def jacobian(self):
s = len(self.mcomplex.Edges)
result = matrix(self.vertex_gram_matrices[0].base_ring(), s, s)
for tet in self.mcomplex.Tetrahedra:
cofactor_matrices = _cofactor_matrices_for_submatrices(
self.vertex_gram_matrices[tet.Index])
vga = self.vertex_gram_adjoints[tet.Index]
for angle_edge, (i, j) in _OneSubsimplicesWithVertexIndices:
cii = vga[i, i]
cij = vga[i, j]
cjj = vga[j, j]
dcij = -1 / sqrt(cii * cjj - cij**2)
tmp = -dcij * cij / 2
dcii = tmp / cii
dcjj = tmp / cjj
a = tet.Class[t3m.comp(angle_edge)].Index
for length_edge, (m, n) in _OneSubsimplicesWithVertexIndices:
l = tet.Class[length_edge].Index
result[a, l] += (
dcij *
_cofactor_derivative(cofactor_matrices, i, j, m, n) +
dcii *
_cofactor_derivative(cofactor_matrices, i, i, m, n) +
dcjj *
_cofactor_derivative(cofactor_matrices, j, j, m, n))
return result
def _compute_R13_point_on_horosphere_for_vertex(tet, V0):
V1, V2, V3 = t3m.VerticesOfFaceCounterclockwise[t3m.comp(V0)]
cusp_length = tet.horotriangles[V0].get_real_lengths()[V0 | V1 | V2]
pts = [ tet.complex_vertices[V] for V in [V0, V1, V2]]
pts[1] = 1.0 / (pts[1] - pts[0])
pts[2] = 1.0 / (pts[2] - pts[0])
base_length = abs(pts[2] - pts[1])
horosphere_height = cusp_length / base_length
return complex_and_height_to_R13_time_vector(pts[0], horosphere_height)