Simplify
Details and Options
- Simplify tries expanding, factoring, and doing many other transformations on expressions, keeping track of the simplest form obtained.
- Simplify can be used on equations, inequalities, and domain specifications.
- Quantities that appear algebraically in inequalities are always assumed to be real.
- FullSimplify does more extensive simplification than Simplify.
- You can specify default assumptions for Simplify using Assuming.
- The following options can be given:
-
Assumptions $Assumptions default assumptions to append to assum ComplexityFunction Automatic how to assess the complexity of each form generated TimeConstraint 300 how many seconds to try doing any particular transformation TransformationFunctions Automatic functions to try in transforming the expression Trig True whether to do trigonometric as well as algebraic transformations - Assumptions can consist of equations, inequalities, domain specifications such as x∈Integers, and logical combinations of these.
- With the setting TimeConstraint->{tloc,ttot}, at most tloc seconds are spent for any particular transformation, and at most ttot seconds are spent for all transformations before the best result is returned.
- Simplify can be used with symbolic array expressions.
Examples
open all close allBasic Examples (3)
Scope (5)
Options (10)
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 are given as an argument, $Assumptions is used as well:
Specifying assumptions as an option value prevents Simplify from using $Assumptions:
ComplexityFunction (2)
The default ComplexityFunction counts the subexpressions and digits of integers:
LeafCount counts only the number of subexpressions:
With the default ComplexityFunction, Abs[x] is simpler than the FullForm of -x:
This complexity function makes Abs more expensive than Times:
ExcludedForms (1)
Excluding transformations of (x-2)^10 allows Simplify to expand the remaining terms:
TimeConstraint (2)
This takes a long time, due to trigonometric expansion, but does not yield a simplification:
Use TimeConstraint to limit the time spent on any single transformation:
A similar example, where the transformation yields a simplification:
In this case, setting TimeConstraint prevents some simplification:
TransformationFunctions (1)
Applications (4)
Properties & Relations (3)
Use Assuming to propagate assumptions:
Use FullSimplify to simplify expressions involving special functions:
ArraySimplify performs only array transformations:
Simplify performs other transformations as well:
Possible Issues (2)
The Wolfram Language evaluates zero times a symbolic expression to zero:
This happens even if the symbolic expression is always infinite:
Because of this, results of simplification of expressions with singularities are uncertain:
In this case, FullSimplify recognizes the zero:
Results of simplification may depend on the names of symbols:
Text
Wolfram Research (1988), Simplify, Wolfram Language function, https://reference.wolfram.com/language/ref/Simplify.html (updated 2025).
CMS
Wolfram Language. 1988. "Simplify." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/Simplify.html.
APA
Wolfram Language. (1988). Simplify. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Simplify.html