os.chdir("../../Yoshida/Scripts") load("Yoshida.sage") os.chdir("../../BergmanFan/Scripts") load("BergmanFansArrangements.sage") # We load the Bergman fan of E6: BergmanFan = load("../../BergmanFan/Scripts/BergmanFanOfE6TruncatedFVectorAndOrbitsPerDimension.sobj") # The input data (vertexIndexListE6,rankE6,pos,alpha) necessary to compute the Bergman complex B(E6) is contained in the two files below: load("settingE6.sage") # "dict" is contained in the following file: load("Input/listsE6.sage") os.chdir("../../NarukiFan/Scripts") def flat_to_vertex(flat): v = zero_vector(36) for root in flat: v[root] = 1 return v def cone_from_flat_numbers(flat_numbers): vs = [flat_to_vertex(vertexIndexListE6[f]) for f in flat_numbers] return vs def yoshida_cone_orbits(yoshida_matrix, orbits, dim): cone_representatives = [] containments = [] overlaps = [] # First, select the full dimensional orbits full_orbits = [] for orbit in orbits: flats = orbit[0] Ycone = [Yoshida_matrix*v for v in cone_from_flat_numbers(flats)] if span(Ycone).dimension() == dim: full_orbits.append(orbit) # Next, arrange the full dimensional orbits by volume. def volume_square(flat_numbers): cone = cone_from_flat_numbers(flat_numbers) basis = span(cone).basis_matrix().gram_schmidt()[0] transform = matrix(cone).transpose()\basis.transpose() return transform.det()^2 / prod([c.norm()^2 for c in cone]) * prod([b.norm()^2 for b in basis.rows()]) full_orbits.sort(key=lambda o: volume_square(o[0]), reverse=True) for orbit in full_orbits: print "Next orbit" flats = orbit[0] Ycone = [Yoshida_matrix*v for v in cone_from_flat_numbers(flats)] if span(Ycone).dimension() < dim: print "Collapsed" continue # Check if the new cone is in the orbit of previous cones def same_as_previous(): for [old_flats,old_vertices] in cone_representatives: Pold = Polyhedron(rays=old_vertices) for flats in orbit: new_vertices = [Yoshida_matrix*v for v in cone_from_flat_numbers(flats)] Pnew = Polyhedron(rays=new_vertices) common = Pnew.intersection(Pold) if common.dim() < dim: continue if Pnew == Pold: return True if common == Pnew: print "New contained in old" containments.append([old_flats, flats]) return True if common == Pold: # Should never happen with sorted full_orbits print "Old contained in new" containments.append([old_flats, flats]) return False else: print "Overlap" overlaps.append([old_flats, flats]) return False if same_as_previous(): continue print ([flats, Ycone]) cone_representatives.append([flats, Ycone]) return (cone_representatives, containments, overlaps) # The following function takes all cones in an orbit and checks which ones have maximal intersection with a fixed cone: def check_overlaps(m, orbits, containment): [big, small] = containment P = Polyhedron(rays=[m*v for v in cone_from_flat_numbers(big)]) dim = P.dim() small_orbit = None overlap = [] contained = [] #Find the orbit of the small cone for orbit in orbits: if small in orbit: small_orbit = orbit for another_small in small_orbit: Q = Polyhedron(rays=[m*v for v in cone_from_flat_numbers(another_small)]) common = P.intersection(Q) if common.dim() == -1: continue elif common == Q: contained.append(another_small) elif common.dim() == dim: overlap.append(another_small) print "Overlap" if not all([v in P.rays() for v in common.rays()]): print "with new rays" return (contained, overlap) # The following function computes the canonical representative in TP^n by making the last coordinate of the vector equal 0: def projection(v): last = v[-1] subtract = vector([v[-1] for i in range(0, len(v))]) return v - subtract # The following functions computes the overlaps of all cones in the Naruki fan with the two maximal cone representatives: def maximal_overlapping_cones(): cones = load("../../NarukiFan/Output/NarukiCones.sobj") max_orbit1 = [orbit for orbit in BergmanFan[1][-1] if cones[0][0][0] in orbit][0] max_orbit2 = [orbit for orbit in BergmanFan[1][-1] if cones[0][1][0] in orbit][0] max1 = max_orbit1[0] max2 = max_orbit2[0] # Computation of overlaps with max1 Poly1 = Polyhedron(rays=[Yoshida_matrix*v for v in cone_from_flat_numbers(max1)]) max1_overlaps = [c for c in max_orbit1+max_orbit2 if Polyhedron(rays=[Yoshida_matrix*v for v in cone_from_flat_numbers(c)]).intersection(Poly1).dim() == 5] save(max1_overlaps, "Input/Overlaps_with_max1.sobj") # Computation of overlaps with max2 Poly2 = Polyhedron(rays=[Yoshida_matrix*v for v in cone_from_flat_numbers(max2)]) max2_overlaps = [c for c in max_orbit1+max_orbit2 if Polyhedron(rays=[Yoshida_matrix*v for v in cone_from_flat_numbers(c)]).intersection(Poly2).dim() == 5] save(max2_overlaps, "Input/Overlaps_with_max2.sobj") return (max_orbit1, max_orbit2) max1_overlaps = load("Overlaps_with_max1.sobj") max2_overlaps = load("Overlaps_with_max2.sobj") # We compute the two maximal orbits and save the data of the overlaps # (max_orbit1, max_orbit2) = maximal_overlapping_cones() # # We save the data: # save(max_orbit1, "Input/max_orbit1.sobj") # save(max_orbit2, "Input/max_orbit2.sobj") # We record the data: # print max_orbit1 # [[0, 1, 4, 36, 687], [0, 1, 4, 42, 687], [0, 1, 4, 51, 692], [0, 1, 4, 55, 692], [0, 1, 4, 73, 691], [0, 1, 4, 81, 691], [0, 1, 5, 36, 689], [0, 1, 5, 45, 689], [0, 1, 5, 46, 690], [0, 1, 5, 55, 690], [0, 1, 5, 73, 691], [0, 1, 5, 90, 691], [0, 1, 8, 36, 688], [0, 1, 8, 44, 688], [0, 1, 8, 48, 693], [0, 1, 8, 55, 693], [0, 1, 8, 73, 691], [0, 1, 8, 109, 691], [0, 1, 29, 44, 692], [0, 1, 29, 45, 692], [0, 1, 29, 46, 687], [0, 1, 29, 48, 687], [0, 1, 29, 90, 691], [0, 1, 29, 109, 691], [0, 1, 32, 42, 693], [0, 1, 32, 45, 693], [0, 1, 32, 46, 688], [0, 1, 32, 51, 688], [0, 1, 32, 81, 691], [0, 1, 32, 90, 691], [0, 1, 33, 42, 690], [0, 1, 33, 44, 690], [0, 1, 33, 48, 689], [0, 1, 33, 51, 689], [0, 1, 33, 81, 691], [0, 1, 33, 109, 691], [0, 3, 5, 39, 700], [0, 3, 5, 45, 700], [0, 3, 5, 46, 690], [0, 3, 5, 72, 690], [0, 3, 5, 84, 695], [0, 3, 5, 90, 695], [0, 3, 13, 38, 687], [0, 3, 13, 39, 687], [0, 3, 13, 66, 696], [0, 3, 13, 72, 696], [0, 3, 13, 84, 695], [0, 3, 13, 133, 695], [0, 3, 17, 39, 688], [0, 3, 17, 40, 688], [0, 3, 17, 65, 694], [0, 3, 17, 72, 694], [0, 3, 17, 84, 695], [0, 3, 17, 145, 695], [0, 3, 29, 40, 696], [0, 3, 29, 45, 696], [0, 3, 29, 46, 687], [0, 3, 29, 65, 687], [0, 3, 29, 90, 695], [0, 3, 29, 145, 695], [0, 3, 32, 38, 694], [0, 3, 32, 45, 694], [0, 3, 32, 46, 688], [0, 3, 32, 66, 688], [0, 3, 32, 90, 695], [0, 3, 32, 133, 695], [0, 3, 35, 38, 690], [0, 3, 35, 40, 690], [0, 3, 35, 65, 700], [0, 3, 35, 66, 700], [0, 3, 35, 133, 695], [0, 3, 35, 145, 695], [0, 4, 14, 42, 700], [0, 4, 14, 43, 700], [0, 4, 14, 51, 692], [0, 4, 14, 75, 697], [0, 4, 14, 81, 697], [0, 4, 14, 138, 692], [0, 4, 17, 40, 701], [0, 4, 17, 42, 701], [0, 4, 17, 51, 692], [0, 4, 17, 65, 694], [0, 4, 17, 81, 694], [0, 4, 17, 145, 692], [0, 4, 29, 40, 691], [0, 4, 29, 43, 691], [0, 4, 29, 65, 687], [0, 4, 29, 75, 687], [0, 4, 29, 138, 692], [0, 4, 29, 145, 692], [0, 4, 34, 36, 694], [0, 4, 34, 43, 694], [0, 4, 34, 55, 692], [0, 4, 34, 73, 701], [0, 4, 34, 75, 701], [0, 4, 34, 138, 692], [0, 4, 35, 36, 697], [0, 4, 35, 40, 697], [0, 4, 35, 55, 692], [0, 4, 35, 65, 700], [0, 4, 35, 73, 700], [0, 4, 35, 145, 692], [0, 5, 7, 37, 701], [0, 5, 7, 45, 701], [0, 5, 7, 46, 690], [0, 5, 7, 82, 698], [0, 5, 7, 90, 698], [0, 5, 7, 103, 690], [0, 5, 33, 37, 691], [0, 5, 33, 39, 691], [0, 5, 33, 72, 690], [0, 5, 33, 82, 689], [0, 5, 33, 84, 689], [0, 5, 33, 103, 690], [0, 5, 34, 36, 698], [0, 5, 34, 39, 698], [0, 5, 34, 55, 690], [0, 5, 34, 72, 690], [0, 5, 34, 73, 701], [0, 5, 34, 84, 701], [0, 5, 35, 36, 695], [0, 5, 35, 37, 695], [0, 5, 35, 55, 690], [0, 5, 35, 73, 700], [0, 5, 35, 82, 700], [0, 5, 35, 103, 690], [0, 7, 10, 37, 687], [0, 7, 10, 41, 687], [0, 7, 10, 82, 698], [0, 7, 10, 97, 699], [0, 7, 10, 103, 699], [0, 7, 10, 121, 698], [0, 7, 14, 37, 688], [0, 7, 14, 43, 688], [0, 7, 14, 75, 697], [0, 7, 14, 82, 698], [0, 7, 14, 103, 697], [0, 7, 14, 138, 698], [0, 7, 29, 43, 699], [0, 7, 29, 45, 699], [0, 7, 29, 46, 687], [0, 7, 29, 75, 687], [0, 7, 29, 90, 698], [0, 7, 29, 138, 698], [0, 7, 32, 41, 697], [0, 7, 32, 45, 697], [0, 7, 32, 46, 688], [0, 7, 32, 90, 698], [0, 7, 32, 97, 688], [0, 7, 32, 121, 698], [0, 7, 34, 41, 690], [0, 7, 34, 43, 690], [0, 7, 34, 75, 701], [0, 7, 34, 97, 701], [0, 7, 34, 121, 698], [0, 7, 34, 138, 698], [0, 8, 10, 41, 700], [0, 8, 10, 44, 700], [0, 8, 10, 48, 693], [0, 8, 10, 97, 699], [0, 8, 10, 109, 699], [0, 8, 10, 121, 693], [0, 8, 13, 38, 701], [0, 8, 13, 44, 701], [0, 8, 13, 48, 693], [0, 8, 13, 66, 696], [0, 8, 13, 109, 696], [0, 8, 13, 133, 693], [0, 8, 32, 38, 691], [0, 8, 32, 41, 691], [0, 8, 32, 66, 688], [0, 8, 32, 97, 688], [0, 8, 32, 121, 693], [0, 8, 32, 133, 693], [0, 8, 34, 36, 696], [0, 8, 34, 41, 696], [0, 8, 34, 55, 693], [0, 8, 34, 73, 701], [0, 8, 34, 97, 701], [0, 8, 34, 121, 693], [0, 8, 35, 36, 699], [0, 8, 35, 38, 699], [0, 8, 35, 55, 693], [0, 8, 35, 66, 700], [0, 8, 35, 73, 700], [0, 8, 35, 133, 693], [0, 10, 17, 40, 689], [0, 10, 17, 41, 689], [0, 10, 17, 65, 694], [0, 10, 17, 97, 699], [0, 10, 17, 121, 694], [0, 10, 17, 145, 699], [0, 10, 29, 40, 698], [0, 10, 29, 44, 698], [0, 10, 29, 48, 687], [0, 10, 29, 65, 687], [0, 10, 29, 109, 699], [0, 10, 29, 145, 699], [0, 10, 33, 37, 