p = 5
m = 2
Rx.<x> = PolynomialRing(GF(p))
f = x^3 + x^2 + 1
C_super = superelliptic(f, m)
Rxy.<x, y> = PolynomialRing(GF(p), 2)
fArS1 = superelliptic_function(C_super, y*x)
fArS2 = superelliptic_function(C_super, y*x^2)
fArS3 = superelliptic_function(C_super, y)
AS1 = as_cover(C_super, [fArS1, fArS2, fArS3], prec=500)
AS2 = as_cover(C_super, [fArS2, fArS3, fArS1], prec=500)
print(AS1.genus() == AS2.genus())
##################
p = 5
m = 2
Rx.<x> = PolynomialRing(GF(p))
f = x^3 + x^2 + 1
C_super = superelliptic(f, m)
Rxy.<x, y> = PolynomialRing(GF(p), 2)
fArS1 = superelliptic_function(C_super, y*x)
fArS2 = superelliptic_function(C_super, y*x^2)
fArS3 = superelliptic_function(C_super, y)
AS1 = as_cover(C_super, [fArS1, fArS2, fArS3], prec=1000)
omega = as_form(AS1, 1/y)
print(omega.expansion_at_infty().valuation() == AS1.exponent_of_different())