Thanks! Barinder has genuine matrices A, B which give a representation of A_4 in 26 dimensions over Q(zeta_11), i.e. A^2=I and B^3 = I and some commutator relation holds. I was surprised when he told me that A.eigenspaces_right() had beeen running for 2 days (though it turned out that that A was wrong, it did satisfy A^2=I).
My example was random: I took J=diag(1,1,...,1,-1,-1,...,-1) with 13 +1's and 13 -1's and conjugated by a random M (which was unsurprisingly invertible) to get an Q whose char poly was (X-1)^13 * (X+1)^13. Using algorithm='pari' gave that correctly, but took quite a while (the time has scrolled off my screen, it was > 2000s I think). But in our computation we know that A and B both have +1 as an eigenvalue and we only want their +1-eigenspaces, which (for my random A) only takes 87s. The matrix is in sagemath:/home/cremona/M26.sobj if you want to play with it; but remember that this is a random M with M^2=I, not one we actually want for real. John On 6 February 2012 17:01, William Stein <wst...@gmail.com> wrote: > On Mon, Feb 6, 2012 at 6:49 AM, John Cremona <john.crem...@gmail.com> wrote: >> I was trying to find eigenspaces of a 26x26 matrix over Q(zeta_11) >> (for a modular forms application) and ran into: > > Can you make your matrix available, e.g., as an sobj on sage.math (or > somewhere) that I can download. > It's possible that the real problem is a bug in the echelon routine, > not the size of the modulus. > If the multimodular echelon fails to stabilize -- due to a bug -- then > the consequence is that eventually > the primes would run out. However, this is highly unlikely to happen > in practice unless the entries of > the answer are truly gigantic. > > -- William > >> >> RuntimeError: we ran out of primes in multimodular charpoly algorithm >> >> which on investigation led me to the following lines in >> sage/ext/multi_modular.pyx: >> >> # We use both integer and double operations, hence the min. >> # MAX_MODULUS = min(int(sqrt(int(MOD_INT_OVERFLOW))-1), int(2)**int(20)) >> >> # Hard coded because currently matrix_modn_dense is implemented using C ints >> # which are always 32-bit. Once this gets fixed, i.e., there is a better >> # matrix_modn class, then this can change. >> MAX_MODULUS = 46341 >> >> so I am just wondering if anyone out there has this on their to-do >> list. Meanwhile using algorithm='pari' will have to do, though it is >> slow.... >> >> This is a small trial run. We'll be doing a 50x50 over Q(zeta_13) for >> real.... >> >> John >> >> -- >> To post to this group, send an email to sage-devel@googlegroups.com >> To unsubscribe from this group, send an email to >> sage-devel+unsubscr...@googlegroups.com >> For more options, visit this group at >> http://groups.google.com/group/sage-devel >> URL: http://www.sagemath.org > > > > -- > William Stein > Professor of Mathematics > University of Washington > http://wstein.org > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