694], [0, 10, 33, 44, 694], [0, 10, 33, 48, 689], [0, 10, 33, 82, 689], [0, 10, 33, 103, 699], [0, 10, 33, 109, 699], [0, 10, 35, 37, 693], [0, 10, 35, 40, 693], [0, 10, 35, 65, 700], [0, 10, 35, 82, 700], [0, 10, 35, 103, 699], [0, 10, 35, 145, 699], [0, 13, 14, 38, 689], [0, 13, 14, 43, 689], [0, 13, 14, 66, 696], [0, 13, 14, 75, 697], [0, 13, 14, 133, 697], [0, 13, 14, 138, 696], [0, 13, 29, 43, 695], [0, 13, 29, 44, 695], [0, 13, 29, 48, 687], [0, 13, 29, 75, 687], [0, 13, 29, 109, 696], [0, 13, 29, 138, 696], [0, 13, 33, 39, 697], [0, 13, 33, 44, 697], [0, 13, 33, 48, 689], [0, 13, 33, 72, 696], [0, 13, 33, 84, 689], [0, 13, 33, 109, 696], [0, 13, 34, 39, 693], [0, 13, 34, 43, 693], [0, 13, 34, 72, 696], [0, 13, 34, 75, 701], [0, 13, 34, 84, 701], [0, 13, 34, 138, 696], [0, 14, 32, 38, 698], [0, 14, 32, 42, 698], [0, 14, 32, 51, 688], [0, 14, 32, 66, 688], [0, 14, 32, 81, 697], [0, 14, 32, 133, 697], [0, 14, 33, 37, 696], [0, 14, 33, 42, 696], [0, 14, 33, 51, 689], [0, 14, 33, 81, 697], [0, 14, 33, 82, 689], [0, 14, 33, 103, 697], [0, 14, 35, 37, 692], [0, 14, 35, 38, 692], [0, 14, 35, 66, 700], [0, 14, 35, 82, 700], [0, 14, 35, 103, 697], [0, 14, 35, 133, 697], [0, 17, 32, 41, 695], [0, 17, 32, 42, 695], [0, 17, 32, 51, 688], [0, 17, 32, 81, 694], [0, 17, 32, 97, 688], [0, 17, 32, 121, 694], [0, 17, 33, 39, 699], [0, 17, 33, 42, 699], [0, 17, 33, 51, 689], [0, 17, 33, 72, 694], [0, 17, 33, 81, 694], [0, 17, 33, 84, 689], [0, 17, 34, 39, 692], [0, 17, 34, 41, 692], [0, 17, 34, 72, 694], [0, 17, 34, 84, 701], [0, 17, 34, 97, 701], [0, 17, 34, 121, 694], [1, 2, 4, 36, 687], [1, 2, 4, 54, 703], [1, 2, 4, 55, 703], [1, 2, 4, 62, 687], [1, 2, 4, 73, 702], [1, 2, 4, 79, 702], [1, 2, 5, 36, 689], [1, 2, 5, 50, 705], [1, 2, 5, 55, 705], [1, 2, 5, 64, 689], [1, 2, 5, 73, 702], [1, 2, 5, 87, 702], [1, 2, 8, 36, 688], [1, 2, 8, 53, 704], [1, 2, 8, 55, 704], [1, 2, 8, 63, 688], [1, 2, 8, 73, 702], [1, 2, 8, 107, 702], [1, 2, 21, 50, 687], [1, 2, 21, 53, 687], [1, 2, 21, 63, 703], [1, 2, 21, 64, 703], [1, 2, 21, 87, 702], [1, 2, 21, 107, 702], [1, 2, 27, 50, 688], [1, 2, 27, 54, 688], [1, 2, 27, 62, 704], [1, 2, 27, 64, 704], [1, 2, 27, 79, 702], [1, 2, 27, 87, 702], [1, 2, 28, 53, 689], [1, 2, 28, 54, 689], [1, 2, 28, 62, 705], [1, 2, 28, 63, 705], [1, 2, 28, 79, 702], [1, 2, 28, 107, 702], [1, 4, 9, 36, 687], [1, 4, 9, 52, 707], [1, 4, 9, 55, 707], [1, 4, 9, 73, 706], [1, 4, 9, 80, 706], [1, 4, 9, 114, 687], [1, 4, 21, 42, 687], [1, 4, 21, 51, 702], [1, 4, 21, 52, 702], [1, 4, 21, 80, 703], [1, 4, 21, 81, 703], [1, 4, 21, 114, 687], [1, 4, 26, 42, 687], [1, 4, 26, 51, 706], [1, 4, 26, 54, 706], [1, 4, 26, 62, 687], [1, 4, 26, 79, 707], [1, 4, 26, 81, 707], [1, 4, 29, 52, 691], [1, 4, 29, 54, 691], [1, 4, 29, 62, 687], [1, 4, 29, 79, 692], [1, 4, 29, 80, 692], [1, 4, 29, 114, 687], [1, 5, 9, 36, 689], [1, 5, 9, 47, 709], [1, 5, 9, 55, 709], [1, 5, 9, 73, 706], [1, 5, 9, 89, 706], [1, 5, 9, 116, 689], [1, 5, 28, 45, 689], [1, 5, 28, 46, 702], [1, 5, 28, 47, 702], [1, 5, 28, 89, 705], [1, 5, 28, 90, 705], [1, 5, 28, 116, 689], [1, 5, 31, 45, 689], [1, 5, 31, 46, 706], [1, 5, 31, 50, 706], [1, 5, 31, 64, 689], [1, 5, 31, 87, 709], [1, 5, 31, 90, 709], [1, 5, 33, 47, 691], [1, 5, 33, 50, 691], [1, 5, 33, 64, 689], [1, 5, 33, 87, 690], [1, 5, 33, 89, 690], [1, 5, 33, 116, 689], [1, 8, 9, 36, 688], [1, 8, 9, 49, 708], [1, 8, 9, 55, 708], [1, 8, 9, 73, 706], [1, 8, 9, 108, 706], [1, 8, 9, 115, 688], [1, 8, 27, 44, 688], [1, 8, 27, 48, 702], [1, 8, 27, 49, 702], [1, 8, 27, 108, 704], [1, 8, 27, 109, 704], [1, 8, 27, 115, 688], [1, 8, 30, 44, 688], [1, 8, 30, 48, 706], [1, 8, 30, 53, 706], [1, 8, 30, 63, 688], [1, 8, 30, 107, 708], [1, 8, 30, 109, 708], [1, 8, 32, 49, 691], [1, 8, 32, 53, 691], [1, 8, 32, 63, 688], [1, 8, 32, 107, 693], [1, 8, 32, 108, 693], [1, 8, 32, 115, 688], [1, 9, 26, 47, 687], [1, 9, 26, 49, 687], [1, 9, 26, 89, 706], [1, 9, 26, 108, 706], [1, 9, 26, 115, 707], [1, 9, 26, 116, 707], [1, 9, 30, 47, 688], [1, 9, 30, 52, 688], [1, 9, 30, 80, 706], [1, 9, 30, 89, 706], [1, 9, 30, 114, 708], [1, 9, 30, 116, 708], [1, 9, 31, 49, 689], [1, 9, 31, 52, 689], [1, 9, 31, 80, 706], [1, 9, 31, 108, 706], [1, 9, 31, 114, 709], [1, 9, 31, 115, 709], [1, 21, 30, 52, 690], [1, 21, 30, 53, 690], [1, 21, 30, 63, 703], [1, 21, 30, 80, 703], [1, 21, 30, 107, 708], [1, 21, 30, 114, 708], [1, 21, 31, 50, 693], [1, 21, 31, 52, 693], [1, 21, 31, 64, 703], [1, 21, 31, 80, 703], [1, 21, 31, 87, 709], [1, 21, 31, 114, 709], [1, 21, 32, 42, 693], [1, 21, 32, 51, 709], [1, 21, 32, 53, 709], [1, 21, 32, 63, 703], [1, 21, 32, 81, 703], [1, 21, 32, 107, 693], [1, 21, 