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Mathematica > Mathematics and Algorithms > Mathematical Functions > Complex Numbers >

Built-in Mathematica Symbol

GaussianIntegers

GaussianIntegers
is an option for FactorInteger, PrimeQ, Factor and related functions which 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.

Factor a polynomial over

Factor an integer over

Factor a polynomial over

Factor an integer over

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: