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 , 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 \$Assumptions default assumptions to append to assum TimeConstraint 30 for how many seconds to try doing any particular transformation

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

cannot be simplified for arbitrary complex :

 Out[1]=

For explicit positive numeric expressions, evaluates to :

 Out[2]=

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

 Out[3]=

Weaker assumptions may result in a weaker simplification:

 Out[4]=

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

 Out[1]=