Suppose we have a list of algebraic numbers, e.g., a1,a2,a3 in QQbar. I want to compute the minimal number field K which contains all these algebraic numbers and I want to get the minimal polynomial of a1,a2,a3 in K. How can I do this?
I know how to convert one element from QQbar to a number field element, e.g.,
sage: a = [QQbar(sqrt(3)), QQbar(sqrt(17)), QQbar(sqrt(5))]
sage: Ka, aK, emb = a[0].as_number_field_element()
sage: aK.absolute_minpoly()
x^2 - 3
I can also define the common number field
sage: K.<u> = NumberField([ai.minpoly() for ai in a])
But now I have no idea how to convert for instance a[0] to an element of K.
