AsciiMath cheat sheet

AsciiMath writes formulas the way you would type them in a message: sqrt(x^2+1), a/b, sum_(n=1)^oo. Here is every symbol, how it looks and the LaTeX it becomes, with a box to try your own.

From AsciiMath to LaTeX

Type AsciiMath

Examples:

How it looks

n = 1 \sum \infty \frac{1}{n ^{2}} = \frac{π ^{2}}{6}

LaTeX

\sum_{n = 1}^{\infty} \frac{1}{n^{2}} = \frac{\pi^{2}}{6}

The conversion runs in your browser, with the same code that typesets the sheets of live-math. Decimal numbers take a point here: 3.14.

What AsciiMath is

AsciiMath is a markup for mathematics made to be quick to type and easy to read even before it is typeset. Fractions, powers and roots are written as on a calculator, (a+1)/(b+1), x^(n+1), sqrt(x); symbols are short words, oo for $\infty$ , -> for $\to$ , in for $\in$ . Brackets grow by themselves, and a matrix is a list of rows.

It was created by Peter Jipsen for writing maths on web pages; MathJax and AsciiDoc read it too. The symbols on this page are those of live-math, which adds the names of Italian textbooks and of linear algebra.

AsciiMath or LaTeX?

LaTeX is the standard for printed mathematics, and the right tool for a paper or a thesis. To write while you explain, it is slow: braces, backslashes and \frac{}{} at every step. AsciiMath says the same in about two thirds of the characters, and its output is LaTeX: each formula can be converted, and a whole sheet exported as a LaTeX file.

live-math is built on this: you type AsciiMath during a lesson and the students see it typeset as you type, with plots drawn from a line. See it on the home page, or open the editor.

Every symbol

In each row, what you can type (any of the forms), how it looks, and its LaTeX. Spaces only separate: sinx and sin x are the same.

Fractions, scripts and roots

/ makes a fraction of what is right before and after it: a symbol, a number, or a group in brackets. ^ and _ do the same for exponents and indices. The brackets around a numerator, a denominator, an exponent or an index are not shown: (a+1)/(b+1) is $\frac{a + 1}{b + 1}$ , x^(n+1) is $x^{n + 1}$ . To keep them there, double them: ((a+b))/2 is $\frac{( a + b )}{2}$ . Elsewhere brackets stay: (a+b)^2 is $(a + b)^{2}$ .

x^2

x^{2}

x^{2}

x_1

x_{1}

x_{1}

x_1^2

x_{1}^{2}

x_{1}^{2}

x^(n+1)

x^{n + 1}

x^{n + 1}

a/b

\frac{a}{b}

\frac{a}{b}

(a+1)/(b+1)

\frac{a + 1}{b + 1}

\frac{a + 1}{b + 1}

frac(a)(b)

\frac{a}{b}

\frac{a}{b}

sqrt x Sqrt x

x

\sqrt{x}

sqrt(x+1)

x + 1

\sqrt{x + 1}

root(3)(x)

3 x

\sqrt[3]{x}

stackrel(def)(=)

= d e f

\stackrel{d e f}{=}

overset(*)(=)

= \cdot

\overset{\cdot}{=}

underset(x->0)(=)

x \to 0 =

\underset{x \to 0}{=}

cancel(x)

x

\cancel{x}

color(red)(x^2)

x^{2}

\textcolor{red}{x^{2}}

color colours only its argument; it takes the names of colours (red, blue, green, orange, purple…).

