Mathematica > Mathematics and Algorithms > Formula Manipulation > Refine
BUILT-IN MATHEMATICA SYMBOL

Refine

Refine[expr, assum]
gives the form of expr that would be obtained if symbols in it were replaced by explicit numerical expressions satisfying the assumptions assum.

Refine[expr]
uses default assumptions specified by any enclosing Assuming constructs.

Details and OptionsDetails and Options

  • Assumptions can consist of equations, inequalities, domain specifications such as xIntegers, and logical combinations of these.
  • Refine can be used on equations, inequalities, and domain specifications.
  • Quantities that appear algebraically in inequalities are always assumed to be real.
  • Refine is one of the transformations tried by Simplify.
  • The following options can be given:
  • Assumptions$Assumptionsdefault assumptions to append to assum
    TimeConstraint30for how many seconds to try doing any particular transformation

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

cannot be simplified for arbitrary complex :

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For explicit positive numeric expressions, evaluates to :

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Refine evaluates to when a symbolic expression is assumed to be positive:

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Weaker assumptions may result in a weaker simplification:

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Use Assuming to specify the same assumptions for several Refine calls:

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Scope (9)Scope (9)

Options (4)Options (4)

Applications (1)Applications (1)

Properties & Relations (4)Properties & Relations (4)

Possible Issues (1)Possible Issues (1)

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