MathJax basic tutorial and quick reference
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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 shown∑i=0i2=(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.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: 1010. But10^{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, andx^{y^z}
is xyz. Observe the difference betweenx_i^2
x2i andx_{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: (√xy3). Using\left(
…\right)
will make the sizes adjust automatically to the formula they enclose:\left(\frac{\sqrt x}{y^3}\right)
is (√xy3).\left
and\right
apply to all the following sorts of parentheses:(
and)
(x),[
and]
[x],\{
and\}
{x},|
|x|,\langle
and\rangle
⟨x⟩,\lceil
and\rceil
⌈x⌉, and\lfloor
and\rfloor
⌊x⌋. There are also invisible parentheses, denoted by.
:\left.\frac12\right\rbrace
is 12}.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
∬.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.
- Use
Radical signs Use
sqrt
, which adjusts to the size of its argument:\sqrt{x^3}
√x3;\sqrt[3]{\frac xy}
3√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
sinx, notsin x
sinx. Use subscripts to attach a notation to\lim
:\lim_{x\to 0}
limx→0There 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 \ge \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
≈∼≃≅≡≺.\infty \aleph_0
∞ℵ0\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
ϵε,\phi \varphi
ϕφ, and others. Script lowercase l is\ell
ℓ.
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
anda␣␣␣␣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 ˆx,\widehat
for a larger formula ^xy. If you make it too wide, it will look silly. Similarly, there are\bar
ˉx and\overline
¯xyz, and\vec
→x and\overrightarrow
→xy and\overleftrightarrow
↔xy. For dots, as in ddxx˙x=˙x2+x¨x, 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.)
It is important that this note be reasonably short and not suffer from too much bloat. To include more topics, please create short addenda and post them as answers instead of inserting them into this post.
25 Answers
Matrices
Use
$$\begin{matrix}…\end{matrix}$$
In between the\begin
and\end
, put the matrix elements. End each matrix row with\\
, and separate matrix elements with&
. For example,$$ \begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}$$
produces:
1xx21yy21zz2
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 replacematrix
withpmatrix
(1234),bmatrix
[1234],Bmatrix
{1234},vmatrix
|1234|,Vmatrix
∥1234∥.Use
\cdots
⋯\ddots
⋱vdots
⋮ when you want to omit some of the entries:(1a1a21⋯an11a2a22⋯an2⋮⋮⋮⋱⋮1ama2m⋯anm)
For "augmented" matrices, put parentheses or brackets around a suitably-formatted table; see arrays below for details. Here is an example:
[123456]
is produced by:
$$ \left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array}\right] $$
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 small inline matrices use
\bigl(\begin{smallmatrix} ... \end{smallmatrix}\bigr)
, e.g. (abcd) 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,
√37=√732−1122=√732122⋅732−1732=√732122√732−1732=7312√1−1732≈7312(1−12⋅732)
is produced by
\begin{align}\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)\end{align}
The usual $$
marks that delimit the display may be omitted here.
align
environment over eqnarray
in LaTeX. In MathJax the spacing seems to be the same , but align
requires one less ampersand per line. – Rahul Aug 28 '12 at 4:41eqnarray
is in this article. – MJD Aug 28 '12 at 4:51align
then? – Rahul Aug 28 '12 at 5:34\\[1ex]
instead of \\
. (And of course the 1
can be changed to another value such as 1.5
or .7
in order to get enough space but not too much.) – David K Jan 30 at 16:29Definitions by cases (piecewise functions)
Use \begin{cases}…\end{cases}
. End each case with a \\
, and use &
before parts that should be aligned.
For example, you get this:
f(n)={n/2,if n is even3n+1,if n is odd
by writing this:
f(n) =\begin{cases}n/2, & \text{if $n$ is even} \\3n+1, & \text{if $n$ is odd}\end{cases}
The brace can be moved to the right:if n is even:n/2if n is odd:3n+1}=f(n)
by writing this:\left.\begin{array}{l}\text{if $n$ is even:}&n/2\\\text{if $n$ is odd:}&3n+1\end{array}\right\}=f(n)
To get a larger vertical space between cases we can use \\[2ex]
instead of \\
. For example, you get this:
f(n)={n2,if n is even3n+1,if n is odd
by writing this:
f(n) =\begin{cases}\frac{n}{2}, & \text{if $n$ is even} \\[2ex]3n+1, & \text{if $n$ is odd}\end{cases}
(An ‘ex’ is a length equal to the height of the letter x
; 2ex
here means the space should be two exes high.)
\displaystyle
when the formulas displayed are more complex ? – jibe Jul 1 '14 at 14:43\displaystyle
is enabled automatically in displays, for example between $$…$$
. You should not ever have to use it. – MJD Jul 1 '14 at 14:50{
notation is just wrong anyways). – yo' Aug 25 '14 at 9:53Symbols
In general, you have to search in long tables about a specific symbol you're looking for, things like Ψ, δ, ζ, ≥, ⊆ ... And it turns out that this operation can be frustrating and time consuming, which can cause the buddy to abandon writing the complete LATEX sentence in his answer, or in some cases, the complete answer itself.
That's why the tool that I will present you in this post was conceived. Basically, it is a LATEX handwritten symbol recognition. Example in image:
Here is the website: Detexify² No more frustration.
Arrays
It is often easier to read tables formatted in MathJax rather than plain text or a fixed width font. Arrays and tables are created with the array
environment. Just after \begin{array}
the format of each column should be listed, use c
for a center aligned column, r
for right aligned, l
for left aligned and a |
for a vertical line. Just as with matrices, cells are separated with &
and rows are broken using \\
. A horizontal line spanning the array can be placed before the current line with \hline
.
For example,nLeftCenterRight10.2411252−1189−83−2020001+10i
$$\begin{array}{c|lcr}n & \text{Left} & \text{Center} & \text{Right} \\\hline1 & 0.24 & 1 & 125 \\2 & -1 & 189 & -8 \\3 & -20 & 2000 & 1+10i\end{array}$$
Arrays can be nested to make an array of tables.
For example,min012300000101112012230123max012300123111232222333333Δ012300123110122210133210
As the source for the preceding array is long, please right-click on one of the tables and choose Show Math As ▸ TeX Commands.
\text
if you don't want allitalics,weird−lookingspacing,an′oddapostrophes. – Rahul Aug 29 '12 at 21:30\vert
gives | and \mid
gives ∣, but neither works in the column spec for an array. If you cannot type it on your keyboard, you can alwaays copy and paste it from another document. – robjohn♦ Mar 28 '13 at 17:39Fussy spacing issues
These are issues that won't affect the correctness of formulas, but might make them look significantly better or worse. Beginners should feel free to ignore this advice; someone else will correct it for them, or more likely nobody will care.
Don't use \frac
in exponents or limits of integrals; it looks bad and can be confusing, which is why it is rarely done in professional mathematical typesetting. Write the fraction horizontally, with a slash:
BadBettereiπ2eiπ2eiπ/2∫π2−π2sinxdx∫π/2−π/2sinxdx
The |
symbol has the wrong spacing when it is used as a divider, for example in set comprehensions. Use \mid
instead:
BadBetter{x|x2∈Z}{x∣x2∈Z}
For double and triple integrals, don't use \int\int
or \int\int\int
. Instead use the special forms \iint
and \iiint
:BadBetter∫∫Sf(x)dydx∬Sf(x)dydx∫∫∫Vf(x)dzdydx∭Vf(x)dzdydx
Use \,
to insert a thin space before differentials; without this TEX will mash them together:
BadBetter∭Vf(x)dzdydx∭Vf(x)dzdydx
\middle
with | to get it to work with \left
and \right
, like \left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}
: {x|x22∈z} – asmeurer Jun 9 '13 at 22:49Colors
Named colors are browser-dependent; if a browser doesn't know a particular color name, it may render the text as black. The following colors are standard in HTML4 and CSS2 and should be interpreted the same by most browsers:\color{black}{text}text\color{gray}{text}text\color{silver}{text}text\color{white}{text}text\color{maroon}{text}text\color{red}{text}text\color{yellow}{text}text\color{lime}{text}text\color{olive}{text}text\color{green}{text}text\color{teal}{text}text\color{aqua}{text}text\color{blue}{text}text\color{navy}{text}text\color{purple}{text}text\color{fuchsia}{text}text
HTML5 and CSS 3 define an additional 124 color names that will be supported on many browsers.
