On Nov 16, 2007 6:27 AM, Jonathan Hanke <[EMAIL PROTECTED]> wrote: > Hi William, > > Here's another one that's not implemented in SAGE: matrix.solve_right()! It > would also be nice if it handled non-square full rank matrices. This is what > I'm trying to do: [...]
solving from the right is implemented in Sage, it just isn't called exactly what you think: sage: A = random_matrix(QQ, 5) sage: v = vector(QQ, 5, [1..5]) sage: A.solve_right(v) (-5/2, -149/26, -353/52, -57/52, 3/13) sage: A \ v (-5/2, -149/26, -353/52, -57/52, 3/13) It is unfortunately implemented for square input matrices right now. Please fill out an enhancement statement and post it to trac to get this implemented in the non-square case (It's best if you include some examples of what nonsquare right solve would do, which could serve as doctests). William William > > Prime_list = [2, 3, 5, 7, 11, 13, 17, 19] > > ## System of eigenvalues at level 420 (at p = 2, 3, 5, 7, 11, 13, 17, 19) > f1 = [0, -1, -1, -1, 2, 4, 6, 6] > f2 = [0, -1, 1, 1, -2, 4, 2, 2] > f3 = [0, 1, -1, 1, 6, -4, 6, 2] > f4 = [0, 1, 1, -1, 2, 4, 2, -2] > > ## System of Eigenvalues (only over QQ) at level 105 > g1 = [1, 1, 1, 1, 0, -6, 2, -8] > > ## Prime coefficients of a cusp form I'd like to decompose > Cusp_at_p = [-2, -3, -20/3, -32/3, -8, -16, -20, -4] > > > ## Try to solve > M1 = Matrix([g1, f1, f2, f3, f4]).transpose(); M1 > M2 = M1.submatrix(0,0,5,5); M2 ## A square submatrix > of full rank > M2.solve_right(Cusp_at_p[:5]) > > Thanks, > > -Jon > =) > > > > > On Nov 16, 2007 2:57 PM, Jonathan Hanke <[EMAIL PROTECTED]> wrote: > > Hi William, > > > > I'm trying to work out an explicit example for a talk later today, and was > having trouble finding an explicit basis of eigenforms of level 420 with > Dirichlet character (420/.). I tried to use SAGE: > > > > ## This makes the space of forms of level 105 and character > (420/.) > > > > N = 420 > > chi = kronecker_character(N) > > M = ModularForms(chi, 2) > > S = M.cuspidal_submodule() > > B = S.q_integral_basis(30) > > print S.dimension(), len(B) > > > > but none of the following worked: > > > > > > S.system_of_eigenvalues(10) > > S.new_submodule() > > S.new_subspace() > > > > Also, the following coercion necessary for adjusting the level of the > character fails: > > > > > > D = DirichletGroup(RationalField(), 420); D > > > > I finally ended up gong to your tables webpage > > > > > > http://modular.fas.harvard.edu/tables/arith_of_factors/data/ > > > > to look up systems of eigenvalues for N=105 and 420 (and all characters). > > I was wondering if you had any plans to implement this kind of computation > in > > SAGE soon, and if there were better tables for this until then. > > > > Thanks, > > > > -Jon > > =) > > > > > > > > -- 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/ -~----------~----~----~----~------~----~------~--~---
