John Cremona (Maths) on Wed, 15 Jul 1998 15:39:52 +0100

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Re: Query about factorpadic

Nigel is wrong: when x is odd, the valuation of 2x+2 can be anything
positive, even infinite (x=-1).  For a quadratic there cannot be any
distinction between lifting a root and lifting a factorization.

It seems that factorpadic(f,p,r) is not the same as factoring f mod
p^r in (Z/p^r)[X], but rather the mod p^r approximation to the ACTUAL
p-adic factorization.  As its name suggests.  For example,
factorpadic(x^2+2^10,2,r) gives one quadratic factor even for r=1.

I think that this discussion should probably not be going on via the
pari users' list...?


John Cremona
University of Exeter
Department of Mathematics
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Exeter EX4 4QE

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