A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

Any combination of equations or inequalities can be thought of as implicitly defining a region in some kind of space. The fundamental function of Reduce is to turn this type ...

Boole[expr] yields 1 if expr is True and 0 if it is False.

There are some close connections between finding a "local minimum" and solving a set of nonlinear equations. Given a set of n equations in n unknowns, seeking a solution r(x) ...

LinearSolve[m, b] finds an x which solves the matrix equation m.x == b. LinearSolve[m] generates a LinearSolveFunction[...] which can be applied repeatedly to different b.

Finding singular values and norms of matrices. The singular values of a matrix m are the square roots of the eigenvalues of m.m^*, where * denotes Hermitian transpose. The ...

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

PrivateNotebookOptions -> {opt_1 -> val_1, opt_2 -> val_2, ...} is an option for notebooks that specifies various low-level notebook settings.

This package contains functions for measuring the performance of Mathematica on your computer and for producing a comparison report that includes benchmark results for other ...