Computing class groups in the imaginary quadratic case is a very special case. For one thing generically they are not 1!! But also one can use a large variety of methods, including modular forms. We could probably use fast polynomial arithmetic in FLINT to do this.
Bill. On 6 Sep, 12:39, David Harvey <[EMAIL PROTECTED]> wrote: > Hi guys, sorry to butt in here since I know nothing about computing > class groups, but I just wanted to mention a paragraph in the > introduction to Andrew Sutherland's PhD recent thesis: > > "We apply these results to compute the ideal class groups of > imaginary quadratic number fields, a standard test case for generic > algorithms. The record class group computation by a generic > algorithm, for discriminant -4(10^30 + 1), involved some 240 million > group operations over the course of 15 days on a Sun SparcStation4. > We accomplish the same task using 1/1000th the group operations, > taking less than 3 seconds on a PC. Comparisons with non-generic > algorithms for class group computation are also favorable in many > cases. We successfully computed several class groups with > discriminants containing more than 100 digits. These are believed to > be the largest class groups ever computed." > > http://groups.csail.mit.edu/cis/theses/sutherland-phd.pdf > > david --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
