NegativeIntegers

NegativeIntegers

represents the domain of strictly negative integers, as in x∈NegativeIntegers.

Details

  • x∈NegativeIntegers evaluates immediately if x is a numeric quantity.
  • Simplify[expr∈NegativeIntegers,assum] can be used to try to determine whether an expression is a negative integer under the given assumptions.
  • (x1|x2|…)∈NegativeIntegers and {x1,x2,…}∈NegativeIntegers test whether all xi are negative integers.
  • NegativeIntegers is output in StandardForm or TraditionalForm as TemplateBox[{}, NegativeIntegers]. This typeset form can be input using nints.

Examples

open allclose all

Basic Examples  (3)

Minus seven is a negative integer:

If is an integer, is a negative integer:

Find negative 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 negative integers:

Test whether several numbers are negative integers:

If any number is explicitly not a negative integer, the result is False:

TraditionalForm formatting:

Applications  (1)

Testing membership in the negative integers is a fast way to verify negativity of a large list of integers:

Properties & Relations  (3)

Membership in NegativeIntegers is equivalent to membership in Integers along with negativity:

NegativeIntegers is contained in NegativeReals and NegativeRationals:

NegativeIntegers is disjoint from NonPositiveIntegers and PositiveIntegers:

Wolfram Research (2019), NegativeIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeIntegers.html.

Text

Wolfram Research (2019), NegativeIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeIntegers.html.

CMS

Wolfram Language. 2019. "NegativeIntegers." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NegativeIntegers.html.

APA

Wolfram Language. (2019). NegativeIntegers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NegativeIntegers.html

BibTeX

@misc{reference.wolfram_2024_negativeintegers, author="Wolfram Research", title="{NegativeIntegers}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeIntegers.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_negativeintegers, organization={Wolfram Research}, title={NegativeIntegers}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeIntegers.html}, note=[Accessed: 21-December-2024 ]}