ca_set_qqbar

A rational x gives an element of \mathbb{Q}, and an irrational x an element of a field \mathbb{Q}(a) with one algebraic generator (never of a field with several generators: \sqrt{2} + \sqrt{3} is not recognised as an element of \mathbb{Q}(\sqrt{2}, \sqrt{3})). A quadratic x is written as an element of \mathbb{Q}(\sqrt{N}), where N is the discriminant of its minimal polynomial with small square factors removed by smooth factorisation, so that for example \sqrt{12} and 1 + \sqrt{3} share the field \mathbb{Q}(\sqrt{3}). Higher-degree numbers are made generators of their own field \mathbb{Q}(x).