33, 42, 690], [1, 21, 33, 50, 708], [1, 21, 33, 51, 708], [1, 21, 33, 64, 703], [1, 21, 33, 81, 703], [1, 21, 33, 87, 690], [1, 26, 27, 49, 690], [1, 26, 27, 54, 690], [1, 26, 27, 62, 704], [1, 26, 27, 79, 707], [1, 26, 27, 108, 704], [1, 26, 27, 115, 707], [1, 26, 28, 47, 693], [1, 26, 28, 54, 693], [1, 26, 28, 62, 705], [1, 26, 28, 79, 707], [1, 26, 28, 89, 705], [1, 26, 28, 116, 707], [1, 26, 32, 42, 693], [1, 26, 32, 49, 705], [1, 26, 32, 51, 705], [1, 26, 32, 81, 707], [1, 26, 32, 108, 693], [1, 26, 32, 115, 707], [1, 26, 33, 42, 690], [1, 26, 33, 47, 704], [1, 26, 33, 51, 704], [1, 26, 33, 81, 707], [1, 26, 33, 89, 690], [1, 26, 33, 116, 707], [1, 27, 29, 44, 692], [1, 27, 29, 48, 709], [1, 27, 29, 54, 709], [1, 27, 29, 62, 704], [1, 27, 29, 79, 692], [1, 27, 29, 109, 704], [1, 27, 31, 49, 692], [1, 27, 31, 50, 692], [1, 27, 31, 64, 704], [1, 27, 31, 87, 709], [1, 27, 31, 108, 704], [1, 27, 31, 115, 709], [1, 27, 33, 44, 690], [1, 27, 33, 48, 707], [1, 27, 33, 50, 707], [1, 27, 33, 64, 704], [1, 27, 33, 87, 690], [1, 27, 33, 109, 704], [1, 28, 29, 45, 692], [1, 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21, 68, 690], [18, 19, 21, 76, 701], [18, 19, 21, 142, 698], [18, 19, 21, 144, 701], [18, 19, 21, 153, 690], [18, 19, 25, 60, 689], [18, 19, 25, 71, 690], [18, 19, 25, 76, 691], [18, 19, 25, 131, 689], [18, 19, 25, 139, 691], [18, 19, 25, 153, 690], [18, 19, 30, 71, 690], [18, 19, 30, 91, 701], [18, 19, 30, 110, 698], [18, 19, 30, 131, 701], [18, 19, 30, 139, 698], [18, 19, 30, 151, 690], [18, 19, 35, 60, 704], [18, 19, 35, 76, 707], [18, 19, 35, 91, 704], [18, 19, 35, 110, 707], [18, 19, 35, 151, 690], [18, 19, 35, 153, 690], [18, 20, 25, 77, 691], [18, 20, 25, 100, 690], [18, 20, 25, 113, 689], [18, 20, 25, 120, 689], [18, 20, 25, 128, 691], [18, 20, 25, 147, 690], [18, 20, 31, 68, 696], [18, 20, 31, 100, 697], [18, 20, 31, 120, 689], [18, 20, 31, 128, 696], [18, 20, 31, 142, 697], [18, 20, 31, 144, 689], [18, 21, 30, 52, 690], [18, 21, 30, 80, 701], [18, 21, 30, 114, 698], [18, 21, 30, 117, 698], [18, 21, 30, 127, 701], [18, 21, 30, 146, 690], [18, 21, 31, 52, 693], [18, 21, 31, 68, 696], [18, 21, 31, 80, 701], [18, 21, 31, 114, 696], [18, 21, 31, 142, 693], [18, 21, 31, 144, 701], [18, 25, 29, 71, 710], [18, 25, 29, 100, 713], [18, 25, 29, 120, 710], [18, 25, 29, 128, 691], [18, 25, 29, 131, 713], [18, 25, 29, 139, 691], [18, 29, 30, 52, 705], [18, 29, 30, 71, 710], [18, 29, 30, 80, 710], [18, 29, 30, 114, 698], [18, 29, 30, 131, 705], [18, 29, 30, 139, 698], [18, 29, 31, 52, 704], [18, 29, 31, 80, 710], [18, 29, 31, 100, 704], [18, 29, 31, 114, 696], [18, 29, 31, 120, 710], [18, 29, 31, 128, 696], [19, 20, 25, 59, 689], [19, 20, 25, 95, 691], [19, 20, 25, 101, 690], [19, 20, 25, 106, 691], [19, 20, 25, 136, 689], [19, 20, 25, 149, 690], [19, 20, 32, 68, 712], [19, 20, 32, 95, 691], [19, 20, 32, 101, 711], [19, 20, 32, 136, 712], [19, 20, 32, 142, 691], [19, 20, 32, 144, 711], [19, 21, 30, 53, 690], [19, 21, 30, 63, 698], [19, 21, 30, 92, 701], [19, 21, 30, 107, 701], [19, 21, 30, 135, 698], [19, 21, 30, 148, 690], [19, 21, 32, 53, 709], [19, 21, 32, 63, 698], [19, 21, 32, 68, 712], [19, 21, 32, 107, 712], [19, 21, 32, 142, 698], [19, 21, 32, 144, 709], [19, 25, 28, 71, 694], [19, 25, 28, 95, 694], [19, 25, 28, 101, 699], [19, 25, 28, 131, 689], [19, 25, 28, 136, 689], [19, 25, 28, 139, 699], [19, 28, 30, 53, 692], [19, 28, 30, 63, 694], [19, 28, 30, 71, 694], [19, 28, 30, 107, 701], [19, 28, 30, 131, 701], [19, 28, 30, 139, 692], [19, 28, 32, 53, 707], [19, 28, 32, 63, 694], [19, 28, 32, 95, 694], [19, 28, 32, 101, 707], [19, 28, 32, 107, 712], [19, 28, 32, 136, 712], [20, 25, 26, 77, 700], [20, 25, 26, 95, 695], [20, 25, 26, 101, 690], [20, 25, 26, 113, 695], [20, 25, 26, 136, 700], [20, 25, 26, 147, 690], [20, 25, 27, 59, 695], [20, 25, 27, 100, 690], [20, 25, 27, 106, 700], [20, 25, 27, 120, 700], [20, 25, 27, 128, 695], [20, 25, 27, 149, 690], [20, 25, 34, 59, 703], [20, 25, 34, 77, 703], [20, 25, 34, 106, 708], [20, 25, 34, 113, 708], [20, 25, 34, 147, 690], [20, 25, 34, 149, 690], [20, 26, 27, 49, 690], [20, 26, 27, 93, 695], [20, 26, 27, 108, 700], [20, 26, 27, 115, 695], [20, 26, 27, 118, 700], [20, 26, 27, 150, 690], [20, 26, 32, 49, 705], [20, 26, 32, 95, 695], [20, 26, 32, 101, 711], [20, 26, 32, 108, 711], [20, 26, 32, 115, 695], [20, 26, 32, 136, 705], [20, 27, 31, 49, 692], [20, 27, 31, 100, 697], [20, 27, 31, 108, 700], [20, 27, 31, 115, 697], [20, 27, 31, 120, 700], [20, 27, 31, 128, 692], [20, 31, 32, 49, 703], [20, 31, 32, 68, 703], [20, 31, 32, 108, 711], [20, 31, 32, 115, 697], [20, 31, 32, 142, 