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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 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.

    Further Examples

    Although is prime over the integers, it factors nontrivially over the complex integers and so is not a prime in that ring.

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    See the Further Examples for Factor, DivisorSigma.