# NonPositiveIntegers

represents the domain of non-positive integers, as in xNonPositiveIntegers.

# Details • xNonPositiveIntegers evaluates immediately if x is a numeric quantity.
• Simplify[exprNonPositiveIntegers,assum] can be used to try to determine whether an expression is a non-positive integer under the given assumptions.
• (x1|x2|)NonPositiveIntegers and {x1,x2,}NonPositiveIntegers test whether all xi are non-positive integers.
• NonPositiveIntegers is output in StandardForm or TraditionalForm as . This typeset form can be input using npints .

# Examples

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## Basic Examples(3)

Negative seven is a non-positive integer:

If is an integer, is a non-positive integer:

Find non-positive integer solutions of a Pell equation:

## Scope(6)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Solve an optimization problem over the non-positive integers:

Test whether several numbers are non-positive integers:

If any number is explicitly not a non-positive integer, the result is False:

## Applications(1)

Testing membership in the non-positive integers is a fast way to verify non-positivity of a large list:

## Properties & Relations(3)

Membership in NonPositiveIntegers is equivalent to membership in Integers and non-positivity:

NonPositiveIntegers is contained in NonPositiveReals and NonPositiveRationals:

NonPositiveIntegers is disjoint from PositiveIntegers:

It intersects NonNegativeIntegers:

Introduced in 2019
(12.0)