DeRhamComputation/sage/as_covers/combination_components.sage

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2022-11-18 15:00:34 +01:00
def combination_components(omega, zmag, w):
'''Given a form omega on AS cover and normal basis element zmag, find the decomposition
sum_g g(zmag) omega_g and return sum_g g(w) omega_g.'''
AS = omega.curve
p = AS.characteristic
group_elts = [(j1, j2) for j1 in range(p) for j2 in range(p)]
zvee = dual_elt(AS, zmag)
result = as_form(AS, 0)
for i in range(p^2):
omegai = ith_magical_component(omega, zvee, i)
aux_fct1 = w.group_action(group_elts[i]).function
aux_fct2 = omegai.form
result += as_form(AS, aux_fct1*aux_fct2)
return result