SockeSchuhRegel on Tue, 22 Jan 2002 20:06:22 +0100

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bnfinit - algorithm in use, timings


i'm new to this subject (number theory), so please forgive me for asking simple questions!(i'm no mathematician, which makes the situation even worse)  I would like to know which algorithm is used within pari for bnfinit and why the output timing is so wide spread even using comparable large polynoms coefficients:(for example: x^3 - 1348000^3 - 1 => 2176s while x^3 - 1349000^3 -1 take only 178s)
Somebody told me the algorithm used in pari would be probabilistic? Is pari using the random squaring method (McCurley, Buchmann, etc.) or is it a generalization of the NFS (Jacobsen Jr.) or am i completely on the wrong way?

i would greatly appritiate your help!

thanks in advance and sorry for my bad English,