Re: Mixing variables in Mod expressions

[Ariel Pacetti <apacetti@math.utexas.edu>]

I have a somehow related problem/question to a computation I tried to do 
sometime ago (and never finished). Let say I have to elements a, b in two 
different number fields L,K (which are given as Mod(x,P) and Mod(y,Q)) and 
I want to know (the not well stated question) "for which rational primes 
they are congruent", meaning I want to know for which primes p, there 
exists a prime ideal dividing it in the composition of the two fields 
which divides the diference Mod(x,P)-Mod(y,Q).

The naive answer is what was mentioned in the answer to John's question, 
just make a composition of the fields and compute the norm for example, 
but the composition might be huge (and hard to compute even when the two 
fields are of a manageable size, say 20 each). Then my question is "is 
there a better approach"?

Any answer is more than welcome.

Ariel