Greek letters

alpha

α

\alpha

beta

β

\beta

gamma

γ

\gamma

Gamma

Γ

\Gamma

delta

δ

\delta

Delta

Δ

\Delta

epsilon epsi

ϵ

\epsilon

varepsilon

ε

\varepsilon

zeta

ζ

\zeta

eta

η

\eta

theta

θ

\theta

Theta

Θ

\Theta

vartheta

ϑ

\vartheta

iota

ι

\iota

kappa

κ

\kappa

lambda lamda

λ

\lambda

Lambda Lamda

Λ

\Lambda

mu

μ

\mu

nu

ν

\nu

xi

ξ

\xi

Xi

Ξ

\Xi

pi

π

\pi

Pi

Π

\Pi

rho

ρ

\rho

sigma

σ

\sigma

Sigma

Σ

\Sigma

tau

τ

\tau

upsilon

υ

\upsilon

phi

ϕ

\phi

Phi

Φ

\Phi

varphi

φ

\varphi

chi

χ

\chi

psi

ψ

\psi

Psi

Ψ

\Psi

omega

ω

\omega

Omega

Ω

\Omega

Operations

a + b

a + b

a + b

a - b

a - b

a - b

a * b a cdot b

a \cdot b

a \cdot b

a ** b a ast b

a * b

a \ast b

a *** b a star b

a ⋆ b

a \star b

a xx b a times b

a \times b

a \times b

a -: b a div b a divide b

a \div b

a \div b

a // b

a / b

a / b

A \\ B A backslash B

A \ B

A \backslash B

A setminus B

A ∖ B

A \setminus B

a +- b a pm b

a \pm b

a \pm b

f @ g f circ g

f \circ g

f \circ g

a o+ b a oplus b

a \oplus b

a \oplus b

a ox b a otimes b

a \otimes b

a \otimes b

a o. b a odot b

a ⊙ b

a \odot b

p ^^ q p wedge q

p \land q

p \wedge q

p vv q p vee q

p \lor q

p \vee q

A nn B A cap B

A \cap B

A \cap B

A uu B A cup B

A \cup B

A \cup B

A |>< B A ltimes B

A ⋉ B

A \ltimes B

A ><| B A rtimes B

A ⋊ B

A \rtimes B

A |><| B A bowtie B

A ⋈ B

A \bowtie B

a mod n

a mod n

a \operatorname{mod} n

Big operators, limits, integrals

The limits go after _ and ^; with brackets when they are more than one symbol. On their own line they are set below and above the operator.

sum_(n=1)^oo a_n

\sum_{n = 1}^{\infty} a_{n}

\sum_{n = 1}^{\infty} a_{n}

prod_(i=1)^n x_i

\prod_{i = 1}^{n} x_{i}

\prod_{i = 1}^{n} x_{i}

int_a^b f(x) dx

\int_{a}^{b} f (x) d x

\int_{a}^{b} f{{\left ( x \right )}} \mathop{}\!dx

oint_gamma f(z) dz

\oint_{γ} f (z) d z

\oint_{\gamma} f{{\left ( z \right )}} \mathop{}\!dz

lim_(x->0) f(x)

lim_{x \to 0} f (x)

\lim_{x \to 0} f{{\left ( x \right )}}

Lim_(n->oo) a_n

Lim_{n \to \infty} a_{n}

\operatorname{Lim}_{n \to \infty} a_{n}

limsup_(n->oo) a_n

lim sup_{n \to \infty} a_{n}

\limsup_{n \to \infty} a_{n}

liminf_(n->oo) a_n

lim inf_{n \to \infty} a_{n}

\liminf_{n \to \infty} a_{n}

max_(x in A) f(x)

max_{x \in A} f (x)

\max_{x \in A} f{{\left ( x \right )}}

min_(x in A) f(x)

min_{x \in A} f (x)

