John Cremona on Sun, 22 Feb 2009 20:10:07 +0100

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I noticed that ffinit(3,582) produces a polynomial with 333 terms.  I
would have thought that using a sparse polynomial as the modulus would
be more efficient (I found x^582 + x^43 + x  - 1, for example).

I found the course code in polarit3.c which refers to various papers
and algorithms (Lenstra and Adleman), but can anyone say what are the
benefits of the polynomials these algorithms produce?  Actually I
could not quite tell whether in my case it might have been adding a
random poly of degree < 582 to x^582, in which case the denseness of
the reslt is not so surprising.

I only tried this with p=3.