On Nov 20, 2007 9:07 PM, mabshoff <[EMAIL PROTECTED]> wrote: > On Nov 21, 4:56 am, Alex Ghitza <[EMAIL PROTECTED]> wrote: > > -----BEGIN PGP SIGNED MESSAGE----- > > Hash: SHA1 > > Hi Alex, > > > > > Hi, > > > > I've been playing with spaces of modular symbols over finite fields, and > > I ran into two issues that seem to be separate (they're tickets #1231 > > and #1232 now): > > > > 1. doing > > > > ModularSymbols(1,8,0,GF(3)).simple_factors()
Unfortunately, the algorithm for computing simple factors doesn't even make sense over finite fields, since Hecke operators -- which are diagonalizable over CC are often not diagonalizable over GF(p). Instead, your best bet is to use the decomposition method, which decomposes the space using Hecke operators T_p with p <= n coprime to the level: sage: M = ModularSymbols(1,8,0,GF(3)) sage: M.decomposition(3) # n [ Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 2 for Gamma_0(1) of weight 8 with sign 0 over Finite Field of size 3, Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 2 for Gamma_0(1) of weight 8 with sign 0 over Finite Field of size 3 ] If you choose n large enough this will decompose as much as you're going to get from Hecke operators. I haven't used sage modular symbols at all in characteristic p yet, I have to admit. Also, you're right that this has nothing to do with reduction modulo a maximal ideal of the ring of integers not yet being implemented, since modular symbols mod p in sage are just the same algorithm but over F_p. Note that in some cases, especially for p = 2,3, the dimension of modular symbols mod p can be larger than the dimension of the same space in characteristic 0. It would be well worth adding an option to have the modular symbols mod p p be the reduction mod of the char 0 modular symbols, so the dimension wouldn't go up. -- William > > gives > > > > - ------------------------------------------------------------ > > Unhandled SIGSEGV: A segmentation fault occured in SAGE. > > This probably occured because a *compiled* component > > of SAGE has a bug in it (typically accessing invalid memory) > > or is not properly wrapped with _sig_on, _sig_off. > > You might want to run SAGE under gdb with 'sage -gdb' to debug this. > > SAGE will now terminate (sorry). > > - ------------------------------------------------------------ Getting that is a bug in any case. > > While I cannot reproduce this particular problem on sage.math, of the > other 4 examples you give the first one also segfaults on sage.math > with 2.8.13.rc1. So I do have something do debug this from. I will see > if anything pops up with valgrind. > > Cheers, > > Michael > > > > > > The same phenomenon occurs over other finite fields. > > > > 2. doing > > > > ModularSymbols(1,6,0,GF(2)).simple_factors() > > > > gives > > > > - > > --------------------------------------------------------------------------- > > <type 'exceptions.AssertionError'> Traceback (most recent call last) > > > > /home/ghitza/sage/<ipython console> in <module>() > > > > /opt/sage/local/lib/python2.5/site-packages/sage/modular/modsym/space.py > > in simple_factors(self) > > 996 ASSUMPTION: self is a module over the anemic Hecke algebra. > > 997 """ > > - --> 998 return [S for S,_ in self.factorization()] > > 999 > > 1000 def star_eigenvalues(self): > > > > /opt/sage/local/lib/python2.5/site-packages/sage/modular/modsym/ambient.py > > in factorization(self) > > 1064 D = sage.structure.all.Factorization(D, cr=True) > > 1065 assert r == s, "bug in factorization -- self has > > dimension %s, but sum of dimensions of factors is %s\n%s"%( > > - -> 1066 r, s, D) > > 1067 self._factorization = D > > 1068 return self._factorization > > > > <type 'exceptions.AssertionError'>: bug in factorization -- self has > > dimension 2, but sum of dimensions of factors is 3 > > (Modular Symbols subspace of dimension 1 of Modular Symbols space of > > dimension 2 for Gamma_0(1) of weight 6 with sign 0 over Finite Field of > > size 2) * > > (Modular Symbols subspace of dimension 1 of Modular Symbols space of > > dimension 2 for Gamma_0(1) of weight 6 with sign 0 over Finite Field of > > size 2) * > > (Modular Symbols subspace of dimension 1 of Modular Symbols space of > > dimension 2 for Gamma_0(1) of weight 6 with sign 0 over Finite Field of > > size 2) > > - ------------------------------------------------------------------------- > > > > I have not looked at the implementation, but as far as I know the > > algorithms with modular symbols work directly over the field of > > definition, so it seems unlikely that this is related to the problem > > that Ifti raised a few days ago, about reduction of coefficients modulo > > prime ideals. > > > > Best, > > Alex > > -----BEGIN PGP SIGNATURE----- > > Version: GnuPG v1.4.7 (GNU/Linux) > > Comment: Using GnuPG with Mozilla -http://enigmail.mozdev.org > > > > iD8DBQFHQ6xYdZTaNFFPILgRAgzMAJ9UhL4+sB/aX4KkTGCMuhKzbpJ1VwCfScqU > > sbMU91l2mRWyVMLdtYEu4vM= > > =7Moa > > -----END PGP SIGNATURE----- > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
