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 x∈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.
  • Refine is one of the transformations tried by Simplify.
  • The following options can be given:
  • Assumptions $Assumptionsdefault assumptions to append to assum
    TimeConstraint 30for how many seconds to try doing any particular transformation

Examples

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Basic Examples  (2)

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:

Scope  (9)

Nested powers:

Product of powers:

Logarithms:

Trigonometric functions:

Equations and inequalities:

Element statements:

Floor, Ceiling, Round, IntegerPart, and FractionalPart:

Mod:

Re, Im, Abs, Arg, Conjugate, and Sign:

Options  (4)

Assumptions  (3)

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:

TimeConstraint  (1)

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 :

Properties & Relations  (4)

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:

Possible Issues  (1)

Expressions appearing algebraically in inequality assumptions are assumed to be real:

Wolfram Research (2003), Refine, Wolfram Language function, https://reference.wolfram.com/language/ref/Refine.html.

Text

Wolfram Research (2003), Refine, Wolfram Language function, https://reference.wolfram.com/language/ref/Refine.html.

CMS

Wolfram Language. 2003. "Refine." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Refine.html.

APA

Wolfram Language. (2003). Refine. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Refine.html

BibTeX

@misc{reference.wolfram_2024_refine, author="Wolfram Research", title="{Refine}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/Refine.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_refine, organization={Wolfram Research}, title={Refine}, year={2003}, url={https://reference.wolfram.com/language/ref/Refine.html}, note=[Accessed: 22-December-2024 ]}