Math Stack Exchange's default style uses a light-colored page background, so avoid using light colors for text. Stick to darker colors like maroon, green, blue, and purple, and remember also that 7–10% of men are color-blind and have difficulty distinguishing red and green.
The color may also have the form #rgb
where r,g,b are in the range or 0
–9
, a
–f
and represent the intensity of red, green, and blue on a scale of 0–15, with a
=10, b
=11, … f
=15. For example:
#000text#00Ftext#0F0text#0FFtext#F00text#F0Ftext#FF0text#FFFtext
#000text#005text#00Atext#00Ftext#500text#505text#50Atext#50Ftext#A00text#A05text#A0Atext#A0Ftext#F00text#F05text#F0Atext#F0Ftext#080text#085text#08Atext#08Ftext#580text#585text#58Atext#58Ftext#A80text#A85text#A8Atext#A8Ftext#F80text#F85text#F8Atext#F8Ftext#0F0text#0F5text#0FAtext#0FFtext#5F0text#5F5text#5FAtext#5FFtext#AF0text#AF5text#AFAtext#AFFtext#FF0text#FF5text#FFAtext#FFFtext
You can have a look here for quick reference on colors in HTML.
System of equations
- Use
\begin{array}…\end{array}
and\left\{…\right.
. For example, you get this:
{a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3
by writing this:
$$\left\{ \begin{array}{c}a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3\end{array}\right. $$
- Alternatively we can use
\begin{cases}…\end{cases}
. The same system
{a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3
is produced by the following code
$$\begin{cases}a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3\end{cases}$$
- To align the
=
signs use\begin{aligned}...\end{aligned}
and\left\{…\right.
(see asmeurer's comment){a1x+b1y+c1z=d1+e1a2x+b2y=d2a3x+b3y+c3z=d3
whose code is
$$\left\{\begin{aligned} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y&=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{aligned} \right. $$
- To align the
=
signs and the terms as in{a1x+b1y+c1z=d1+e1a2x+b2y=d2a3x+b3y+c3z=d3
use array
with l
(for "align left"; there are also c
and r
) parameters
$$\left\{\begin{array}{ll}a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y &=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{array} \right.$$
- Vertical space between equations. As explained in Definition by cases to get a larger vertical space between equations we can use
\\[2ex]
instead of\\
. The system
{a1x+b1y+c1z=p1q1a2x+b2y+c2z=p2q2a3x+b3y+c3z=p3q3
is generated by the following code
$$\begin{cases} a_1x+b_1y+c_1z=d_1 \\[2ex] a_2x+b_2y+c_2z=d_2 \\[2ex] a_3x+b_3y+c_3z=d_3 \end{cases} $$
in comparison with
{a1x+b1y+c1z=p1q1a2x+b2y+c2z=p2q2a3x+b3y+c3z=p3q3
whose code is
$$\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\ a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\ a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases} $$
In response to elect's comment. The following code
$$ \left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right. $$
produces
{0=cx−ax0−dx0(cx−ax0)⋅dx0∥dx0∥2+cx−ax1−dx1(cx−ax1)⋅dx1∥dx1∥20=cy−ay0−dy0(cy−ay0)⋅dy0∥dy0∥2+cy−ay1−dy1(cy−ay1)⋅dy1∥dy1∥2
Continued fractions
To make a continued fraction, use \cfrac
, which works just like \frac
but typesets the results differently:
x=a0+12a1+22a2+32a3+44a4+⋯
Don't use regular \frac
or \over
, or it will look awful:
x=a0+12a1+22a2+32a3+44a4+⋯
You can of course use \frac
for the compact notation:
x=a0+12a1+22a2+32a3+44a4+⋯
Continued fractions are too big to put inline. Display them with $$
…$$
or use a notation like [a0;a1,a2,a3,…].
\frac12{\vphantom{1}\atop+}\frac34
) – MJD Sep 17 '12 at 22:30\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}
to get∞Kj=1ajbj=a1b1+a2b2+a3b3+⋱. – Américo Tavares Jan 24 '13 at 9:15\mathop
instead of \overset
and \underset
: \mathop{\LARGE\mathrm K}_{i=1}^\infty \frac{a_i}{b_i}
∞Ki=1aibi – AlexR Feb 21 '15 at 20:48Crossing things out
Use \require{cancel}
in the first formula in your post that requires cancelling; you need it only once per page. Then use:
y+\cancel{x}y+x\cancel{y+x}y+xy+\bcancel{x}y+xy+\xcancel{x}y+xy+\cancelto{0}{x}y+x0\frac{1\cancel9}{\cancel95} = \frac151995=15
Use \require{enclose}
for the following:
\enclose{horizontalstrike}{x+y}x+y\enclose{verticalstrike}{\frac xy}xy\enclose{updiagonalstrike}{x+y}x+y\enclose{downdiagonalstrike}{x+y}x+y\enclose{horizontalstrike,updiagonalstrike}{x+y}x+y
\enclose
can also produce enclosing boxes, circles, and other notations; see MathML menclose
documentation for a complete list.
\enclose{counterstrike}
? :P – Akiva Weinberger Jul 27 '15 at 19:19Additional decorations
\overline
: ¯A ¯AA ¯AAA
\underline
: B_ BB_ BBB_
\widetilde
: ˜C ~CC ~CCC
\widehat
: ˆD ^DD ^DDD
\fbox
: E EE EEE
\underleftarrow
: F← FF← FFF←
\underrightarrow
: G→ GG→ GGG→
\underleftrightarrow
: H↔ HH↔ HHH↔
\overbrace
: ⏞(n−2)+⏞(n−1)+n+(n+1)+(n+2)
\underbrace
: (n−2)+(n−1)+n+(n+⏟1)+(n+⏟2)
\overbrace
and \underbrace
accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}}
isa⋅a⋯a⏟b times
Additional accents
\check
: ˇI
\acute
: ˊJ
\grave
: ˊK
\implies
(⟹) is a marginally preferable alternative to \Rightarrow
(⇒) for implication.
There's also \iff
⟺ and \impliedby
⟸.
\to
(→) is preferable to \rightarrow
or \longrightarrow
for things like f:A→B. The reverse is \gets
(←).
\to
and \mapsto
as in T:R→R,x↦x+1 produced by T:\mathbb R\to \mathbb R,\; x\mapsto x+1
– yo' Aug 25 '14 at 9:57\to
when it appears as part of a larger propositional formula, rather than at the top level, i.e. p∧((q∨r)→s), because the spacing is similar to that of other binary operators. \implies
is better for sentence- or clause-level implications, or in displays, i.e.x+2=4−x⟹x=1. – Mario Carneiro Feb 2 '15 at 14:22Tags & References
For longer calculations (or referring to other post's results) it is convenient to use the tagging/labelling/referencing system. To tag an equation use\tag{yourtag}
, and if you want to refer to that tag later on, add \label{somelabel}
right after the \tag
. It is not necessary that yourtag
and somelabel
are the same, but it usually is more convenient to do so:
$$ a := x^2-y^3 \tag{*}\label{*} $$
a:=x2−y3
In order to refer to an equation, just use \eqref{somelabel}
$$ a+y^3 \stackrel{\eqref{*}}= x^2 $$
a+y3(*)=x2
or \ref{somelabel}
Equations are usually referred to as $\eqref{*}$, but you can also use $\ref{*}$.
Equations are usually referred to as (*), but you can also use *.
As you can see, references are even turned into hyperlinks, which you can use externally as well, e.g. like this. Note that you can also reference labels in other posts as long as they appear on the same site, which is especially useful when referring to a question with multiple equations, or when commenting on a post.
