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 Section 3.3.6.
See also: Modulus, Algebraics.
New in Version 3.