Igor Schein on Mon, 10 Jan 2000 14:22:36 -0500

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Re: Bug in classno, qbfclassno?

On Mon, Jan 10, 2000 at 05:55:18PM +0100, Henri Cohen wrote:
> >  classno(-174660)= 168 
> >  classno(-272580)= 180
> This function (written by me) should definitely be removed, or rewritten correctly.
> It is based on a naive version of Shanks baby step giant step method which assumes
> that the approximate class number obtained by an Euler product is good enough, and
> that the class group is not too far from cyclic. The main reason for the bug is that
> the class group has large 2 rank. It is not difficult to write a correct baby step
> giant step method which completely avoids this (one has to take into account the
> full group structure, and I give the algorithm in my GTM 138 book, starting from
> the second printing, the first printing has serious errors), but in 10 years I have
> been lazy to do so because of the much more powerful quadclassunit algorithms
> based on Hafner-McCurley subexponential methods (assuming GRH).
> Henri Cohen

Powerful yet not flawless (at least implementation-wise) :-)

? setrand(1);quadclassunit(-108760)[1]
? setrand(58);quadclassunit(-108760)[1]