697], [20, 31, 32, 144, 711], [21, 22, 23, 61, 695], [21, 22, 23, 78, 700], [21, 22, 23, 99, 690], [21, 22, 23, 129, 695], [21, 22, 23, 137, 700], [21, 22, 23, 152, 690], [21, 22, 30, 53, 690], [21, 22, 30, 63, 695], [21, 22, 30, 107, 700], [21, 22, 30, 117, 700], [21, 22, 30, 127, 695], [21, 22, 30, 146, 690], [21, 22, 32, 53, 709], [21, 22, 32, 63, 695], [21, 22, 32, 99, 713], [21, 22, 32, 107, 713], [21, 22, 32, 129, 695], [21, 22, 32, 137, 709], [21, 23, 30, 52, 690], [21, 23, 30, 80, 700], [21, 23, 30, 92, 695], [21, 23, 30, 114, 695], [21, 23, 30, 135, 700], [21, 23, 30, 148, 690], [21, 23, 31, 52, 693], [21, 23, 31, 80, 700], [21, 23, 31, 99, 699], [21, 23, 31, 114, 699], [21, 23, 31, 129, 693], [21, 23, 31, 137, 700], [21, 30, 33, 92, 703], [21, 30, 33, 117, 703], [21, 30, 33, 127, 708], [21, 30, 33, 135, 708], [21, 30, 33, 146, 690], [21, 30, 33, 148, 690], [21, 31, 32, 68, 703], [21, 31, 32, 99, 703], [21, 31, 32, 129, 693], [21, 31, 32, 137, 709], [21, 31, 32, 142, 693], [21, 31, 32, 144, 709], [22, 23, 24, 61, 689], [22, 23, 24, 78, 691], [22, 23, 24, 94, 691], [22, 23, 24, 102, 690], [22, 23, 24, 119, 689], [22, 23, 24, 152, 690], [22, 23, 30, 94, 695], [22, 23, 30, 102, 690], [22, 23, 30, 105, 700], [22, 23, 30, 111, 695], [22, 23, 30, 119, 700], [22, 23, 30, 125, 690], [22, 23, 34, 61, 704], [22, 23, 34, 78, 707], [22, 23, 34, 105, 704], [22, 23, 34, 111, 707], [22, 23, 34, 125, 690], [22, 23, 34, 152, 690], [22, 24, 28, 69, 696], [22, 24, 28, 94, 696], [22, 24, 28, 102, 697], [22, 24, 28, 119, 689], [22, 24, 28, 123, 689], [22, 24, 28, 140, 697], [22, 28, 30, 53, 692], [22, 28, 30, 63, 697], [22, 28, 30, 94, 692], [22, 28, 30, 102, 697], [22, 28, 30, 107, 700], [22, 28, 30, 119, 700], [22, 28, 32, 53, 707], [22, 28, 32, 63, 697], [22, 28, 32, 69, 707], [22, 28, 32, 107, 713], [22, 28, 32, 123, 713], [22, 28, 32, 140, 697], [23, 24, 29, 70, 712], [23, 24, 29, 94, 691], [23, 24, 29, 102, 711], [23, 24, 29, 119, 712], [23, 24, 29, 122, 691], [23, 24, 29, 132, 711], [23, 29, 30, 52, 705], [23, 29, 30, 80, 711], [23, 29, 30, 94, 695], [23, 29, 30, 102, 711], [23, 29, 30, 114, 695], [23, 29, 30, 119, 705], [23, 29, 31, 52, 704], [23, 29, 31, 70, 704], [23, 29, 31, 80, 711], [23, 29, 31, 114, 699], [23, 29, 31, 122, 699], [23, 29, 31, 132, 711], [24, 26, 27, 54, 690], [24, 26, 27, 62, 698], [24, 26, 27, 79, 701], [24, 26, 27, 93, 701], [24, 26, 27, 118, 698], [24, 26, 27, 150, 690], [24, 26, 28, 54, 693], [24, 26, 28, 62, 696], [24, 26, 28, 69, 696], [24, 26, 28, 79, 701], [24, 26, 28, 123, 701], [24, 26, 28, 140, 693], [24, 27, 29, 54, 709], [24, 27, 29, 62, 698], [24, 27, 29, 70, 712], [24, 27, 29, 79, 712], [24, 27, 29, 122, 698], [24, 27, 29, 132, 709], [24, 28, 29, 54, 708], [24, 28, 29, 62, 696], [24, 28, 29, 79, 712], [24, 28, 29, 94, 696], [24, 28, 29, 102, 708], [24, 28, 29, 119, 712], [25, 26, 27, 54, 690], [25, 26, 27, 62, 695], [25, 26, 27, 79, 700], [25, 26, 27, 124, 690], [25, 26, 27, 126, 695], [25, 26, 27, 134, 700], [25, 26, 28, 54, 693], [25, 26, 28, 62, 699], [25, 26, 28, 79, 700], [25, 26, 28, 95, 693], [25, 26, 28, 101, 699], [25, 26, 28, 136, 700], [25, 27, 29, 54, 709], [25, 27, 29, 62, 695], [25, 27, 29, 79, 713], [25, 27, 29, 100, 713], [25, 27, 29, 120, 709], [25, 27, 29, 128, 695], [25, 28, 29, 54, 708], [25, 28, 29, 62, 699], [25, 28, 29, 71, 708], [25, 28, 29, 79, 713], [25, 28, 29, 131, 713], [25, 28, 29, 139, 699], [26, 27, 33, 93, 704], [26, 27, 33, 118, 707], [26, 27, 33, 124, 690], [26, 27, 33, 126, 707], [26, 27, 33, 134, 704], [26, 27, 33, 150, 690], [26, 28, 32, 69, 707], [26, 28, 32, 95, 693], [26, 28, 32, 101, 707], [26, 28, 32, 123, 705], [26, 28, 32, 136, 705], [26, 28, 32, 140, 693], [27, 29, 31, 70, 704], [27, 29, 31, 100, 704], [27, 29, 31, 120, 709], [27, 29, 31, 122, 692], [27, 29, 31, 128, 692], [27, 29, 31, 132, 709], [28, 29, 30, 71, 708], [28, 29, 30, 94, 692], [28, 29, 30, 102, 708], [28, 29, 30, 119, 705], [28, 29, 30, 131, 705], [28, 29, 30, 139, 692]] # print max_orbit2 # [[0, 1, 4, 158, 691], [0, 1, 4, 172, 692], [0, 1, 4, 204, 687], [0, 1, 5, 156, 691], [0, 1, 5, 175, 690], [0, 1, 5, 214, 689], [0, 1, 8, 157, 691], [0, 1, 8, 185, 693], [0, 1, 8, 205, 688], [0, 1, 29, 158, 691], [0, 1, 29, 165, 687], [0, 1, 29, 238, 692], [0, 1, 32, 157, 691], [0, 1, 32, 166, 688], [0, 1, 32, 229, 693], [0, 1, 33, 156, 691], [0, 1, 33, 167, 689], [0, 1, 33, 211, 690], [0, 3, 5, 159, 695], [0, 3, 5, 173, 690], [0, 3, 5, 276, 700], [0, 3, 13, 169, 695], [0, 3, 13, 192, 696], [0, 3, 13, 204, 687], [0, 3, 17, 168, 695], [0, 3, 17, 189, 694], [0, 3, 17, 205, 688], [0, 3, 29, 169, 695], [0, 3, 29, 