Evaluate a mathematical expression and return its numeric value.

Supports + - * / // % **, parentheses, the constants pi, e, tau and functions such as sqrt, sin, cos, log, exp, factorial, gcd, hypot. Evaluation is sandboxed: no Python eval is used and only whitelisted names are allowed.

Example: "sqrt(2) * sin(pi / 4)" -> 1.0.

Return summary statistics for a list of numbers.

Includes count, sum, min, max, mean, median, population and sample standard deviation, and variance. Requires at least one value (sample stdev/variance require at least two and are null otherwise).

Return whether the integer n is a prime number.

Uses trial division up to sqrt(n). Values below 2 are not prime.

Return the prime factorization of a positive integer n.

The result is a list of {"prime": p, "exponent": k} entries, ordered by prime. prime_factorization(360) -> 2^3 * 3^2 * 5^1.

Return the greatest common divisor and least common multiple.

Accepts two or more integers, e.g. [12, 18, 24].

Solve a*x^2 + b*x + c = 0 and return its roots.

Reports the discriminant and the (real or complex) roots. Requires a != 0; use a linear solve otherwise.

Convert an integer number from one base to another.

number is given as a string in from_base (2-36); the result is a string in to_base (2-36). Example: ("ff", 16, 2) -> "11111111".

Return the matrix product A @ B.

Columns of A must match rows of B. Matrices are lists of rows.

Return the transpose of a matrix.

Return the determinant of a square matrix.

Return the inverse of a square, non-singular matrix.

Solve A x = b for x, where A is square and non-singular.

Simplify a symbolic expression, e.g. sin(x)**2 + cos(x)**2 -> 1.

Expand a symbolic expression, e.g. (x + 1)**2 -> x**2 + 2*x + 1.

Factor a symbolic expression, e.g. x**2 - 1 -> (x - 1)*(x + 1).

Differentiate expression w.r.t. variable (optionally to a higher order).

Return the indefinite integral of expression w.r.t. variable.

Solve an equation for a variable, e.g. "x**2 = 4" -> ["-2", "2"].

Accepts a bare expression (assumed = 0) or an explicit = equation.

Definite integral of expression from lower to upper.

Bounds are expressions, so oo / -oo / pi are accepted.

Limit of expression as variable -> point (oo allowed).

direction: "+" (right), "-" (left) or "+-" (two-sided).

Taylor series of expression about point up to order terms (O-term dropped).