Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

Mathematica has a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of ...

Mathematica includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated ...

Integrated into the Mathematica system are powerful functions for analyzing large volumes of discrete and integer data—often conveniently specified using Mathematica's ...

Mathematica incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling ...

ToRules[eqns] takes logical combinations of equations, in the form generated by Roots and Reduce, and converts them to lists of rules, of the form produced by Solve.

DirichletCharacter[k, j, n] gives the Dirichlet character \[Chi] {k, j} (n) with modulus k and index j.

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 ...

The built-in function Reduce provides the functionality previously found in Algebra`InequalitySolve`.

C[i] is the default form for the i\[Null]\[Null]^th parameter or constant generated in representing the results of various symbolic computations.