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# Refine

 Refinegives 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 \$Assumptions default assumptions to append to assum TimeConstraint 30 for 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 :
 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]=
 Scope   (9)
Nested powers:
Product of powers:
Logarithms:
Trigonometric functions:
Equations and inequalities:
Element statements:
 Options   (4)
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 :
 Applications   (1)
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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