\min_{x \in A} f{{\left ( x \right )}}

sup A

sup A

\sup A

inf A

in f A

\inf A

lub A

lub A

\operatorname{lub} A

glb A

glb A

\operatorname{glb} A

dim V

dim V

\dim V

^^^_(i in I) p_i bigwedge_(i in I) p_i

⋀_{i \in I} p_{i}

\bigwedge_{i \in I} p_{i}

vvv_(i in I) p_i bigvee_(i in I) p_i

⋁_{i \in I} p_{i}

\bigvee_{i \in I} p_{i}

nnn_(i in I) A_i bigcap_(i in I) A_i

⋂_{i \in I} A_{i}

\bigcap_{i \in I} A_{i}

uuu_(i in I) A_i bigcup_(i in I) A_i

⋃_{i \in I} A_{i}

\bigcup_{i \in I} A_{i}

Relations

a = b

a = b

a = b

a != b a ne b

a \neq = b

a \ne b

a < b a lt b

a < b

a < b

a > b a gt b

a > b

a > b

a <= b a le b

a \leq b

a \le b

a lt= b a leq b

a \leq b

a \leq b

a >= b a ge b

a \geq b

a \ge b

a gt= b a geq b

a \geq b

a \geq b

a -< b a -lt b a prec b

a ≺ b

a \prec b

a -<= b a preceq b

a ⪯ b

a \preceq b

a >- b a succ b

a ≻ b

a \succ b

a >-= b a succeq b

a ⪰ b

a \succeq b

x in A

x \in A

x \in A

x !in A x notin A

x \in / A

x \notin A

A sub B A subset B

A \subset B

A \subset B

A sube B A subseteq B

A \subseteq B

A \subseteq B

A supset B

A \supset B

A \supset B

A supe B A supseteq B

A \supseteq B

A \supseteq B

a -= b a equiv b

a \equiv b

a \equiv b

a ~= b a cong b

a ≅ b

a \cong b

a ~~ b a approx b

a \approx b

a \approx b

a prop b a propto b

a \propto b

a \propto b

a := b

a := b

a := b

a :|: b

a ∣ : b

a \rvert : b

Logic

p and q

p and q

p \quad\text{and}\quad q

p or q

p or q

p \quad\text{or}\quad q

not p neg p

\neg p

\neg p

p => q

p \Rightarrow q

p \Rightarrow q

p implies q

p ⟹ q

p \implies q

p <=> q

p \Leftrightarrow q

p \Leftrightarrow q

p iff q

p ⟺ q

p \iff q

y = 1 if x > 0

y = 1 if x > 0

y = 1 \quad\text{if}\quad x > 0

AA x forall x

\forall x

\forall x

EE x exists x

\exists x

\exists x

_|_ bot

⊥

\bot

TT top

⊤

\top

p |-- q p vdash q

p ⊢ q

p \vdash q

p |== q p models q

p ⊨ q

p \models q

:. therefore

∴

\therefore

:' because

∵

\because

Brackets

Brackets grow with what they hold. {: x :} is an invisible pair, useful to group; (: :) are angle brackets. |x| is the absolute value: the bars pair up inside brackets, so |x - a| < delta works as it reads.

(x)

(x)

{\left ( x \right )}

[x]

[x]

{\left [ x \right ]}

{x}

{x}

{\left \lbrace x \right \rbrace}

|x|

∣ x ∣

{\left \lvert x \right \rvert}

(: x :) << x >> langle x rangle

⟨ x ⟩

{\left \langle x \right \rangle}

|: x :|

∣ x ∣

{\left \lvert x \right \rvert}

{: x :}

x

{\left . x \right .}

lbrace x rbrace

{x}

{\left \lbrace x \right \rbrace}

abs(x) Abs(x)

∣ x ∣

{\left | x \right |}

norm(x)

∥ x ∥

{\left \| x \right \|}

floor(x) |__ x __| lfloor x rfloor

⌊ x ⌋

{\left \lfloor x \right \rfloor}

ceil(x) |~ x ~| lceil x rceil lceiling x rceiling

⌈ x ⌉

{\left \lceil x \right \rceil}

Arrows

uarr uparrow

↑

\uparrow

darr downarrow

↓

\downarrow

rarr rightarrow

\to

\rightarrow

-> to

\to

\to

>-> rightarrowtail

↣

\rightarrowtail

->> twoheadrightarrow

↠

\twoheadrightarrow

>->> twoheadrightarrowtail

↠

\twoheadrightarrow

x |-> y x mapsto y

x \mapsto y

x \mapsto y

larr leftarrow

\leftarrow

\leftarrow

harr leftrightarrow

\leftrightarrow

\leftrightarrow

rArr Rightarrow

\Rightarrow

\Rightarrow

lArr Leftarrow

\Leftarrow

\Leftarrow

hArr Leftrightarrow

\Leftrightarrow

\Leftrightarrow

Functions

A function's name is set upright and its argument follows, with or without brackets: sin x, sin(x), sin^2 x. f and g are functions only before a bracket: f(x), but f g stays a product.

sin x

sin x

\sin{x}

cos x

cos x

\cos{x}

tan x

tan x

\tan{x}

cot x

cot x

\cot{x}

sec x

sec x

\sec{x}

csc x

csc x

\csc{x}

arcsin x

arcsin x

\arcsin{x}

arccos x

arccos x

\arccos{x}

arctan x

arctan x

\arctan{x}

sinh x

sinh x

\sinh{x}

cosh x

cosh x

\cosh{x}

tanh x

tanh x

\tanh{x}

coth x

coth x

\coth{x}

sech x

sech x

\operatorname{sech}{x}

csch x

csch x

\operatorname{csch}{x}

exp x

exp x

\exp{x}

log x

lo g x

\log{x}

ln x

ln x

\ln{x}

det A

det A

\det{A}

gcd(a, b)

g cd (a, b)

\gcd{{\left ( a , b \right )}}

lcm(a, b)

lcm (a, b)

\operatorname{lcm}{{\left ( a , b \right )}}

f(x)

f (x)

f{{\left ( x \right )}}

g(x)

g (x)

g{{\left ( x \right )}}

Capitalised names

Sin x

Sin x

\operatorname{Sin}{x}

Cos x

Cos x

\operatorname{Cos}{x}

Tan x

Tan x

\operatorname{Tan}{x}

Cot x

Cot x

\operatorname{Cot}{x}

Sec x

Sec x

\operatorname{Sec}{x}

Csc x

Csc x

\operatorname{Csc}{x}

Arcsin x

Arcsin x

\operatorname{Arcsin}{x}

Arccos x

Arccos x

\operatorname{Arccos}{x}

Arctan x

Arctan x

\operatorname{Arctan}{x}

Sinh x

Sinh x

\operatorname{Sinh}{x}

Cosh x

Cosh x

\operatorname{Cosh}{x}

Tanh x

Tanh x

\operatorname{Tanh}{x}

Log x

Log x

\operatorname{Log}{x}

Ln x

Ln x

\operatorname{Ln}{x}

Italian names and linear algebra

The names of Italian textbooks, and the operators of linear algebra. Im is the image only before a bracket: Im(f), while Im z stays a product.

