Eliminate[eqns, vars] eliminates variables between a set of simultaneous equations.

Eigensystem[m] gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m. Eigensystem[{m, a}] gives the generalized eigenvalues and ...

Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...

Tan[z] gives the tangent of z.

Mathematica's approach to differential operators provides both an elegant and a convenient representation of mathematical structures, and an immediate framework for strong ...

SemialgebraicComponentInstances[ineqs, {x_1, x_2, ...}] gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs ...

TransformationFunctions is an option for Simplify and FullSimplify which gives the list of functions to apply to try to transform parts of an expression.

There are many ways to use symbols in Mathematica. Here we use symbols as 'tags' for different types of objects. Working with physical units gives one simple example. When ...

Cancel[expr] cancels out common factors in the numerator and denominator of expr.

PowerMod[a, b, m] gives a^b mod m. PowerMod[a, -1, m] finds the modular inverse of a modulo m.PowerMod[a, 1/r, m] finds a modular r\[Null]^th root of a.