2016-12-05 19:51:47 +0200 received badge ● Student (source) 2016-08-17 18:53:03 +0200 asked a question Defining a number field in sage I know how to define a number field in sage by an irreducible polynomial over $\mathbb{Q}$, for example sage: K. = NumberField(x^3 - 2) sage: a.minploy()  But how do I define any number field like $\mathbb{Q}(\sqrt{d_1},\sqrt{d_2})$ in sage, where $d_1$ and $d_2$ are two distinct squarefree integers? So how do I find the defining minimal polynomial of the field extension $\mathbb{Q}(\sqrt{d_1},\sqrt{d_2})$ over $\mathbb{Q}$?