The Wolfram Language includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated algorithms, many developed and refined at Wolfram Research.

General Operations

Simplify — apply transformations to try to simplify an expression

FullSimplify — apply a full set of simplification transformations

FunctionExpand — attempt to expand in terms of more elementary functions

PowerExpand — expand powers, assuming positive real variables, etc.

ComplexExpand — expand complex functions into real and imaginary parts, etc.

Polynomial Functions »

Expand — expand out products and powers

Factor — factor sums into products and powers

Collect — collect similar terms together

Rational Functions »

Together — put over a common denominator

Apart — break apart into partial fractions

ExpandNumerator  ▪  ExpandAll  ▪  Cancel  ▪  ...

Piecewise Functions

PiecewiseExpand — expand out piecewise functions into explicit components

Trigonometric Functions »

TrigToExp, ExpToTrig — convert between exponentials and trigonometric functions

TrigExpand  ▪  TrigFactor  ▪  TrigReduce

Algebraic Numbers & Functions »

RootReduce — try to merge all roots to a single root

ToRadicals — try to convert roots to explicit radicals

MeijerG Functions

MeijerGReduce — try to reduce special functions to MeijerG functions

FoxHReduce — try to reduce special functions to FoxH functions

Holonomic Functions and Sequences

DifferentialRootReduce — reduce function combinations to a holonomic function

DifferenceRootReduce — reduce sequence combinations to a holonomic sequence

Logical & Boolean Operations »

LogicalExpand — expand out Boolean expressions

BooleanConvert — convert a Boolean expression into canonical forms (DNF, CNF, etc.)

BooleanMinimize — find a minimal two-level Boolean form

FindEquationalProof — generate proofs based on arbitrary equational axiom systems

Simplification Control

Assumptions — assumptions to make

ComplexityFunction — how to rank the complexity of expressions

TimeConstraint  ▪  ExcludedForms  ▪  TransformationFunctions