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Returns the simplest form of an expression—Wolfram Documentation

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• See Also
  • Simplify
  • Factor
  • Expand
  • PowerExpand
  • ComplexExpand
  • TrigExpand
  • Element
  • FunctionExpand
  • Assuming
  • RootReduce
  • TrigFactor
  • TrigReduce
  • FindEquationalProof
  • ArraySimplify
  • ArrayExpand
• Related Guides
  • Formula Manipulation
  • Trigonometric Functions
  • Theorem Proving
  • Assumptions and Domains
  • Algebraic Transformations
  • Mathematical Data
  • Algebraic Numbers
  • Prime Numbers
• Tech Notes
  • Simplifying Algebraic Expressions
  • Simplification
  • Using Assumptions
  • Working with Special Functions
  • Implementation notes: Algebra and Calculus

FullSimplify[expr]

tries a wide range of transformations on expr involving elementary and special functions and returns the simplest form it finds.

FullSimplify[expr,assum]

does simplification using assumptions.

• FullSimplify will always yield at least as simple a form as Simplify, but may take substantially longer.
• FullSimplify uses RootReduce on expressions that involve Root objects.
• FullSimplify does transformations on most kinds of special functions.
• With assumptions of the form ForAll[vars,axioms], FullSimplify can simplify expressions and equations involving symbolic functions. »
• You can specify default assumptions for FullSimplify using Assuming.
• The following options can be given:
• Assumptions can consist of equations, inequalities, domain specifications such as x∈Integers, and logical combinations of these.
• With the setting TimeConstraint->{t_loc,t_tot}, at most t_loc seconds are spent for any particular transformation, and at most t_tot seconds are spent for all transformations before the best result is returned.
• FullSimplify can be used with symbolic array expressions.

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:

By default, this expression is not simplified:

This complexity function makes ChebyshevT more expensive than other functions:

This gives a result in terms of Arg[x]:

This specifies that Log[x] should not be transformed:

This takes a long time due to expansion of trigonometric functions:

The most time‐consuming transformation is not the one that does the simplification:

With transformations restricted to 100 ms, the simplification does not happen:

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 (⋀):

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:

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