DeRhamComputation/sage/as_covers/tests/dual_element_test.sage

p = 5
m = 1
F = GF(p)
Rx.<x> = PolynomialRing(F)
f = x
C_super = superelliptic(f, m)

Rxy.<x, y> = PolynomialRing(F, 2)
f1 = superelliptic_function(C_super, x^2)
f2 = superelliptic_function(C_super, x^3)
AS = as_cover(C_super, [f1, f2], prec=500)
zmag = (AS.magical_element())[0]
zdual = dual_elt(AS, zmag)

for i in range(p):
    for j in range(p):
        if (i, j) == (0, 0):
            print((zmag*(zdual.group_action([i, j]))).trace().function == 1)
        else:
            print((zmag*(zdual.group_action([i, j]))).trace().function == 0)