Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...

Important for elliptical shapes and periodic potentials, Mathematica achieves a new level of implementation for Mathieu-related functions, supporting arbitrary-precision ...

 

Mathematica 's powerful spline functionality includes both numeric and symbolic support. Built-in basis polynomials and efficient spline construction provide a way to ...

Mathieu and related functions. The Mathieu functions MathieuC[a,q,z] and MathieuS[a,q,z] are solutions to the equation y^′′+[a-2qcos(2z)]y0. This equation appears in many ...

Mathematica can efficiently handle both univariate and multivariate rational functions, with built-in functions immediately implementing standard algebraic transformations.

Mathematica offers multiple ways of plotting functions of one variable. These include ordinary plots, log plots, parametric plots, and polar plots.

Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

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