Ariel Pacetti on Tue, 27 Jan 2015 20:21:31 +0100

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Re: Mixing variables in Mod expressions

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.