Simple Algebraic Extension Field Coefficients

Polynomials with coefficients in simple algebraic extensions of the rational numbers can be factored. Here, aa and bb are symbolic roots of polynomials.

Note that the second argument to factor can be a list of algebraic extensions to factor over.

This factors x^2+3 over the integers.

Factor the same polynomial over the field obtained by adjoining aa to the rational numbers.

Factor x^6+108 over the same field.

Factor again over the field obtained by adjoining both aa and bb to the rational numbers.