This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

FullSimplify

 FullSimplify[expr]tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds. FullSimplifydoes simplification using assumptions.
• FullSimplify will always yield at least as simple a form as Simplify, but may take substantially longer.
• The following options can be given:
 Assumptions \$Assumptions default assumptions to append to assum ComplexityFunction Automatic how to assess the complexity of each form generated ExcludedForms {} patterns specifying forms of subexpression that should not be touched TimeConstraint Infinity for how many seconds to try doing any particular transformation TransformationFunctions Automatic functions to try in transforming the expression
• FullSimplify does transformations on most kinds of special functions.
• With assumptions of the form ForAll, FullSimplify can simplify expressions and equations involving symbolic functions. »
Simplify an expression involving special functions:
Simplify using assumptions:
Prove a simple theorem from the assumption of associativity:
Simplify an expression involving special functions:
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Simplify using assumptions:
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Prove a simple theorem from the assumption of associativity:
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 Scope   (8)
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:
 Options   (8)
Assumptions can be given both as an argument and as an option value:
The default value of the Assumptions option is \$Assumptions:
When assumptions are given as an argument, \$Assumptions are used as well:
Specifying assumptions as an option value prevents FullSimplify from using \$Assumptions:
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 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:
By default FullSimplify does not use Reduce:
This makes FullSimplify use Reduce with respect to x over the real domain:
By default FullSimplify uses trigonometric identities:
With Trig->False, FullSimplify does not use trigonometric identities:
 Applications   (6)
Prove that a solution satisfies its equations:
Simplify expressions involving Mod:
Prove that an operation 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:
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:
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:
FullSimplify knows about Fermat's last theorem: