Simplify an expression involving special functions:

Simplify using assumptions:

Prove a simple theorem from the assumption of associativity:

Simplify polynomials:

Simplify a hyperbolic expression to an exponential form:

Simplify an exponential expression to a trigonometric form:

Simplify an algebraic number:

Simplify transcendental numbers:

Simplify expressions involving special functions:

Simplify expressions using assumptions:

Prove theorems based on axiom systems:

Any expression can be used as a variable:

Variables not quantified in the axioms are treated as constants:

Prove existence of right inverses assuming left identity and left inverses exist:

Simplify symbolic arrays expressions:

Prove that a solution satisfies its equations:

Simplify expressions involving Mod:

Prove that an operation g with associativity, left neutral element, and left inverse defines a group:

Prove commutativity from Wolfram's minimal axiom for Boolean algebra:

Prove that a fixed-point combinator exists:

Prove a theorem about meet (⋁) and join (⋀):

The output is generically equivalent to the input:

FullSimplify uses a wider range of transformations than Simplify:

FullSimplify uses several expansion transformations, including Expand:

TrigExpand:

PiecewiseExpand:

FunctionExpand:

LogicalExpand:

PowerExpand makes special assumptions on input and is not used by FullSimplify:

ComplexExpand assumes variables to be real and is also not used by FullSimplify:

FullSimplify uses several factoring transformations, including Factor:

FactorSquareFree:

TrigFactor:

For algebraic numbers, RootReduce and ToRadicals are used:

For rational functions, Together and Apart are used:

Some of the transformations used by FullSimplify are only generically correct:

Results of simplification of singular expressions are uncertain:

This result is caused by automatic evaluation:

Results of simplification may depend on the names of symbols:

FullSimplify knows about Fermat's last theorem: