Syntax

Everything the input understands, written as you would type it in the LaTeX source. The formula editor produces the same LaTeX. Results in this page are from Physics mode unless noted.

Numbers

Input	Meaning	Result
2.5 or 2{,}5	decimal point or decimal comma	$2{,}5$
1.5 \times 10^3, 1{,}5 \cdot 10^3	scientific notation	$1500$
20\%	percent, a unit	$20\,\%$
\pi, e	the constants $\pi$ and $e$
i	the imaginary unit, in Imaginary mode only

caution

1.5e3 is not scientific notation: it is $1{,}5 \cdot e \cdot 3$. Write 1.5 \times 10^3.

Operators

Input	Meaning
+, -	sum, difference
\cdot, \times, *, \ast, or nothing (2x)	product
/, \div, \frac{a}{b}, \dfrac, \tfrac	quotient
a^b, a^{b}	power
\sqrt{x}, \sqrt[n]{x}	square root, n-th root
n!	factorial
a \bmod b	remainder
( ), [ ], \left( \right)	brackets
|x|, \left|x\right|, \lvert x \rvert	absolute value (keeps the unit)
\lfloor x \rfloor, \lceil x \rceil	floor, ceiling

Operators bind as usual: powers before products, products and quotients from left to right before sums.

Functions

Input	Notes
\sin, \cos, \tan, \cot, \sec, \csc	radians, or degrees with 30^\circ; exact where the value is rational ($\sin 30^\circ = 0{,}5$)
\arcsin, \arccos, \arctan, \sin^{-1}	result in radians
\sinh, \cosh, \tanh
\exp, e^{x}
\ln, \log (base 10), \lg, \log_b	arguments must be positive; $\log_2 8 = 3$
\max(a; b), \min(a; b)	separate the arguments with ;, since , is the decimal comma
\binom{n}{k}, \dbinom, \tbinom	exact; non-negative whole numbers
\det\begin{pmatrix} … \end{pmatrix}, vmatrix	determinant, exact, up to 8×8
\Re, \Im, \arg, \overline{z}	Imaginary mode: real part, imaginary part, argument, conjugate

Calculus

Input	Notes
\sum_{k=1}^{10} k	exact, up to 1,000,000 terms. The body is one term: \sum k + 1 is $(\sum k) + 1$
\int_0^1 x^2\,dx	numerical, at most 30 digits. Differentials dx, d x, \mathrm{d}x
\int_1^{\infty} \frac{1}{x^2}\,dx	improper integrals with \infty bounds
\lim_{x \to 0} f, \lim_{x \to 0^+} f, \lim_{x \to \infty} f	two-sided, one-sided, at infinity; \rightarrow works too
\left.\frac{d}{dx} x^3\right|_{x=2}	derivative at a point, symbolic

An integral needs bounds and a derivative needs a point; for antiderivatives and derivatives as functions use Curve sketching.

Equations

Input	Result
2x + 3 = 11	$x = 4$
x^2 = 4	$x = -2 \lor x = 2$
x^3 - 2x - 5 = 0	$x = 2{,}0945514815\ldots$ (numerical)

One unknown per equation. Degree up to 2 is solved exactly, higher degrees numerically on $[-100, 100]$.

A system of linear equations has several unknowns and is the whole input:

Input	Result
2x + y = 5; x - y = 1	$x = 2 \land y = 1$
\begin{cases} 2x + y = 5 \\ x - y = 1 \end{cases}	the same

& for alignment (2x + y &= 5) is allowed. A comma cannot separate equations, it is the decimal separator.

Labels and variables

Input	Meaning
m_1 = 2kg	defines the session variable $m_1$
F = m_1 \cdot g_n	names the line $F$
\omega_0, v_{max}	any letter or Greek letter with an index is a variable name

Greek letters: \alpha … \omega, the capitals that differ from Latin ones (\Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Upsilon, \Phi, \Psi, \Omega) and the variants \varepsilon, \vartheta, \varphi.

Units

Input	Notes
2kg, 9.81\frac{m}{s^2}	bare letters after a number are units (Physics mode)
2\,\mathrm{kg}, 3\text{ m}	explicit, works in every mode
\qty{12}{cm}, \SI{12}{cm}, \num{12}, \unit{cm}, \si{cm}	siunitx; the unit is written with symbols, not \kilo\metre
25°C, 30^\circ	degree Celsius, degree of angle

The full list is in Units and constants.

Ignored layout

\displaystyle, \textstyle, \limits, \quad, \qquad and \, are accepted and change nothing.