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 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

Examples

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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)

Options  (4)

Applications  (1)

Properties & Relations  (4)

Possible Issues  (1)

See Also

Simplify  PowerExpand  Assuming  Assumptions

Tutorials

Introduced in 2003
(5.0)