188, 687], [0, 3, 29, 290, 696], [0, 3, 32, 168, 695], [0, 3, 32, 195, 688], [0, 3, 32, 282, 694], [0, 3, 35, 159, 695], [0, 3, 35, 196, 700], [0, 3, 35, 211, 690], [0, 4, 14, 163, 697], [0, 4, 14, 170, 692], [0, 4, 14, 276, 700], [0, 4, 17, 164, 694], [0, 4, 17, 171, 692], [0, 4, 17, 303, 701], [0, 4, 29, 165, 687], [0, 4, 29, 172, 692], [0, 4, 29, 309, 691], [0, 4, 34, 171, 692], [0, 4, 34, 198, 701], [0, 4, 34, 282, 694], [0, 4, 35, 170, 692], [0, 4, 35, 200, 700], [0, 4, 35, 319, 697], [0, 5, 7, 160, 698], [0, 5, 7, 174, 690], [0, 5, 7, 303, 701], [0, 5, 33, 167, 689], [0, 5, 33, 175, 690], [0, 5, 33, 309, 691], [0, 5, 34, 174, 690], [0, 5, 34, 181, 701], [0, 5, 34, 342, 698], [0, 5, 35, 173, 690], [0, 5, 35, 196, 700], [0, 5, 35, 350, 695], [0, 7, 10, 183, 698], [0, 7, 10, 187, 699], [0, 7, 10, 204, 687], [0, 7, 14, 182, 698], [0, 7, 14, 194, 697], [0, 7, 14, 205, 688], [0, 7, 29, 179, 687], [0, 7, 29, 183, 698], [0, 7, 29, 373, 699], [0, 7, 32, 180, 688], [0, 7, 32, 182, 698], [0, 7, 32, 319, 697], [0, 7, 34, 160, 698], [0, 7, 34, 181, 701], [0, 7, 34, 211, 690], [0, 8, 10, 161, 699], [0, 8, 10, 176, 693], [0, 8, 10, 276, 700], [0, 8, 13, 162, 696], [0, 8, 13, 184, 693], [0, 8, 13, 303, 701], [0, 8, 32, 166, 688], [0, 8, 32, 185, 693], [0, 8, 32, 309, 691], [0, 8, 34, 184, 693], [0, 8, 34, 191, 701], [0, 8, 34, 290, 696], [0, 8, 35, 176, 693], [0, 8, 35, 199, 700], [0, 8, 35, 373, 699], [0, 10, 17, 178, 694], [0, 10, 17, 186, 699], [0, 10, 17, 214, 689], [0, 10, 29, 179, 687], [0, 10, 29, 187, 699], [0, 10, 29, 342, 698], [0, 10, 33, 186, 699], [0, 10, 33, 197, 689], [0, 10, 33, 282, 694], [0, 10, 35, 161, 699], [0, 10, 35, 199, 700], [0, 10, 35, 229, 693], [0, 13, 14, 177, 696], [0, 13, 14, 193, 697], [0, 13, 14, 214, 689], [0, 13, 29, 188, 687], [0, 13, 29, 192, 696], [0, 13, 29, 350, 695], [0, 13, 33, 177, 696], [0, 13, 33, 190, 689], [0, 13, 33, 319, 697], [0, 13, 34, 162, 696], [0, 13, 34, 191, 701], [0, 13, 34, 229, 693], [0, 14, 32, 180, 688], [0, 14, 32, 194, 697], [0, 14, 32, 342, 698], [0, 14, 33, 190, 689], [0, 14, 33, 193, 697], [0, 14, 33, 290, 696], [0, 14, 35, 163, 697], [0, 14, 35, 200, 700], [0, 14, 35, 238, 692], [0, 17, 32, 189, 694], [0, 17, 32, 195, 688], [0, 17, 32, 350, 695], [0, 17, 33, 178, 694], [0, 17, 33, 197, 689], [0, 17, 33, 373, 699], [0, 17, 34, 164, 694], [0, 17, 34, 198, 701], [0, 17, 34, 238, 692], [1, 2, 4, 203, 702], [1, 2, 4, 213, 687], [1, 2, 4, 251, 703], [1, 2, 5, 201, 702], [1, 2, 5, 216, 689], [1, 2, 5, 254, 705], [1, 2, 8, 202, 702], [1, 2, 8, 223, 688], [1, 2, 8, 261, 704], [1, 2, 21, 165, 687], [1, 2, 21, 203, 702], [1, 2, 21, 242, 703], [1, 2, 27, 166, 688], [1, 2, 27, 202, 702], [1, 2, 27, 241, 704], [1, 2, 28, 167, 689], [1, 2, 28, 201, 702], [1, 2, 28, 236, 705], [1, 4, 9, 212, 687], [1, 4, 9, 225, 706], [1, 4, 9, 320, 707], [1, 4, 21, 213, 687], [1, 4, 21, 242, 703], [1, 4, 21, 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27, 353, 698], [16, 27, 31, 367, 692], [16, 27, 31, 377, 697], [16, 27, 31, 387, 700], [16, 27, 33, 193, 697], [16, 27, 33, 298, 707], [16, 27, 33, 388, 713], [17, 18, 20, 197, 689], [17, 18, 20, 356, 702], [17, 18, 20, 419, 705], [17, 18, 21, 198, 701], [17, 18, 21, 203, 702], [17, 18, 21, 407, 713], [17, 20, 26, 168, 695], [17, 20, 26, 231, 705], [17, 20, 26, 372, 711], [17, 20, 32, 231, 705], [17, 20, 32, 327, 711], [17, 20, 32, 362, 695], [17, 20, 34, 253, 705], [17, 20, 34, 299, 708], [17, 20, 34, 367, 692], [17, 21, 22, 168, 695], [17, 21, 22, 237, 709], [17, 21, 22, 370, 713], [17, 21, 32, 267, 695], [17, 21, 32, 370, 713], [17, 21, 32, 409, 709], [17, 21, 33, 274, 699], [17, 21, 33, 299, 708], [17, 21, 33, 331, 713], [17, 22, 24, 197, 689], [17, 22, 24, 368, 709], [17, 22, 24, 371, 706], [17, 22, 32, 237, 709], [17, 22, 32, 267, 695], [17, 22, 32, 329, 713], [17, 22, 34, 297, 704], [17, 22, 34, 336, 709], [17, 22, 34, 413, 692], [17, 24, 26, 198, 701], [17, 24, 26, 225, 706], [17, 24, 26, 275, 711], [17, 26, 32, 362, 695], [17, 26, 32, 372, 711], [17, 26, 32, 411, 705], [17, 26, 33, 297, 704], [17, 26, 33, 347, 711], [17, 26, 33, 400, 699], [18, 19, 20, 268, 689], [18, 19, 20, 321, 691], [18, 19, 20, 381, 690], [18, 19, 21, 239, 690], [18, 19, 21, 357, 701], [18, 19, 21, 396, 698], [18, 19, 25, 358, 691], [18, 19, 25, 381, 690], [18, 19, 25, 397, 689], [18, 19, 30, 239, 690], [18, 19, 30, 271, 698], [18, 19, 30, 322, 701], [18, 19, 35, 173, 690], [18, 19, 35, 421, 707], [18, 19, 35, 425, 704], [18, 20, 25, 268, 689], [18, 20, 25, 300, 690], [18, 20, 25, 358, 691], [18, 20, 31, 215, 689], [18, 20, 31, 328, 697], [18, 20, 31, 360, 696], [18, 21, 30, 