This section is designed to discuss how to make compiled functions run efficiently. It will cover features that make them run faster, as well as problems that can make them ...

FindIntegerNullVector[{x_1, x_2, ..., x_n}] finds a list of integers a_i such that a_1 x_1 + a_2 x_2 + \[CenterEllipsis] + a_n x_n == 0. FindIntegerNullVector[{x_1, x_2, ..., ...

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...

GaussianIntegers is an option for FactorInteger, PrimeQ, Factor, and related functions that specifies whether factorization should be done over Gaussian integers.

SumConvergence[f, n] gives conditions for the sum \[Sum]_n^\[Infinity] f to be convergent.SumConvergence[f, {n_1, n_2, ...}] gives conditions for the multiple sum \[Sum]_n ...

Undefined is a symbol that represents a quantity with no defined value.

There are often many different ways to write the same algebraic expression. As one example, the expression (1+x)^2 can be written as 1+2x+x^2. Mathematica provides a large ...

If you make a definition like f[x_]:=x Sin[x], Mathematica will store the expression x Sin[x] in a form that can be evaluated for any x. Then when you give a particular value ...

In many kinds of numerical computations, it is convenient to introduce approximate functions. Approximate functions can be thought of as generalizations of ordinary ...

Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...