p = 3
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^7)
f2 = superelliptic_function(C_super, x^4)
AS = as_cover(C_super, [f1, f2], prec=1000)
print(AS.uniformizer())

def rep_jumps(AS, threshold = 30):
    ile = 1
    i = 1
    result = []
    flag = 0
    while(flag == 0):
        if len(AS.at_most_poles(i, threshold = threshold)) > ile:
            ile = len(AS.at_most_poles(i, threshold = threshold))
            result += [i]
            if i%p != 0:
                flag = 1
        i+=1
    return result

#print(rep_jumps(AS, threshold = 30))

def uniformizer(AS, threshold = 30):
    p = AS.characteristic
    n = AS.height
    variable_names = 'x, y'
    for i in range(n):
        variable_names += ', z' + str(i)
    Rxyz = PolynomialRing(F, n+2, variable_names)
    x, y = Rxyz.gens()[:2]
    z = Rxyz.gens()[2:]
    zmag = AS.magical_element()[0]
    v_x = as_function(AS, x).expansion_at_infty().valuation()
    dprim = AS.exponent_of_different_prim()
    d, a, b = xgcd(v_x, -dprim)
    return as_function(AS, x^a*zmag.function^b)