Assuming

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`Assuming`

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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.

Details

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)Summary of the most common use cases

Give the same assumptions to Refine and Integrate:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-c50xbx

Out[1]=1

Specify the same assumptions for several Refine calls:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-ecuuk5

Out[1]=1

Scope (3)Survey of the scope of standard use cases

Specify assumptions for simplifiers:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-b9hoth

In[2]:=2

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https://wolfram.com/xid/0ldhq4y-eq8izc

Out[2]=2

Specify assumptions for Integrate and in integral transforms:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-11osd

Out[1]=1

Specify assumptions for Limit and Series:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-iplxsp

Out[1]=1

Applications (1)Sample problems that can be solved with this function

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

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-6rorc

In[2]:=2

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https://wolfram.com/xid/0ldhq4y-hb8fd9

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0ldhq4y-rtve

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0ldhq4y-e0wzh2

Out[4]=4

Properties & Relations (5)Properties of the function, and connections to other functions

Assuming locally sets the value of $Assumptions:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-b09veq

Out[1]=1

Assumptions from nested invocations of Assuming are combined:

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-iqexaa

Out[1]=1

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

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-duzrhj

Out[1]=1

Here the assumptions from Assuming are not used inside Block:

In[2]:=2

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https://wolfram.com/xid/0ldhq4y-e0ud4o

Out[2]=2

This is equivalent to using nested Assuming:

In[3]:=3

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https://wolfram.com/xid/0ldhq4y-f4d9f8

Out[3]=3

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

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-go5sme

Out[1]=1

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

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-d7eor0

Out[1]=1

Possible Issues (1)Common pitfalls and unexpected behavior

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

In[1]:=1

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https://wolfram.com/xid/0ldhq4y-fj4acx

Out[1]=1

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