40 lines
1.8 KiB
Python
40 lines
1.8 KiB
Python
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def quaternion_group_action_matrices(F, space, list_of_group_elements, basis):
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n = len(list_of_group_elements)
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d = len(space)
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A = [matrix(F, d, d) for i in range(n)]
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for i, g in enumerate(list_of_group_elements):
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for j, omega in enumerate(space):
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omega1 = omega.group_action(g)
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v1 = omega1.coordinates(basis = basis)
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A[i][:, j] = vector(v1)
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return A
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def quaternion_group_action_matrices_holo(AS, basis=0, threshold=10):
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n = AS.height
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generators = QuaternionGroup().gens()
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if basis == 0:
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basis = AS.holomorphic_differentials_basis(threshold=threshold)
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F = AS.base_ring
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return quaternion_group_action_matrices(F, basis, generators, basis = basis)
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quaternion_cover.group_action_matrices_holo = quaternion_group_action_matrices_holo
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def quaternion_group_action_matrices_dR(AS, threshold=8):
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n = AS.height
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generators = QuaternionGroup().gens()
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holo_basis = AS.holomorphic_differentials_basis(threshold = threshold)
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str_basis = AS.cohomology_of_structure_sheaf_basis(holo_basis = holo_basis, threshold = threshold)
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dr_basis = AS.de_rham_basis(holo_basis = holo_basis, cohomology_basis = str_basis, threshold=threshold)
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F = AS.base_ring
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basis = [holo_basis, str_basis, dr_basis]
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return quaternion_group_action_matrices(F, basis[2], generators, basis = basis)
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quaternion_cover.group_action_matrices_dR = quaternion_group_action_matrices_dR
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def quaternion_group_action_matrices_log_holo(AS):
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n = AS.height
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generators = QuaternionGroup().gens()
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F = AS.base_ring
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return quaternion_group_action_matrices(F, AS.at_most_poles_forms(1), generators, basis = AS.at_most_poles_forms(1))
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quaternion_cover.group_action_matrices_log_holo = quaternion_group_action_matrices_log_holo
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