95 lines
3.1 KiB
Python
95 lines
3.1 KiB
Python
def group_action_matrices(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 group_action_matrices_holo(AS, basis=0, threshold=10):
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n = AS.height
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generators = []
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for i in range(n):
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ei = n*[0]
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ei[i] = 1
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generators += [ei]
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if basis == 0:
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basis = AS.holomorphic_differentials_basis(threshold=threshold)
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return group_action_matrices(basis, generators, basis = basis)
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def group_action_matrices_dR(AS, threshold=8):
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n = AS.height
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generators = []
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for i in range(n):
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ei = n*[0]
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ei[i] = 1
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generators += [ei]
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basis = [AS.holomorphic_differentials_basis(threshold = threshold), AS.cohomology_of_structure_sheaf_basis(threshold = threshold), AS.de_rham_basis(threshold=threshold)]
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return group_action_matrices(basis[2], generators, basis = basis)
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def group_action_matrices_old(C_AS):
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F = C_AS.base_ring
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n = C_AS.height
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holo = C_AS.holomorphic_differentials_basis()
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holo_forms = [omega.form for omega in holo]
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denom = LCM([denominator(omega) for omega in holo_forms])
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variable_names = 'x, y'
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for j in range(n):
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variable_names += ', z' + str(j)
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Rxyz = PolynomialRing(F, n+2, variable_names)
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x, y = Rxyz.gens()[:2]
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z = Rxyz.gens()[2:]
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holo_forms = [Rxyz(omega*denom) for omega in holo_forms]
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A = [[] for i in range(n)]
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for omega in holo:
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for i in range(n):
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ei = n*[0]
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ei[i] = 1
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omega1 = omega.group_action(ei)
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omega1 = denom * omega1
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v1 = omega1.coordinates(holo_forms)
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A[i] += [v1]
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for i in range(n):
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A[i] = matrix(F, A[i])
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A[i] = A[i].transpose()
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return A
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def group_action_matrices_log(AS):
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n = AS.height
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generators = []
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for i in range(n):
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ei = n*[0]
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ei[i] = 1
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generators += [ei]
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return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.at_most_poles_forms(1))
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def group_action_matrices_log_old(C_AS):
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F = C_AS.base_ring
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n = C_AS.height
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holo = C_AS.at_most_poles_forms(1)
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holo_forms = [omega for omega in holo]
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denom = LCM([denominator(omega) for omega in holo_forms])
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variable_names = 'x, y'
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for j in range(n):
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variable_names += ', z' + str(j)
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Rxyz = PolynomialRing(F, n+2, variable_names)
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x, y = Rxyz.gens()[:2]
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z = Rxyz.gens()[2:]
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holo_forms = [Rxyz(omega*denom) for omega in holo_forms]
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A = [[] for i in range(n)]
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for omega in holo:
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for i in range(n):
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ei = n*[0]
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ei[i] = 1
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omega1 = omega.group_action(ei)
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omega1 = denom * omega1
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v1 = omega1.coordinates(holo_forms)
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A[i] += [v1]
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for i in range(n):
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A[i] = matrix(F, A[i])
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A[i] = A[i].transpose()
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return A
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