Compute symbolic indefinite or definite integrals.

Compute symbolic derivatives of arbitrary order.

Compute limits of expressions.

Compute Taylor or Laurent series expansions.

Compute symbolic finite or infinite summations.

Compute symbolic finite or infinite products.

Solve ordinary differential equations symbolically.

Compute the Laplace transform of a time-domain expression.

Compute the inverse Laplace transform.

Numerically integrate a scalar function.

Find a root of a scalar function numerically.

Solve an initial value problem numerically.

Interpolate scattered one-dimensional data.

Fit a nonlinear model to data with least squares.

Multiply two matrices A @ B.

Solve a square linear system Ax = b.

Compute a least-squares solution to Ax ≈ b.

Compute standard matrix decompositions.

Compute eigenvalues and optionally eigenvectors.

Compute structural and numerical information about a matrix.

Compute comprehensive descriptive statistics for a dataset.

Evaluate, fit, and sample probability distributions.

Perform a named statistical hypothesis test.

Perform regression analysis for linear, polynomial, or logistic models.

Estimate bootstrap confidence intervals and uncertainty.

Generate random samples from NumPy distributions.

Factor an integer into prime factors.

Test whether an integer is prime.

List primes in a range or generate the first N primes.

Compute GCD, LCM, or Euclidean algorithm steps.

Perform modular arithmetic operations.

Evaluate combinatorial number sequences and counting functions.

Count or list integer partitions.

Solve Diophantine equations over the integers.

Create a graph from a named specification, edge list, or adjacency matrix.

Compute shortest paths on an edge-list graph.

Compute a minimum or maximum spanning tree.

Compute common graph-theoretic summary metrics.

Compute maximum flow in a capacitated directed graph.

Multiply two matrices with GPU acceleration when beneficial.

Compute FFTs on GPU when beneficial, otherwise on CPU.

Compute batched eigen decompositions with GPU fallback.

Solve batched linear systems with GPU fallback.

Convert a mathematical expression to LaTeX and render it.

Render arbitrary LaTeX math to a PNG data URI.

Plot one or more functions as 2D curves.

Plot implicit equations or inequalities in x and y.