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May 14, 2013 at 16:05 comment added Peter Mueller @Randall: Isn't your question essentially the same one as your question mathoverflow.net/questions/24513/… from 3 years ago? How are your numbers $pxy$ given, by minimal polynomials or complex floats up to some precision?
May 14, 2013 at 15:16 comment added Harm Derksen What is p42? Is that the same as p4 in the first paragraph?
May 14, 2013 at 6:19 comment added P Vanchinathan Perhaps you have more info that could reduce the degree. For example, the fields generated individually by $p_{41}$ and $p_{21}$ could intersect in a field of degree 16. and similar things.Also possibly a a convenient automorphism (a Galois group element) might send your number $p_4$ to a number more amenable for computations.
May 14, 2013 at 2:51 history edited ARupinski CC BY-SA 3.0
fixed tex formatting, changed tags to be more appropriate to question
May 13, 2013 at 20:27 history asked Randall CC BY-SA 3.0