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Documentation / Mathematica / Built-in Functions / Algebraic Computation / Basic Algebra /

Further Examples: Simplify

Simplify factors these polynomials.

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Simplify may not factor completely.

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Here Simplify does nothing at all. Simplicity is largely based on the expression's LeafCount.

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The leaf count is not the only consideration, however. Here, Log[256] is considered simpler than 4 Log[4], but Log[10000] is not simpler than 4 Log[10]. You can override this behavior; see the Further Examples for ComplexityFunction.

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This integral returns a sum of three terms.

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Differentiating the result gives an expression that is more complicated than the original integrand, but mathematically equivalent to it.

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Simplify gets back to the original form of the expression.

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Using Assumptions

Variables in an inequality are implicitly assumed to be real.

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The first assumption says that m and n are both integers.

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It is not true in general that .

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If both exponents are integers, simplifies to .

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Here are some more examples using assumptions.

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FullSimplify, ComplexityFunction and TransformationFunctions

See also the Further Examples for FullSimplify and for the options ComplexityFunction and TransformationFunctions.