Vert
$Vert xVert$,langle
andrangle
$langle x rangle$,lceil
andrceil
$lceil x rceil$, andlfloor
andrfloor
$lfloor x rfloor$.middle
can be used to add additional dividers. There are also invisible parentheses, denoted by.
:left.frac12rightrbrace
is $left.frac12rightrbrace$.
If manual size adjustments are required:Biggl(biggl(Bigl(bigl((x)bigr)Bigr)biggr)Biggr)
gives $Biggl(biggl(Bigl(bigl((x)bigr)Bigr)biggr)Biggr)$. - Sums and integrals
sum
andint
; the subscript is the lower limit and the superscript is the upper limit, so for examplesum_1^n
$sum_1^n$. Don’t forget{…}
if the limits are more than a single symbol. For example,sum_{i=0}^infty i^2
is $sum_{i=0}^infty i^2$. Similarly,prod
$prod$,int
$int$,bigcup
$bigcup$,bigcap
$bigcap$,iint
$iint$,iiint
$iiint$,idotsint
$idotsint$. - Fractions There are three ways to make these.
frac ab
applies to the next two groups, and produces $frac ab$; for more complicated numerators and denominators use{…}
:frac{a+1}{b+1}
is $frac {a+1} {b+1}$. If the numerator and denominator are complicated, you may preferover
, which splits up the group that it is in:{a+1over b+1}
is ${a+1over b+1}$. Using `cfrac{a}{b}’ command is useful for continued fractions $cfrac{a}{b}$, more details for which are given in this sub-article. - Fonts
Command | Font | Uppercase | Lowercase |
---|---|---|---|
mathbb |
Bbb’ for “blackboard bold” | $mathbb{ABCDEFG}$ | $mathbb{abcdefg}$ |
mathbf |
boldface | $mathbf{ABCDEFG}$ | $mathbf{abcdefg}$ |
mathit |
italics | $mathit{ABCDEFG}$ | $mathit{abcdefg}$ |
pmb |
boldfaced italics | $pmb {ABCDEFG}$ | $pmb {abcdefg}$ |
mathtt |
“typewriter” font | $mathtt{ABCDEFG}$ | $mathtt {abcdefg}$ |
mathrm |
roman font | $mathrm {ABCDEFG}$ | $mathrm {abcdefg}$ |
mathsf |
sans-serif font | $mathsf{ABCDEFG}$ | $mathsf{abcdefg}$ |
mathcal |
“calligraphic” letters | $mathcal{ABCDEFG}$ | $mathcal{abcdefg}$ |
mathscr |
script letters | $mathscr{ABCDEFG}$ | $mathscr {abcdefg}$ |
mathfrak |
“Fraktur” (old German style) letters | $mathfrak {ABCDEFG}$ | $mathfrak {abcdefg}$ |
- Radical signs Use sqrt, which adjusts to the size of its argument:
'sqrt{x^3}
$sqrt{x^3}$;sqrt[3]{frac xy}
$sqrt[3]{frac xy}$. 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
: $sin x$, notsin x
: $sinx$. Use subscripts to attach a notation tolim
: $lim_{xto 0}$. - 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
: $lt$,gt
: $gt$,le
: $le$,leq
: $leq$,leqq
: $leqq$,leqslant
: $leqslant$,ge
: $ge$,geq
: $geq$,geqq
: $geqq$,geqslant
: $geqslant$,neq
: $neq$.
You can usenot
to put a slash through almost anything:notlt
: $notlt$ but it often looks bad.times
: $times$,div
: $div$,pm
: $pm$,mp
: $mp$,cdot
is a centered dot: $x cdot y$.cup
: $cup$,cap
: $cap$,setminus
: $setminus$,subset
: $subset$,subseteq
: $subseteq$,subsetneq
: $subsetneq$,supset
: $supset$,in
: $in$,notin
: $notin$,emptyset
: $emptyset$,varnothing
: $varnothing$.{n+1 choose 2k}
: ${n+1 choose 2k}$ orbinom{n+1}{2k}
: $binom{n+1}{2k}$,to
: $to$,rightarrow
: $rightarrow$,leftarrow
: $leftarrow$,Rightarrow
: $Rightarrow$,Leftarrow
: $Leftarrow$,mapsto
: $mapsto$land
: $land$,lor
: $lor$,lnot
: $lnot$,forall
: $forall$,exists
: $exists$,top
: $top$,bot
: $bot$,vdash
: $vdash$,vDash
: $vDash$.star
: $star$,ast
: $ast$,oplus
: $oplus$,circ
: $circ$,bullet
: $bullet$approx
: $approx$,sim
: $sim$,simeq
: $simeq$,cong
: $cong$,equiv
: $equiv$,prec
: $prec$,lhd
: $lhd$,therefore
: $therefore$infty
: $infty$,aleph_0
: $aleph_0$nabla
: $nabla$,partial
: $partial$Im
: $Im$,Re
: $Re$- For modular equivalence, use
pmod
like this:aequiv bpmod n
: $aequiv bpmod n$. ldots
is the dots in $a_1, a_2, a_3, ldots, a_n$a1,a2,…,an
,cdots
is the dots in $a_1 + a_2 + a_3 + cdots + a_n$- Some Greek letters have variant forms:
epsilon
: $epsilon$,varepsilon
: $varepsilon$,phi
: $phi$,varphi
: $varphi$, and others. - Script lowercase l is
ell
: $ell$. - 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.
Matrices
- Use
$$begin{matrix}…end{matrix}$$
In between thebegin
andend
, put the matrix elements. End each matrix row with\
, and separate matrix elements with&
. For example:1
2
3
4
5
6
7$$ begin{matrix} 1 & x & x^2 \ 1 & y & y^2 \ 1 & z & z^2 \ end{matrix} $$
produces:
MathJax will adjust the sizes of the rows and columns so that everything fits. -
To add brackets, either use left…right as in section 6 of the tutorial, or replace matrix with:
pmatrix
:
bmatrix
:
Bmatrix
:
vmatrix
:
Vmatrix
: - Use
cdots
$cdots$ddots
$ddots$vdots
$vdots$ when you want to omit some of the entries:
- For horizontally “augmented” matrices, put parentheses or brackets around a suitably-formatted table; see arrays below for details. Here is an example:
is produced by:1
2
3
4
5
6$$ left[ begin{array}{cc|c} 1&2&3 \ 4&5&6 end{array} right] $$
The
cc|c
is the crucial part here; it says that there are three centered columns with a vertical bar between the second and third. - For vertically “augmented” matrices, use
hline
. For example:
is produced by:1
2
3
4
5
6
7
8
9$$ begin{pmatrix} a & b \ c & d \ hline 1 & 0 \ 0 & 1 end{pmatrix} $$
- For small inline matrices use
bigl(begin{smallmatrix} ... end{smallmatrix}bigr)
, e.g. is produced by:$$bigl({begin{smallmatrix}a & b \ c & d end{smallmatrix}}bigr)$$
.
Aligned equations
Often people want a series of equations where the equals signs are aligned. To get this, use begin{align}…end{align}
. Each line should end with \
, and should contain an ampersand at the point to align at, typically immediately before the equals sign.
For example:
The usual $$
marks that delimit the display may be omitted here.
Symbols
In general, you have to search in long tables about a specific symbol you’re looking for, things like Ψ, δ, ζ, ≥, ⊆ … And it turns out that this operation can be frustrating and time consuming, which can cause the buddy to abandon writing the complete $LaTeX$ sentence in his answer, or in some cases, the complete answer itself.
Here is the website: Detexify² No more frustration.
Definitions by cases (piecewise functions)
Use begin{cases}…end{cases}
. End each case with a \
, and use &
before parts that should be aligned.
For example, you get this:
by write this:
1 |
|
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