Mathematical Equations

NovaType offers professional-quality mathematical rendering with an intuitive syntax.

Basic Syntax

Inline Equations

The formula $ E = m c^2 $ is famous.

Centered Equations

$ E = m c^2 $

An equation on its own line is automatically centered.

Numbered Equations

#set math.equation(numbering: "(1)")

$ E = m c^2 $ <eq:einstein>

See equation @eq:einstein for the energy-mass relationship.

Basic Operations

Fractions

// Simple fraction
$ a/b $

// Fraction with frac()
$ frac(a + b, c + d) $

// Complex fraction
$ frac(1, 1 + frac(1, 1 + frac(1, x))) $

Roots

// Square root
$ sqrt(x) $

// Nth root
$ root(3, x) $     // Cube root
$ root(n, x) $     // Nth root

Sums and Products

// Sum
$ sum_(i=1)^n i^2 $

// Product
$ product_(i=1)^n i $

// Double sum
$ sum_(i=1)^n sum_(j=1)^m a_(i j) $

Integrals

// Simple integral
$ integral f(x) dif x $

// Definite integral
$ integral_a^b f(x) dif x $

// Double integral
$ integral.double_D f(x,y) dif x dif y $

// Contour integral
$ integral.cont f(z) dif z $

Limits

// Limit
$ lim_(x -> infinity) f(x) $

// Left/right limit
$ lim_(x -> 0^+) 1/x = +infinity $

Matrices

// Simple matrix
$ mat(
  a, b;
  c, d
) $

// 3x3 matrix
$ mat(
  1, 0, 0;
  0, 1, 0;
  0, 0, 1
) $

// Matrix with delimiters
$ mat(delim: "[",
  a, b;
  c, d
) $

Vectors

// Column vector
$ vec(x, y, z) $

// Vector with arrow
$ arrow(v) $

// Bold vector
$ bold(v) $

Systems of Equations

$ cases(
  x + y = 10,
  2x - y = 5
) $

Greek Symbols

Operators and Symbols

Complete Examples

// Euler's formula
$ e^(i pi) + 1 = 0 $

// Gaussian integral
$ integral_(-infinity)^(+infinity) e^(-x^2) dif x = sqrt(pi) $

// Generalized Pythagorean theorem
$ c^2 = a^2 + b^2 - 2 a b cos(gamma) $

// Schrodinger equation
$ i hbar frac(partial, partial t) Psi = hat(H) Psi $

// Taylor series
$ f(x) = sum_(n=0)^infinity frac(f^((n))(a), n!) (x - a)^n $