############################################################################################################################################## # Calculation of expected and certain tropicalization of the 5 points at infinity of the potential tropical lines indexed by extremal curves # ############################################################################################################################################## # This script computes the tropical matrices, with and without considering ties between valuations (and hence posible cancelations that increase the total valuation of the coefficients). We reflect potential ties with a "None" in the entries. We calculate the matrices without nones for the maximal cones (assuming no cancellation). For the lower dimensional cones, the matrices without nones can be taken to be the matrices of the maximal cells containing them, but we must compute the matrices with nones for all cells. # All outputs will be stored in the software/ComputeLines/Script/Input folder. We use them with the scripts "ComputationOfLinesForAllCones.sage" and "ComputationOfLinesForAcone.sage." load("computeTMsMacros.sage") ############################### # MAXIMAL CONES ############################### ############## # AAAA Types # ############## print 'aa2a3a4' cone = load("../../ComputeLines/Scripts/Input/aa2a3a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa2a3a4_no_nones_signed_ordered_permutedCols.sobj") # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa2a3a4_with_nones_signed_ordered_permutedCols.sobj") print '' ############## # AAAB Types # ############## print 'aa2a3b' cone = load("../../ComputeLines/Scripts/Input/aa2a3bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa2a3b_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa2a3b_with_nones_signed_ordered_permutedCols.sobj") print '' ############################### # TWO CONES ############################### # Note: for all lower dimensional cones, we don't need to compute the tropicalmatrices with no nones. We can use the ones for maximal cones because the inequalities in the interior translate to the boundary by continuity. We will detect ties when we compute the matrix with nones. # For completeness we've computed these lower dimensional cases as well. ############# # AAA Types # ############# print 'aa2a3' cone = load("../../ComputeLines/Scripts/Input/aa2a3Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa2a3_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa2a3_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'aa2a4' cone = load("../../ComputeLines/Scripts/Input/aa2a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa2a4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa2a4_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'aa3a4' cone = load("../../ComputeLines/Scripts/Input/aa3a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 20 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa3a4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa3a4_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a2a3a4' cone = load("../../ComputeLines/Scripts/Input/a2a3a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa2a3a4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa2a3a4_with_nones_signed_ordered_permutedCols.sobj") print '' ############# # AAB Types # ############# print 'aa2b' cone = load("../../ComputeLines/Scripts/Input/aa2bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa2b_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa2b_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'aa3b' cone = load("../../ComputeLines/Scripts/Input/aa3bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa3b_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa3b_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a2a3b' cone = load("../../ComputeLines/Scripts/Input/a2a3bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa2a3b_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa2a3b_with_nones_signed_ordered_permutedCols.sobj") print '' ############################### # EDGES ############################### ############ # AA Types # ############ print 'aa2' cone = load("../../ComputeLines/Scripts/Input/aa2Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa2_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa2_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'aa3' cone = load("../../ComputeLines/Scripts/Input/aa3Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa3_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa3_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'aa4' cone = load("../../ComputeLines/Scripts/Input/aa4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMaa4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMaa4_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a2a3' cone = load("../../ComputeLines/Scripts/Input/a2a3Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa2a3_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa2a3_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a2a4' cone = load("../../ComputeLines/Scripts/Input/a2a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa2a4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa2a4_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a3a4' cone = load("../../ComputeLines/Scripts/Input/a3a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa3a4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa3a4_with_nones_signed_ordered_permutedCols.sobj") print '' ############ # AB Types # ############ print 'ab' cone = load("../../ComputeLines/Scripts/Input/abCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMab_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMab_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a2b' cone = load("../../ComputeLines/Scripts/Input/a2bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa2b_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa2b_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a3b' cone = load("../../ComputeLines/Scripts/Input/a3bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa3b_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa3b_with_nones_signed_ordered_permutedCols.sobj") print '' ############################### # VERTICES ############################### ########### # A Types # ########### print 'a' cone = load("../../ComputeLines/Scripts/Input/aCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a2' cone = load("../../ComputeLines/Scripts/Input/a2Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa2_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa2_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a3' cone = load("../../ComputeLines/Scripts/Input/a3Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa3_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa3_with_nones_signed_ordered_permutedCols.sobj") print '' ##### print 'a4' cone = load("../../ComputeLines/Scripts/Input/a4Cell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMa4_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMa4_with_nones_signed_ordered_permutedCols.sobj") print '' ########### # B Types # ########### print 'b' cone = load("../../ComputeLines/Scripts/Input/bCell.sobj") M = {extremal_curve:tropical_matrix(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalMb_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones(pds[extremal_curve], cone, keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalMb_with_nones_signed_ordered_permutedCols.sobj") print '' ########## # 0 Type # ########## print 'apex' origin = vector(ZZ,{39:0}) #cone = load("../../ComputeLines/Scripts/Input/0Cell.sobj") M = {extremal_curve:tropical_matrix_origin(pds[extremal_curve], keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M, "../../ComputeLines/Scripts/Input/TropicalM0_no_nones_signed_ordered_permutedCols.sobj") M_with_nones = {extremal_curve:tropical_matrix_with_nones_origin(pds[extremal_curve], keys) for extremal_curve in pds.keys()} # Takes about 15 minutes on a 2.4 GHz Intel(R) Core 2 Duo with 3MB # cache and 2GB RAM. # save(M_with_nones, "../../ComputeLines/Scripts/Input/TropicalM0_with_nones_signed_ordered_permutedCols.sobj") print '' # We check that the matrix has no zeros: entriesZero = [(extremalCurves, i,k) for extremalCurves in pds.keys() for i in range(0,5) for k in range(0,45) if M_with_nones[extremalCurves][i][k] == 0] print entriesZero []