Sounds like you are doing 2-descent! John Cremona
On Jun 1, 1:34 am, zsharon <[email protected]> wrote: > Hi, > > I'm trying to form subgroups of the class group and unit group of a > number field. To get the subgroup of squares in C, I start with > > PolynomialRing(ZZ, 'x') > A=-2 > B=15 > f=x^3 + A*x +B > D=-4*A^3-27*B^2 > L.<c> = NumberField(f) > C = L.class_group() > CSq = [n*n for n in C.gens()] > > Then, then I run > > C.subgroup(CSq) > > I get the following error: > > Traceback (click to the left of this block for traceback) > ... > executing gensH:=[Fractional ideal class (4, c^2 - c - 1)]; > > What am I doing wrong? From looking at archived posts here, it seems > that class groups used to be missing some functionality, but as far as > I can tell, I'm just not using the subgroup command correctly. I > *was* using sage 4.3.3, but I just upgraded to 4.7, and now I'm > getting a different error. C.cayley_table() works fine, so I'm > guessing that the class group now has full functionality. (I haven't > tried anything with the group of units yet). > > Ultimately, I don't actually need the subgroup of squares in C (I will > need the 2-torsion subgroup, though), but it seemed like a simple > enough example to start with. I will also need to form a subgroup of > primes in the group of fractional ideals that divide a certain number, > and then the quotient of that subgroups with the subgroup of its > squares. I will also need to form a particular subgroup of the group > of units, then the quotient of that with its subgroup of squares. > > Thanks, > Zach -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
