DeRhamComputation/as_covers/group_action_matrices.sage

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

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]
    if basis == 0:
        basis = AS.holomorphic_differentials_basis(threshold=threshold)
    F = AS.base_ring
    return as_group_action_matrices(F, basis, generators, basis = basis)

as_cover.group_action_matrices_holo = as_group_action_matrices_holo
    
def as_group_action_matrices_dR(AS, basis = 0, threshold=8):
    n = AS.height
    generators = []
    F = AS.base_ring
    for i in range(n):
        ei = n*[0]
        ei[i] = 1
        generators += [ei]
    if basis == 0:
        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)
        basis = [holo_basis, str_basis, dr_basis]
    return as_group_action_matrices(F, basis[2], generators, basis = basis)

as_cover.group_action_matrices_dR = as_group_action_matrices_dR

def as_group_action_matrices_log_holo(AS):
    n = AS.height
    generators = []
    for i in range(n):
        ei = n*[0]
        ei[i] = 1
        generators += [ei]
    F = AS.base_ring
    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