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


  • 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.
  • xReals 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.


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Basic Examples  (1)

Properties & Relations  (3)

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

Assuming locally sets the value of $Assumptions:

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

Here the assumptions from Assuming are not used inside Block:

Assumptions from nested Assuming are combined:

Wolfram Research (1996), Assumptions, Wolfram Language function, (updated 2003).


Wolfram Research (1996), Assumptions, Wolfram Language function, (updated 2003).


Wolfram Language. 1996. "Assumptions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003.


Wolfram Language. (1996). Assumptions. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_assumptions, author="Wolfram Research", title="{Assumptions}", year="2003", howpublished="\url{}", note=[Accessed: 15-June-2024 ]}


@online{reference.wolfram_2024_assumptions, organization={Wolfram Research}, title={Assumptions}, year={2003}, url={}, note=[Accessed: 15-June-2024 ]}