Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

Just as the equation x^2+3x==2 asserts that x^2+3x is equal to 2, so also the inequality x^2+3x>2 asserts that x^2+3x is greater than 2. In Mathematica, Reduce works not only ...

RootReduce[expr] attempts to reduce expr to a single Root object.

PolynomialReduce[poly, {poly_1, poly_2, ...}, {x_1, x_2, ...}] yields a list representing a reduction of poly in terms of the poly_i. The list has the form {{a_1, a_2, ...}, ...

With careful attention to branch cuts, Mathematica supports trigonometric functions everywhere in the complex plane, with extensive exact and algebraic transformations, ...

LatticeReduce[{v_1, v_2, ...}] gives a reduced basis for the set of vectors v_i.

TrigReduce[expr] rewrites products and powers of trigonometric functions in expr in terms of trigonometric functions with combined arguments.

RowReduce[m] gives the row-reduced form of the matrix m.

The built-in functions in Mathematica operate in a wide variety of ways. But many of the mathematical functions share an important approach: they are set up so as to reduce ...