GaussianIntegers is an option for FactorInteger, PrimeQ, Factor and related functions which specifies whether factorization should be done over Gaussian integers.
False, factorization is done over the ordinary ring of integers .
True, factorization is done over the ring of integers with adjoined .
Example: FactorInteger[13, GaussianIntegers -> True].
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.
See the Mathematica book: Section 3.2.4.
See also: Extension, ComplexExpand.
Although is prime over the integers, it factors nontrivially over the complex integers and so is not a prime in that ring.
See the Further Examples for Factor, DivisorSigma.
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