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

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