Refine
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:
-
Examples
open all close allBasic 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)
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:
See Also
Tech Notes
Related Guides
History
Introduced in 2003 (5.0)
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_2025_refine, author="Wolfram Research", title="{Refine}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/Refine.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_refine, organization={Wolfram Research}, title={Refine}, year={2003}, url={https://reference.wolfram.com/language/ref/Refine.html}, note=[Accessed: 05-December-2025]}