Due to a bug blocks containing a \label
will break in preview, as a workaround you can put $\def\label#1{}$
in your post while editing and remove that on submission - unfortunately this means you won't spot misspelled references before submitting... Just don't forget to remove that \def
again
\eqref{*}
yields a clickable (*) – Tobias Kienzler Oct 31 '13 at 10:22\begin{align}
etc.... Though personally I'd agree with this – Tobias Kienzler Jan 21 at 7:19Using \newcommand
I would like to remark that it is possible to define LaTeX commands as you do in your TeX files. I felt so happy when I first discovered it! It's enough to insert something like
$ \newcommand{\SES}[3]{ 0 \to #1 \to #2 \to #3 \to 0 } $
at the top of your post (remember the dollars!). Then you can just use your commands as you are used to do: in my example typing $$ \SES{A}{B}{C} $$
will produce the following:
0→A→B→C→0
It's also possible to use plain \def
:
\def\ses#1#2#3{0 \to #1 \to #2 \to #3 \to 0}
and then $\ses{A}{B}{C}$
will produce the same output.
Commutative diagrams
AMScd diagrams must start with a "require":
$\require{AMScd}$\begin{CD} A @>a>> B\\ @V b V V= @VV c V\\ C @>>d> D\end{CD}
to get this diagram: Aa→Bb↓=↓cC→dD
@>>>
is used for arrow right
@<<<
is used for arrow left
@VVV
is used for arrow down
@AAA
is used for arrow up
@=
is used for horizontal double line
@|
is used for vertical double line
@.
is used for no arrow
Another example:
\begin{CD} A @>>> B @>{\text{very long label}}>> C \\ @. @AAA @| \\ D @= E @<<< F \end{CD}
A→Bvery long label→C↑∥D=E←F
Long labels increase the length of the arrow and in this version also automatically increase corresponding arrows.
$\require{AMScd}$\begin{CD} RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}>> (RCOR')+NaCl+SO_2+ H_2O \end{CD}
RCOHR′SO3NaHydrolysis,Δ,Dil.HCl→(RCOR′)+NaCl+SO2+H2O
Big braces
Use \left
and \right
to make braces - (round), [square] and {curly} - scale up to be the size of their arguments. Thus
$$f\left( \left[ \frac{ 1+\left\{x,y\right\} }{ \left( \frac{x}{y}+\frac{y}{x} \right) \left(u+1\right) }+a \right]^{3/2}\right)$$
renders asf([1+{x,y}(xy+yx)(u+1)+a]3/2).
Note that curly braces need to be escaped as \{ \}
.
If you start a big brace with \left
and then need to match that to a \right
brace that's on a different line, use the forms \right.
and \left.
to make "shadow" braces. Thus,
$$\begin{aligned}a=&\left(1+2+3+ \cdots \right. \\& \cdots+ \left. \infty-2+\infty-1+\infty\right)\end{aligned}$$
renders asa=(1+2+3+⋯⋯+∞−2+∞−1+∞).
There is also a \middle
construct which is useful when one has a mid-expression brace which must also scale up:
$$\left\langle q\middle\| \frac{\frac{x}{y}}{\frac{u}{v}}\middle| p \right\rangle$$
renders as⟨q∥xyuv|p⟩.
Note that constructs like \left\langle
, \left|
and \left\|
are also possible.
\Big( ... \Big)
produces (…) but this bracket size is fixed in all situations unlike \left( ... \right)
which varies in size with its contents. \Big
can be useful in various situations. – Nick Dec 19 '14 at 6:34Arbitrary operators
If an operator is not available as a built-in command, use \operatorname{…}
. So for things likearsinh(x)
\operatorname{arsinh}(x)
since \arsinh(x)
will give an error and arsinh(x)
has wrong font and spacing: arsinh(x).This was already mentioned in a comment by Charles Staats. You might consider this an addition to the FAQ section on \lim
, \sin
and so on.
For operators which need limits above and below the operator, use \operatorname*{…}
, as inResz=1(1z2−z)=1
\rm
will change the font but not the spacing. \operatorname{arsinh}x
renders as “arsinhx” while {\rm arsinh}x
renders as “arsinhx”. Notice the added space between operator and operand in the first example, which is missing in the second. On the whole, I'd say that operatorname
is a lot more in the spirit of semantic markup, declaring what you want to write instead of how you want to write it, so I'd strongly suggest using this. – MvG Aug 13 '14 at 11:27\operatorname
in the main post, and decided to leave it out. The reason is simple: If a beginner omits \operatorname
, the resulting formula will still be perfectly clear, and a more experienced user will have no trouble inserting the\operatorname
where it is needed. So including it in the main post would not be a good use of space. – MJD Aug 16 '14 at 6:28\DeclareMathOperator{\arsinh}{arsinh}
at the post's top. Never tried it though… – MickG Aug 15 '15 at 17:28Limits
To make a limit (like limx→1x2−1x−1), use this syntax:
First, start off with $\lim
. This renders as lim. The backslash is there to prevent things like lim, where the letters are slanted.
Second, add \limits_{x \to 1}
inside. The code now looks like $\lim \limits_{x \to 1}$
, and renders as limx→1. The \to
inside makes the right arrow, rendered as →. The_
makes the x→1 go underneath the lim. Finally, the pair of curly braces { }
makes sure that x→1 is treated as a whole object, and not two separate things.
Lastly, add the function you want to apply the limit to. To make the limit mentioned above, limx→1x2−1x−1, simply use $\lim\limits_{x \to 1} \frac{x^2-1}{x-1}$
.
And that is how you make a limit using MathJax.
\lim_{x\to 1}
limx→1? As I understand it \limits
is only needed for operations that don't already understand limits, for example if you want to use +
and getk+i=1 instead of +ki=1 When used inline, your suggestion will produce limx→1 instead of the more compact form limx→1 that mathjax normally chooses. Are you sure this is good advice? – MJD Feb 26 '14 at 14:10$\lim_{x\to 1}
renders to limx→1, and $\lim\limits_{x\to 1
renders as lim\limits_{x\to 1}. Note how the x→1 is separated from the first limit, and not directly underneath. We do not write limits like that in real life, so we use \limits
. – JChau Feb 26 '14 at 16:19\lim\limits_{x\mapsto 1}\dfrac1x
: limx↦11x. On the other hand, when I let TEX do what it wants to do, using \lim_{x\mapsto 1}\frac1x
, the spacing between the lines stays the same, which is much neater: limx↦11x. This is much easier on the eyes. If you want to make your math mode more prominent then take a new line using $$-$$
– user1729 Jul 17 '14 at 12:30Absolute values and norms
The absolute value of some expression can be denoted as \lvert x\rvert
or, more generally, as \left\lvert … \right\rvert
. It renders as ∣x∣.
The norm of a vector (or similar) can be denoted as \lVert v\rVert
or, more generally, as \left\lVert … \right\rVert
. It renders as ∥v∥. (You may also write\left\|…\right\|
instead.)
In both cases, the rendering is better than what you'd get from |x|
or ||v||
, which render with bars that don't descend low enough and sub-optimal spacing. At least on some browsers, so here is a screenshot how it looks for me, using Firefox 31 on OS X:
And here is the same formula rendered by your browser:
|x|,||v||⟶∣x∣,∥v∥
It was typeset as
$$|x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert$$
\|x\|
instead of \lVert x \rVert
; ∥x∥ and ∥x∥. (I don't think that there is a difference between them. I've tried [asking on SE](tex.stackexchange.com/questions/77767/whats-the-correct-way-to-write-norm).) – Martin Sleziak Jun 24 '14 at 8:48|x|
and \lvert x\rvert
(|x| and ∣x∣) look identical, contrary to your claim. Perhaps you need to show an example more complicated than just 'x'? – MJD Jun 24 '14 at 12:39||
version. On Linux they looked the same. – MJD Aug 13 '14 at 17:02Left and Right Implication Arrows
Another way to display the arrows for right and left implication instead of using
$\Rightarrow$
, $\Leftarrow$
and $\Leftrightarrow$
which produces ⇒, ⇐ and ⇔ respectively, you can use
$\implies$
for ⟹, $\impliedby$
for ⟸ and $\iff$
for ⟺
The latter of which produces longer arrows which may be more desirable to some.
