DeRhamComputation/as_covers/combination_components.sage

14 lines
588 B
Python

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 g in AS.group:
omegag = ith_magical_component(omega, zvee, g)
aux_fct1 = w.group_action(g).function
aux_fct2 = omegag.form
result += as_form(AS, aux_fct1*aux_fct2)
return result