Henri Cohen on Mon, 10 Jan 2000 17:55:18 +0100 (MET)

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Re: Bug in classno, qbfclassno?

>  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