GaussianIntegers

is an option for FactorInteger, PrimeQ, Factor, and related functions that specifies whether factorization should be done over Gaussian integers.

Details

• With , factorization is done over the ordinary ring of integers .
• With , factorization is done over the ring of integers with i adjoined .
• The Gaussian primes used when are chosen to have both real and imaginary parts positive.
• The first entry in the list given by FactorInteger with may be -1 or -I.

Examples

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Basic Examples(1)

Factor a polynomial over :

Factor an integer over :

Scope(3)

By default polynomial factorization is performed over the rationals:

This specifies that the factorization should be done over :

By default integer factorization is performed over the integers:

This specifies that the factorization should be done over the Gaussian integers:

A number prime over the integers may not be prime over the Gaussian integers:

Properties & Relations(1)

For Factor, is equivalent to :

Wolfram Research (1991), GaussianIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/GaussianIntegers.html.

Text

Wolfram Research (1991), GaussianIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/GaussianIntegers.html.

CMS

Wolfram Language. 1991. "GaussianIntegers." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GaussianIntegers.html.

APA

Wolfram Language. (1991). GaussianIntegers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GaussianIntegers.html

BibTeX

@misc{reference.wolfram_2024_gaussianintegers, author="Wolfram Research", title="{GaussianIntegers}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/GaussianIntegers.html}", note=[Accessed: 25-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_gaussianintegers, organization={Wolfram Research}, title={GaussianIntegers}, year={1991}, url={https://reference.wolfram.com/language/ref/GaussianIntegers.html}, note=[Accessed: 25-July-2024 ]}