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FullSimplify

â-ª FullSimplify[ expr ] tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds.
â-ª FullSimplify will always yield at least as simple a form as Simplify, but may take substantially longer.
â-ª The following options can be given:

â-ª FullSimplify uses RootReduce on expressions that involve Root objects.
â-ª FullSimplify does transformations on most kinds of special functions.
â-ª See the Mathematica book: Section 1.4.4, Section 3.3.9.
â-ª See also: Simplify, Factor, Expand, PowerExpand, ComplexExpand, TrigExpand, FunctionExpand.


Further Examples

FullSimplify versus Simplify
FullSimplify can handle expressions that Simplify leaves unchanged.

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Here are more rules that FullSimplify knows about.

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Differentiating a complicated indefinite integral should yield the integrand.

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FullSimplify can handle the simplification.

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Options: ExcludedForms, Trig
In the absence of any constraints, Factorial and Gamma cancel out in this expression.

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Setting the option ExcludedForms to Factorial inhibits the simplification.

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Setting it to Gamma does not, because Factorial is expressed in terms of Gamma.

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In this example, partial simplification not involving Factorial is allowed to happen.

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Here both the trigonometric and the gamma function are simplified.

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By contrast, here the trigonometric functions are left untouched.

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The same effect is obtained by explicitly excluding expressions matching Sin[_] from the simplification.

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Options: ComplexityFunction
See the Further Examples for ComplexityFunction.