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Assumptions

is an option for functions such as Simplify, Refine, and Integrate that specifies default assumptions to be made about symbolic quantities.

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Assumptions

Assumptions

is an option for functions such as Simplify, Refine, and Integrate that specifies default assumptions to be made about symbolic quantities.

Details

  • The typical default setting is Assumptions:>$Assumptions.
  • The assumptions can be equations, inequalities, or domain specifications, or lists or logical combinations of these.
  • Assuming modifies $Assumptions and so modifies the value of default settings for Assumptions options.
  • x∈Reals can be used to specify that x should be treated as a real variable.
  • Quantities that appear algebraically in inequalities are always assumed to be real.

Examples

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Basic Examples  (3)

Refine:

Wolfram Language code: Refine[Sqrt[x ^ 2], Assumptions -> x < 0]

Simplify:

Wolfram Language code: Simplify[Cos[k Pi] ^ m, Assumptions -> Element[k, Integers] && Mod[m, 2] == 0]

FunctionExpand:

Wolfram Language code: FunctionExpand[Factorial2[n], Assumptions -> n∈Integers]

Integrate:

Wolfram Language code: Integrate[x ^ a, {x, 0, 1}, Assumptions -> a > 0]

FourierTransform:

Wolfram Language code: FourierTransform[1 / (x ^ 2 + a), x, w, Assumptions -> a > 0]

Limit:

Wolfram Language code: Limit[x ^ a, x -> Infinity, Assumptions -> a < 0]

Series:

Wolfram Language code: Series[Min[x ^ 2, 1 + a]Cos[x] + Sin[x], {x, 0, 2}, Assumptions -> a > 0]

Properties & Relations  (3)

$Assumptions is the default value of Assumptions for most functions that have the option:

Wolfram Language code: Quiet[Select[ToExpression /@ Names["System`*"], Head[#] === Symbol && MemberQ[Options[#], Assumptions :> $Assumptions]&]]

Assuming locally sets the value of $Assumptions:

Wolfram Language code: Assuming[x > 0, {$Assumptions, Refine[Sqrt[x ^ 2]]}]

Block can also be used to locally set the value of $Assumptions:

Wolfram Language code: Block[{$Assumptions = x > 0}, {$Assumptions, Refine[Sqrt[x ^ 2]]}]

Here the assumptions from Assuming are not used inside Block:

Wolfram Language code: Assuming[x ≥ 0, Block[{$Assumptions = y < 0}, Refine[Sqrt[x ^ 2y ^ 2]]]]

Assumptions from nested Assuming are combined:

Wolfram Language code: Assuming[x ≥ 0, Assuming[y < 0, Refine[Sqrt[x ^ 2y ^ 2]]]]
Wolfram Research (1996), Assumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/Assumptions.html (updated 2003).

Text

Wolfram Research (1996), Assumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/Assumptions.html (updated 2003).

CMS

Wolfram Language. 1996. "Assumptions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/Assumptions.html.

APA

Wolfram Language. (1996). Assumptions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Assumptions.html

BibTeX

@misc{reference.wolfram_2026_assumptions, author="Wolfram Research", title="{Assumptions}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/Assumptions.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_assumptions, organization={Wolfram Research}, title={Assumptions}, year={2003}, url={https://reference.wolfram.com/language/ref/Assumptions.html}, note=[Accessed: 12-June-2026]}