Do we have a function which returns (Z/NZ)* as an abelian group? Should not be hard since you could use pari's znstar function. Then you'll just run into the less than perfect abelian group code....which as far as I know does not have a function returning all subgroups of a group.
John 2009/5/6 daveloeffler <dave.loeff...@gmail.com>: > > Just now I was doing some tinkering in sage.rings.integer_mod_ring > with the aim of fixing ticket #5250, where Sage wrongly claims that > (Z / 162Z)^* is non-cyclic when it is. That turned out to be easy to > fix, but in the process I discovered something more nasty: the method > "multiplicative_subgroups" for the IntegerModRing class returns > answers that are wrong. > > For example, take N = 341 = 11 * 31. Then (Z / NZ)^* is isomorphic to > C_10 x C_30. The current method just calculates all subgroups of C_10 > and all subgroups of C_30, and returns the products of those. This is > clearly wrong, since not all subgroups of a direct product are > products of subgroups of the factors. In fact in this example there > are 80 subgroups -- I checked in GAP -- and Sage only finds 32 of > them. > > Does anyone know a good, fast algorithm for solving this problem > (correctly)? Alternatively, can someone give me a hint on how to use > Gap for this? It has the right command (SubgroupsSolvableGroup) but > I'm struggling to work out how to convert Gap's output back into Sage. > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
