Integers

Integers

represents the domain of integers, as in x∈Integers.

Details

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

Examples

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Basic Examples  (3)

Seven is an integer:

If is an integer, so is :

Find positive integer solutions of a Pell equation:

Scope  (7)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Find integer roots of a high-degree polynomial:

Find a representation of an integer as a sum of seven squares:

Solve an optimization problem over the integers:

Test whether several numbers are integers:

If any number is explicitly non-integer, the result is False:

TraditionalForm formatting:

Properties & Relations  (3)

Integers contains Primes:

Integers is contained in Complexes, Reals, Algebraics, and Rationals:

IntegerQ returns True for explicit integers and False otherwise:

Element remains unevaluated when it cannot decide whether an expression is an integer:

Wolfram Research (1999), Integers, Wolfram Language function, https://reference.wolfram.com/language/ref/Integers.html (updated 2017).

Text

Wolfram Research (1999), Integers, Wolfram Language function, https://reference.wolfram.com/language/ref/Integers.html (updated 2017).

CMS

Wolfram Language. 1999. "Integers." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Integers.html.

APA

Wolfram Language. (1999). Integers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Integers.html

BibTeX

@misc{reference.wolfram_2024_integers, author="Wolfram Research", title="{Integers}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Integers.html}", note=[Accessed: 30-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_integers, organization={Wolfram Research}, title={Integers}, year={2017}, url={https://reference.wolfram.com/language/ref/Integers.html}, note=[Accessed: 30-December-2024 ]}