DeRhamComputation/as_covers/group_action_matrices.sage

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def as_group_action_matrices(F, space, list_of_group_elements, basis):
n = len(list_of_group_elements)
d = len(space)
A = [matrix(F, d, d) for i in range(n)]
for i, g in enumerate(list_of_group_elements):
for j, omega in enumerate(space):
omega1 = omega.group_action(g)
v1 = omega1.coordinates(basis = basis)
A[i][:, j] = vector(v1)
return A
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def as_group_action_matrices_holo(AS, basis=0, threshold=10):
n = AS.height
generators = []
for i in range(n):
ei = n*[0]
ei[i] = 1
generators += [ei]
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if basis == 0:
basis = AS.holomorphic_differentials_basis(threshold=threshold)
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F = AS.base_ring
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return as_group_action_matrices(F, basis, generators, basis = basis)
as_cover.group_action_matrices_holo = as_group_action_matrices_holo
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def as_group_action_matrices_dR(AS, threshold=8):
n = AS.height
generators = []
for i in range(n):
ei = n*[0]
ei[i] = 1
generators += [ei]
holo_basis = AS.holomorphic_differentials_basis(threshold = threshold)
str_basis = AS.cohomology_of_structure_sheaf_basis(holo_basis = holo_basis, threshold = threshold)
dr_basis = AS.de_rham_basis(holo_basis = holo_basis, cohomology_basis = str_basis, threshold=threshold)
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F = AS.base_ring
basis = [holo_basis, str_basis, dr_basis]
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return as_group_action_matrices(F, basis[2], generators, basis = basis)
as_cover.group_action_matrices_dR = as_group_action_matrices_dR
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def as_group_action_matrices_log_holo(AS):
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n = AS.height
generators = []
for i in range(n):
ei = n*[0]
ei[i] = 1
generators += [ei]
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F = AS.base_ring
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return as_group_action_matrices(F, AS.at_most_poles_forms(1), generators, basis = AS.at_most_poles_forms(1))
as_cover.group_action_matrices_log_holo = as_group_action_matrices_log_holo