is an option for FactorInteger, PrimeQ, Factor, and related functions that specifies whether factorization should be done over Gaussian integers.
- With GaussianIntegers->False, factorization is done over the ordinary ring of integers .
- With GaussianIntegers->True, factorization is done over the ring of integers with i adjoined .
- The Gaussian primes used when GaussianIntegers->True are chosen to have both real and imaginary parts positive.
- The first entry in the list given by FactorInteger with GaussianIntegers->True may be -1 or -I.
Examplesopen allclose all
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, GaussianIntegers->True is equivalent to Extension->I:
Wolfram Research (1991), GaussianIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/GaussianIntegers.html.
Wolfram Language. 1991. "GaussianIntegers." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GaussianIntegers.html.
Wolfram Language. (1991). GaussianIntegers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GaussianIntegers.html