271, 698], [18, 21, 30, 300, 690], [18, 21, 30, 357, 701], [18, 21, 31, 272, 696], [18, 21, 31, 333, 701], [18, 21, 31, 410, 693], [18, 25, 29, 158, 691], [18, 25, 29, 273, 710], [18, 25, 29, 407, 713], [18, 29, 30, 183, 698], [18, 29, 30, 359, 710], [18, 29, 30, 419, 705], [18, 29, 31, 192, 696], [18, 29, 31, 344, 710], [18, 29, 31, 425, 704], [19, 20, 25, 300, 690], [19, 20, 25, 321, 691], [19, 20, 25, 397, 689], [19, 20, 32, 157, 691], [19, 20, 32, 270, 711], [19, 20, 32, 399, 712], [19, 21, 30, 300, 690], [19, 21, 30, 322, 701], [19, 21, 30, 396, 698], [19, 21, 32, 182, 698], [19, 21, 32, 323, 712], [19, 21, 32, 365, 709], [19, 25, 28, 216, 689], [19, 25, 28, 324, 694], [19, 25, 28, 395, 699], [19, 28, 30, 334, 701], [19, 28, 30, 398, 694], [19, 28, 30, 424, 692], [19, 28, 32, 189, 694], [19, 28, 32, 351, 712], [19, 28, 32, 421, 707], [20, 25, 26, 232, 690], [20, 25, 26, 266, 695], [20, 25, 26, 387, 700], [20, 25, 27, 232, 690], [20, 25, 27, 325, 700], [20, 25, 27, 362, 695], [20, 25, 34, 174, 690], [20, 25, 34, 363, 703], [20, 25, 34, 418, 708], [20, 26, 27, 266, 695], [20, 26, 27, 325, 700], [20, 26, 27, 381, 690], [20, 26, 32, 168, 695], [20, 26, 32, 327, 711], [20, 26, 32, 411, 705], [20, 27, 31, 269, 697], [20, 27, 31, 283, 700], [20, 27, 31, 367, 692], [20, 31, 32, 194, 697], [20, 31, 32, 348, 711], [20, 31, 32, 363, 703], [21, 22, 23, 239, 690], [21, 22, 23, 361, 695], [21, 22, 23, 386, 700], [21, 22, 30, 326, 700], [21, 22, 30, 361, 695], [21, 22, 30, 379, 690], [21, 22, 32, 168, 695], [21, 22, 32, 329, 713], [21, 22, 32, 409, 709], [21, 23, 30, 267, 695], [21, 23, 30, 379, 690], [21, 23, 30, 386, 700], [21, 23, 31, 274, 699], [21, 23, 31, 283, 700], [21, 23, 31, 364, 693], [21, 30, 33, 175, 690], [21, 30, 33, 251, 703], [21, 30, 33, 385, 708], [21, 31, 32, 185, 693], [21, 31, 32, 251, 703], [21, 31, 32, 337, 709], [22, 23, 24, 301, 690], [22, 23, 24, 390, 691], [22, 23, 24, 401, 689], [22, 23, 30, 239, 690], [22, 23, 30, 267, 695], [22, 23, 30, 326, 700], [22, 23, 34, 174, 690], [22, 23, 34, 366, 704], [22, 23, 34, 408, 707], [22, 24, 28, 216, 689], [22, 24, 28, 330, 697], [22, 24, 28, 392, 696], [22, 28, 30, 284, 700], [22, 28, 30, 402, 697], [22, 28, 30, 413, 692], [22, 28, 32, 194, 697], [22, 28, 32, 332, 713], [22, 28, 32, 408, 707], [23, 24, 29, 158, 691], [23, 24, 29, 275, 711], [23, 24, 29, 406, 712], [23, 29, 30, 169, 695], [23, 29, 30, 393, 711], [23, 29, 30, 414, 705], [23, 29, 31, 187, 699], [23, 29, 31, 348, 711], [23, 29, 31, 366, 704], [24, 26, 27, 301, 690], [24, 26, 27, 389, 701], [24, 26, 27, 404, 698], [24, 26, 28, 334, 701], [24, 26, 28, 405, 696], [24, 26, 28, 412, 693], [24, 27, 29, 183, 698], [24, 27, 29, 368, 709], [24, 27, 29, 391, 712], [24, 28, 29, 192, 696], [24, 28, 29, 351, 712], [24, 28, 29, 415, 708], [25, 26, 27, 362, 695], [25, 26, 27, 381, 690], [25, 26, 27, 387, 700], [25, 26, 28, 284, 700], [25, 26, 28, 400, 699], [25, 26, 28, 416, 693], [25, 27, 29, 169, 695], [25, 27, 29, 388, 713], [25, 27, 29, 422, 709], [25, 28, 29, 187, 699], [25, 28, 29, 332, 713], [25, 28, 29, 418, 708], [26, 27, 33, 175, 690], [26, 27, 33, 261, 704], [26, 27, 33, 320, 707], [26, 28, 32, 185, 693], [26, 28, 32, 254, 705], [26, 28, 32, 320, 707], [27, 29, 31, 172, 692], [27, 29, 31, 261, 704], [27, 29, 31, 337, 709], [28, 29, 30, 172, 692], [28, 29, 30, 254, 705], [28, 29, 30, 385, 708]] # We load the two maximal orbits: max_orbit1 = load("Input/max_orbit1.sobj") max_orbit2 = load("Input/max_orbit1.sobj") # We load the precomputed data of the overlaps: max1_overlaps = load("Input/Overlaps_with_max1.sobj") max2_overlaps = load("Input/Overlaps_with_max2.sobj") # We record the data: print max1_overlaps [[0, 1, 4, 36, 687], [0, 1, 4, 55, 692], [0, 1, 4, 73, 691]] print max2_overlaps [[0, 1, 4, 158, 691], [0, 1, 4, 172, 692], [0, 1, 4, 204, 687], [0, 1, 29, 165, 687], [0, 1, 29, 238, 692], [0, 4, 29, 165, 687], [0, 4, 29, 172, 692], [0, 4, 29, 309, 691], [1, 4, 29, 204, 687], [1, 4, 29, 238, 692], [1, 4, 29, 309, 691]] # all = [Polyhedron(rays=[projection(Yoshida_matrix*v) for v in cone_from_flat_numbers(c) if projection(Yoshida_matrix*v) != 0]) for c in max2_overlaps] # [(i,j) for i in range(0,9) for j in range(0,9) if all[i].intersection(all[j]).dim() < 4] # [(1, 6), (2, 8), (3, 5), (5, 3), (6, 1), (8, 2)] # The following function computes the image of a cone in the Bergman fan (given by the corresponding flat numbers) under the Yoshida_matrix: def Yoshida_map(c): return Polyhedron(rays=[projection(Yoshida_matrix*v) for v in cone_from_flat_numbers(c) if projection(Yoshida_matrix*v) != 0 ]) # The following functions takes