Built-in Mathematica Symbol

Assuming

Assuming[assum, expr]
evaluates expr with assum appended to $Assumptions, so that assum is included in the default assumptions used by functions such as Refine, Simplify and Integrate.

MORE INFORMATION

Assuming affects the default assumptions for all functions that have an Assumptions option.

The assumptions can be equations, inequalities or domain specifications, or lists or logical combinations of these.

Assumptions from nested invocations of Assuming are combined.

Assuming[assum, expr] is effectively equivalent to Block[{$Assumptions=$Assumptions&&assum}, expr].

Assuming converts lists of assumptions {a₁, a₂, ...} to a₁&&a₂&&....

EXAMPLES

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Basic Examples (2)

Give the same assumptions to Refine and Integrate:

Specify the same assumptions for several Refine calls:

Give the same assumptions to Refine and Integrate:

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Specify the same assumptions for several Refine calls:

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Scope (3)

Specify assumptions for simplifiers:

Specify assumptions for Integrate and in integral transforms:

Specify assumptions for Limit and Series:

Applications (1)

Write code that uses assumptions; find the number of real roots of a x²+b x+c:

Properties & Relations (5)

Assuming locally sets the value of $Assumptions:

Assumptions from nested invocations of Assuming are combined:

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

Here the assumptions from Assuming are not used inside Block:

This is equivalent to using nested Assuming:

Assuming affects functions using the Assumptions :> $Assumptions option setting:

For some functions assumptions can be given both as an argument and as an option value:

Possible Issues (1)

When Assumptions option is set directly, assumptions specified with Assuming are not used: