Algebraic Transformations

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