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Extension

  • Extension is an option for Factor, PolynomialGCD and related functions which specifies what algebraic numbers to allow in the coefficients of resulting polynomials.
  • With the setting Extension-> , , ... any rational combination of the can appear.
  • The must be exact numbers. They can involve I, n roots, and Root objects.
  • The can be viewed as generators for the algebraic number field in which the coefficients are assumed to lie.
  • With the default setting Extension->None all coefficients are required to be rational numbers, and any algebraic numbers that appear in input polynomials are treated like independent variables.
  • Extension->Automatic includes any algebraic numbers from the input polynomials in the coefficient field.
  • Extension-> , , ... includes both the and any algebraic numbers from the input polynomials in the coefficient field.
  • GaussianIntegers->True is equivalent to Extension->I.
  • See the Mathematica book: Section 3.3.6.
  • See also: Modulus.

    Further Examples

    See the Further Examples for Factor, Cancel, Together, PolynomialGCD.