sen x

sen x

\operatorname{sen}{x}

arcsen x

arcsen x

\operatorname{arcsen}{x}

tg x

tg x

\operatorname{tg}{x}

arctg x

arctg x

\operatorname{arctg}{x}

cotg x

cotg x

\operatorname{cotg}{x}

arccotg x

arccotg x

\operatorname{arccotg}{x}

sh x

sh x

\operatorname{sh}{x}

ch x

ch x

\operatorname{ch}{x}

th x

th x

\operatorname{th}{x}

settsh x

settsh x

\operatorname{settsh}{x}

settch x

settch x

\operatorname{settch}{x}

rg A

rg A

\operatorname{rg}{A}

rank A

rank A

\operatorname{rank}{A}

Ker f

Ker f

\operatorname{Ker}{f}

Im(f)

Im (f)

\operatorname{Im}{{\left ( f \right )}}

tr A

tr A

\operatorname{tr}{A}

span(v, w)

span (v, w)

\operatorname{span}{{\left ( v , w \right )}}

Accents

hat x

x^

\hat{x}

bar x overline(x)

x

\overline{x}

vec v

v

\vec{v}

tilde x

x ~

\tilde{x}

dot x

x ˙

\dot{x}

ddot x

x ¨

\ddot{x}

ul(x) underline(x)

x

\underline{x}

ubrace(1+2)_3 underbrace(1+2)_3

3 1 + 2

\underbrace{1 + 2}_{3}

obrace(1+2)^3 overbrace(1+2)^3

1 + 2 3

\overbrace{1 + 2}^{3}

Fonts

bb(A) mathbf(A)

A

\mathbf{A}

bbb(R) mathbb(R)

R

\mathbb{R}

cc(F) mathcal(F)

F

\mathcal{F}

tt(x) mathtt(x)

x

\mathtt{x}

fr(g) mathfrak(g)

g

\mathfrak{g}

sf(x) mathsf(x)

x

\mathsf{x}

Text inside a formula

Between double quotes, words stay words: x = 1 " if " y > 0. A thin space is added where the text touches a symbol, so "for all"x does not stick. and, or, if as words are already spaced.

x = 1 "and" y = 2

x = 1 and y = 2

x = 1 \,\text{and}\, y = 2

text(text) mbox(text)

text

\text{text}

Matrices, vectors, systems

A matrix is a list of rows, each in brackets, separated by commas: [[1,2],[3,4]] with square brackets, ((1,2),(3,4)) with round ones, |(a,b),(c,d)| for a determinant. A column vector is a matrix of one column. A system is a matrix with { on the left and nothing on the right, :}:

A = [[1,2],[3,4]]
det A = |(1,2),(3,4)| = -2
vec v = ((x),(y),(z))
{(x + y = 1),(x - y = 2):}
|x| = {(x, " if " x >= 0),(-x, " if " x < 0):}

A = [1324]

det A = 1324 = - 2

v = x y z

{x + y = 1 x - y = 2

∣ x ∣ = {x - x if x \geq 0 if x < 0

Other symbols

del partial

\partial

\partial

grad nabla

\nabla

\nabla

oo infty

\infty

\infty

O/ emptyset

\emptyset

\emptyset

aleph

ℵ

\aleph

/_ angle

∠

\angle

/_\ triangle

△

\triangle

diamond

⋄

\diamond

square boxempty

□

\square

frown

⌢

\frown

... ldots

\dots

\ldots

cdots

\dots

\cdots

vdots

⋮

\vdots

ddots

⋱

\ddots

a quad b

a b

a \quad b

a qquad b

a b

a \qquad b

a \ b

a b

a \, b

50%

50%

50 \%

NN

N

\mathbb{N}

ZZ

Z

\mathbb{Z}

QQ

Q

\mathbb{Q}

RR

R

\mathbb{R}

CC

C

\mathbb{C}

f'(x) f prime(x)

f^{'} (x)

f ' {\left ( x \right )}

f''(x)

f^{''} (x)

f '' {\left ( x \right )}

f'''(x)

f^{'''} (x)

f ''' {\left ( x \right )}

x^2 dx

x^{2} d x

x^{2} \mathop{}\!dx

dy

d y

\mathop{}\!dy

dz

d z

\mathop{}\!dz

dt

d t

\mathop{}\!dt