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Refine

Refine
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.
  • Assumptions can consist of equations, inequalities, domain specifications such as Integers, 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.
  • The following options can be given:
Assumptions$Assumptionsdefault assumptions to append to assum
TimeConstraint30for how many seconds to try doing any particular transformation
cannot be simplified for arbitrary complex :
For explicit positive numeric expressions, evaluates to :
Refine evaluates to when a symbolic expression is assumed to be positive:
Weaker assumptions may result in a weaker simplification:
Use Assuming to specify the same assumptions for several Refine calls:
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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Nested powers:
Product of powers:
Logarithms:
Trigonometric functions:
Equations and inequalities:
Element statements:
Assumptions can be given both as an argument and as an option value:
The default value of the Assumptions option is $Assumptions:
When Assumptions is given as an argument, $Assumptions is used as well:
Specifying Assumptions as an option value prevents Refine from using $Assumptions:
Checking whether a condition follows from assumptions may take a long time:
If a condition does not follow from assumptions, checking this may still take a long time:
The time spent on a single condition check is restricted by the value of TimeConstraint:
With a time constraint of 1 second, Refine cannot prove that :
Write code that uses assumptions; find the number of real roots of :
Refine rules correspond to automatic simplification rules for numeric expressions:
Use Assuming to propagate assumptions:
Use Simplify for more simplification rules:
Use FullSimplify for special function simplification:
Expressions appearing algebraically in inequality assumptions are assumed to be real:
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