Long division
$$\require{enclose}\begin{array}{r} 13 \\[-3pt]4 \enclose{longdiv}{52} \\[-3pt] \underline{4}\phantom{2} \\[-3pt] 12 \\[-3pt] \underline{12}\end{array}$$
134524_1212_
One important trick shown here is the use of \phantom{2}
to make a blank space that is the same size and shape as the digit 2
just above it.
This is adapted from http://stackoverflow.com/a/22871404/3466415 (which uses slightly different but not less valid formatting).
The degree symbol for angles is not ^\circ
. Although many people use this notation, the result looks quite different from the canonical degree symbol shipped with the font:
90°
renders as 90° while 90^\circ
renders as 90∘.
If your keyboard doesn't have a ° key, feel free to copy from this post here, or follow these suggestions.
Note that comments below indicate that on some configurations at least, °
renders inferior to ^\circ
. And I recently had a post of mine edited just for the sake of turning °
into ^\circ
, indicating that someone felt rather strongly about this. So the suggestion above does seem somewhat controversial at the moment. I maintain that from a semantic point of view, °
is superior to ^\circ
, and if the rendering suffers from this, then it's a bug in MathJax. After all, LaTeX offers a proper degree symbol in the tex companion fonts, indicating that someone there, too, decided that ^\circ
is not perfect. But if things are broken now, I can't fault people from pragmatically sticking with the rendering they prefer. Personally I prefer semantics, also for the sake of screen readers.
\degree
macro. There should be one, imho. – MvG Feb 17 '15 at 23:39^\circ
looks good: a.pomf.se/xnlfyg.png – MJD Mar 24 '15 at 21:10To highlight an equation, \bbox can be used. E.g,
$$ \bbox[yellow]{e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n\qquad (1)}$$
produces
ex=limn→∞(1+xn)n(1)
or
$$ \bbox[border:2px solid red]{e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n\qquad (2) }$$
produces
ex=limn→∞(1+xn)n(2)
Giving reasons on each line of a sequence of equations
To produce this:v+w=0Given−w=−w+0additive identity−w+0=−w+(v+w)equations (1) and (2)
write this:
\begin{align} v + w & = 0 &&\text{Given} \tag 1\\ -w & = -w + 0 && \text{additive identity} \tag 2\\ -w + 0 & = -w + (v + w) && \text{equations $(1)$ and $(2)$}\end{align}
Pack of cards
If you are asking (or answering) a combinatorics question involving packs of cards you can make it look more elegant by using \spadesuit
, \heartsuit
,\diamondsuit
, \clubsuit
in math mode:♠♡♢♣
\color{red}{\heartsuit}
and \color{red}{\diamondsuit}
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\mathrm{B}
: B – robjohn♦ Aug 28 '12 at 2:06\varphi
and\varepsilon
were very close to the threshhold for inclusion. Martin Sleziak has since added them, which I agree is a good idea. – MJD Aug 28 '12 at 16:33\operatorname
: e.g.,\operatorname{Spec} A
gives SpecA. – Charles Staats Aug 28 '12 at 16:45_5C_3
5C3. You could also mention\frac
vs\dfrac
. – axblount Aug 29 '12 at 18:09\big
,\left
, and\right
for this reason, and trimming the section on spacing. – MJD Aug 30 '12 at 2:06(
and)
automatically resizeable. I can in LaTeX. – Loop Space Sep 11 '12 at 16:04\mathrm
in many places; e.g. dx in integrals and derivatives and for operator names that don't need the full force of\operatorname
.\mathrm
was intended for roman symbols in math mode;\text
was intended for text because of the way it spaces things. See this TEX thread. Since I don't believe we can use preambles in MathJax, we can't use\DeclareMathOperator
, though we can use\newcommand
, but that is orthogonal to the use of\mathrm
vs\text
for math symbols. – robjohn♦ Jun 10 '13 at 16:23