Orthogonalize[{v_1, v_2, ...}] gives an orthonormal basis found by orthogonalizing the vectors v_i.Orthogonalize[{e_1, e_2, ...}, f] gives a basis for the e_i orthonormal ...

RootApproximant[x] converts the number x to one of the "simplest" algebraic numbers that approximates it well.RootApproximant[x, n] finds an algebraic number of degree at ...

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 ...

SymmetricReduction[f, {x_1, ..., x_n}] gives a pair of polynomials {p, q} in x_1, ..., x_n such that f == p + q, where p is the symmetric part and q is the ...

This example shows how to generate a reusable progress bar panel and use it as a modeless dialog for displaying progress with your own Mathematica calculations. There are ...

Mathematica's handling of polynomial systems is a tour de force of algebraic computation. Building on mathematical results spanning more than a century, Mathematica for the ...

GroupCentralizer[group, g] returns the centralizer of the element g in group.

On[symbol::tag] switches on a message, so that it can be printed. On["name"] switches on a named group of messages.On[s] switches on tracing for the symbol s. On[m_1, m_2, ...

Prolog is an option for graphics functions which gives a list of graphics primitives to be rendered before the main part of the graphics is rendered.

Nested logical and piecewise functions can be expanded out much like nested arithmetic functions. You can do this using LogicalExpand and PiecewiseExpand. Expanding out ...