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:

Introduced in 1996
Updated in 2003