two polyhedra and check if the rays of each is a ray of the intersection. def good_intersection(P1, P2): common = P1.intersection(P2) # return all([v in P1.rays() and v in P2.rays() for v in common.rays()]) if False in [bool(v in P1.rays() and v in P2.rays()) for v in common.rays()]: return False else: return True # We load the Naruki cones computed in 'BergmanAndNarukiCones.sage' (ie. the list of maximal cones in Berg(E6) whose image under the Yoshida map has dimension is 5 in R^40. narukiCones = load("../Output/NarukiCones.sobj") first = narukiCones[0][0][0] second = narukiCones[0][1][0] print first [0, 1, 4, 36, 687] print second [0, 1, 4, 158, 691] # intersections11 = [good_intersection(Yoshida_map(first), Yoshida_map(o)) for o in max_orbit1] # We check that all the entries are "True" # False in intersections11 # False # intersections12 = [good_intersection(Yoshida_map(first), Yoshida_map(o)) for o in max_orbit2] # We check that not all the entries are "True" # False in intersections12 # True # badIntersections12 = [k for k in range(0,len(intersections12)) if intersections21[k]==False] # len(badIntersections12) # 36 # # We record the members of max_orbit1 corresponding to badIntersections21: # print [max_orbit2[k] for k in badIntersections12] # [[0, 8, 32, 166, 688], [0, 8, 32, 185, 693], [0, 8, 32, 309, 691], [0, 8, 34, 184, 693], [0, 8, 34, 191, 701], [0, 8, 34, 290, 696], [2, 16, 34, 160, 698], [2, 16, 34, 236, 705], [2, 16, 34, 249, 710], [2, 19, 21, 245, 687], [2, 19, 21, 274, 699], [2, 19, 21, 353, 698], [11, 12, 27, 230, 692], [11, 12, 27, 294, 694], [11, 12, 27, 333, 701], [11, 12, 31, 230, 692], [11, 12, 31, 264, 694], [11, 12, 31, 389, 701], [11, 14, 26, 182, 698], [11, 14, 26, 231, 705], [11, 14, 26, 289, 710], [11, 14, 32, 231, 705], [11, 14, 32, 313, 710], [11, 14, 32, 404, 698], [11, 22, 24, 311, 691], [11, 22, 24, 379, 690], [11, 22, 24, 401, 689], [11, 22, 32, 157, 691], [11, 22, 32, 265, 710], [11, 22, 32, 403, 713], [11, 24, 35, 173, 690], [11, 24, 35, 415, 708], [11, 24, 35, 420, 703], [11, 26, 27, 262, 698], [11, 26, 27, 301, 690], [11, 26, 27, 312, 701]] # intersections21 = [good_intersection(Yoshida_map(second), Yoshida_map(o)) for o in max_orbit1] # We check that not all the entries are "True" # False in intersections21 # True # badIntersections21 = [k for k in range(0,len(intersections21)) if intersections21[k]==False] # len(badIntersections21) # 36 # # We record the members of max_orbit1 corresponding to badIntersections21: # print [max_orbit1[k] for k in badIntersections21] # [[0, 4, 29, 40, 691], [0, 4, 29, 43, 691], [0, 4, 29, 65, 687], [0, 4, 29, 75, 687], [0, 4, 29, 138, 692], [0, 4, 29, 145, 692], [1, 4, 29, 52, 691], [1, 4, 29, 54, 691], [1, 4, 29, 62, 687], [1, 4, 29, 79, 692], [1, 4, 29, 80, 692], [1, 4, 29, 114, 687], [4, 18, 29, 40, 691], [4, 18, 29, 52, 691], [4, 18, 29, 65, 710], [4, 18, 29, 80, 710], [4, 18, 29, 114, 713], [4, 18, 29, 145, 713], [4, 23, 29, 43, 691], [4, 23, 29, 52, 691], [4, 23, 29, 75, 711], [4, 23, 29, 80, 711], [4, 23, 29, 114, 712], [4, 23, 29, 138, 712], [4, 24, 29, 40, 691], [4, 24, 29, 54, 691], [4, 24, 29, 62, 711], [4, 24, 29, 65, 712], [4, 24, 29, 79, 712], [4, 24, 29, 145, 711], [4, 25, 29, 43, 691], [4, 25, 29, 54, 691], [4, 25, 29, 62, 710], [4, 25, 29, 75, 713], [4, 25, 29, 79, 713], [4, 25, 29, 138, 710]] # intersections22 = [good_intersection(Yoshida_map(second), Yoshida_map(o)) for o in max_orbit2] # We check that not all the entries are "True" # False in intersections22 # True # badIntersections22 = [k for k in range(0,len(intersections22)) if intersections21[k]==False] # len(badIntersections22) # 36 # # We record the members of max_orbit1 corresponding to badIntersections21: # print [max_orbit2[k] for k in badIntersections22] # [[0, 8, 32, 166, 688], [0, 8, 32, 185, 693], [0, 8, 32, 309, 691], [0, 8, 34, 184, 693], [0, 8, 34, 191, 701], [0, 8, 34, 290, 696], [2, 16, 34, 160, 698], [2, 16, 34, 236, 705], [2, 16, 34, 249, 710], [2, 19, 21, 245, 687], [2, 19, 21, 274, 699], [2, 19, 21, 353, 698], [11, 12, 27, 230, 692], [11, 12, 27, 294, 694], [11, 12, 27, 333, 701], [11, 12, 31, 230, 692], [11, 12, 31, 264, 694], [11, 12, 31, 389, 701], [11, 14, 26, 182, 698], [11, 14, 26, 231, 705], [11, 14, 26, 289, 710], [11, 14, 32, 231, 705], [11, 14, 32, 313, 710], [11, 14, 32, 404, 698], [11, 22, 24, 311, 691], [11, 22, 24, 379, 690], [11, 22, 24, 401, 689], [11, 22, 32, 157, 691], [11, 22, 32, 265, 710], [11, 22, 32, 403, 713], [11, 24, 35, 173, 690], [11, 24, 35, 415, 708], [11, 24, 35, 420, 703], [11, 26, 27, 262, 698], [11, 26, 27, 301, 690], [11, 26, 27, 312, 701]]