Adjoining possibly "redundant" number field elements to QQ?

[Sam Bloom]

Hello,

I'd like to make a subfield of a number field K by adjoining to QQ a list of elements from K, with the possibility that for some i, that the minimal polynomial over QQ of a_(i+1) is not irreducible over QQ[a_0, ..., a_i]. 

As a basic example, I'd like to have 

K.<alpha> = NumberField(x^2-2);

QQ[alpha, alpha+1]

 

output

Number Field in alpha with defining polynomial x^2 - 2

Is there any way to do this?

Thanks, 

Sam

[Sam Bloom]

I think I found what I need with composite_fields. Sorry for the post!