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ModulusExtension

GaussianIntegers

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

FilledSmallSquare With GaussianIntegers -> False, factorization is done over the ordinary ring of integers .

FilledSmallSquare With GaussianIntegers -> True, factorization is done over the ring of integers with adjoined .

FilledSmallSquare Example: FactorInteger[13, GaussianIntegers -> True] LongRightArrow.

FilledSmallSquare The Gaussian primes used when GaussianIntegers -> True are chosen to have both real and imaginary parts positive.

FilledSmallSquare The first entry in the list given by FactorInteger with GaussianIntegers -> True may be -1 or -I.

FilledSmallSquare See The Mathematica Book: Section 3.2.4.

FilledSmallSquare See also: Extension, ComplexExpand.

Further Examples

ModulusExtension