Extension

Usage

• Extension is an option for Factor, PolynomialGCD and related functions which specifies what algebraic numbers to allow in the coefficients of resulting polynomials.

Notes

• 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.

Further Examples