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, Algebraics.

Further Examples