126 lines
3.8 KiB
Python
126 lines
3.8 KiB
Python
|
class as_function:
|
||
|
|
def __init__(self, C, g):
|
||
|
|
self.curve = C
|
||
|
|
F = C.base_ring
|
||
|
|
n = C.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:]
|
||
|
|
RxyzQ = FractionField(Rxyz)
|
||
|
|
self.function = RxyzQ(g)
|
||
|
|
#self.function = as_reduction(AS, RxyzQ(g))
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return str(self.function)
|
||
|
|
|
||
|
|
def __add__(self, other):
|
||
|
|
C = self.curve
|
||
|
|
g1 = self.function
|
||
|
|
g2 = other.function
|
||
|
|
return as_function(C, g1 + g2)
|
||
|
|
|
||
|
|
def __sub__(self, other):
|
||
|
|
C = self.curve
|
||
|
|
g1 = self.function
|
||
|
|
g2 = other.function
|
||
|
|
return as_function(C, g1 - g2)
|
||
|
|
|
||
|
|
def __rmul__(self, constant):
|
||
|
|
C = self.curve
|
||
|
|
g = self.function
|
||
|
|
return as_function(C, constant*g)
|
||
|
|
|
||
|
|
def __mul__(self, other):
|
||
|
|
C = self.curve
|
||
|
|
g1 = self.function
|
||
|
|
g2 = other.function
|
||
|
|
return as_function(C, g1*g2)
|
||
|
|
|
||
|
|
def expansion_at_infty(self, i = 0):
|
||
|
|
C = self.curve
|
||
|
|
delta = C.nb_of_pts_at_infty
|
||
|
|
F = C.base_ring
|
||
|
|
x_series = C.x[i]
|
||
|
|
y_series = C.y[i]
|
||
|
|
z_series = C.z[i]
|
||
|
|
n = C.height
|
||
|
|
variable_names = 'x, y'
|
||
|
|
for j in range(n):
|
||
|
|
variable_names += ', z' + str(j)
|
||
|
|
Rxyz = PolynomialRing(F, n+2, variable_names)
|
||
|
|
x, y = Rxyz.gens()[:2]
|
||
|
|
z = Rxyz.gens()[2:]
|
||
|
|
RxyzQ = FractionField(Rxyz)
|
||
|
|
prec = C.prec
|
||
|
|
Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
|
||
|
|
g = self.function
|
||
|
|
g = RxyzQ(g)
|
||
|
|
sub_list = {x : x_series, y : y_series} | {z[j] : z_series[j] for j in range(n)}
|
||
|
|
return g.substitute(sub_list)
|
||
|
|
|
||
|
|
def group_action(self, ZN_tuple):
|
||
|
|
C = self.curve
|
||
|
|
n = C.height
|
||
|
|
F = C.base_ring
|
||
|
|
variable_names = 'x, y'
|
||
|
|
for j in range(n):
|
||
|
|
variable_names += ', z' + str(j)
|
||
|
|
Rxyz = PolynomialRing(F, n+2, variable_names)
|
||
|
|
x, y = Rxyz.gens()[:2]
|
||
|
|
z = Rxyz.gens()[2:]
|
||
|
|
RxyzQ = FractionField(Rxyz)
|
||
|
|
sub_list = {x : x, y : y} | {z[j] : z[j]+ZN_tuple[j] for j in range(n)}
|
||
|
|
g = self.function
|
||
|
|
return as_function(C, g.substitute(sub_list))
|
||
|
|
|
||
|
|
def trace(self):
|
||
|
|
C = self.curve
|
||
|
|
C_super = C.quotient
|
||
|
|
n = C.height
|
||
|
|
F = C.base_ring
|
||
|
|
variable_names = 'x, y'
|
||
|
|
for j in range(n):
|
||
|
|
variable_names += ', z' + str(j)
|
||
|
|
Rxyz = PolynomialRing(F, n+2, variable_names)
|
||
|
|
x, y = Rxyz.gens()[:2]
|
||
|
|
z = Rxyz.gens()[2:]
|
||
|
|
RxyzQ = FractionField(Rxyz)
|
||
|
|
g = self.function
|
||
|
|
g = as_reduction(C, g)
|
||
|
|
result = RxyzQ(0)
|
||
|
|
g_num = Rxyz(numerator(g))
|
||
|
|
g_den = Rxyz(denominator(g))
|
||
|
|
z = prod(z[i] for i in range(n))^(p-1)
|
||
|
|
for a in g_num.monomials():
|
||
|
|
if (z.divides(a)):
|
||
|
|
result += g_num.monomial_coefficient(a)*a/z
|
||
|
|
result /= g_den
|
||
|
|
result = as_reduction(C, result)
|
||
|
|
Rxy.<x, y> = PolynomialRing(F, 2)
|
||
|
|
Qxy = FractionField(Rxy)
|
||
|
|
return superelliptic_function(C_super, Qxy(result))
|
||
|
|
|
||
|
|
def trace2(self):
|
||
|
|
C = self.curve
|
||
|
|
C_super = C.quotient
|
||
|
|
n = C.height
|
||
|
|
F = C.base_ring
|
||
|
|
variable_names = 'x, y'
|
||
|
|
for j in range(n):
|
||
|
|
variable_names += ', z' + str(j)
|
||
|
|
Rxyz = PolynomialRing(F, n+2, variable_names)
|
||
|
|
x, y = Rxyz.gens()[:2]
|
||
|
|
z = Rxyz.gens()[2:]
|
||
|
|
RxyzQ = FractionField(Rxyz)
|
||
|
|
result = as_function(C, 0)
|
||
|
|
for i in range(0, p):
|
||
|
|
for j in range(0, p):
|
||
|
|
result += self.group_action([i, j])
|
||
|
|
result = result.function
|
||
|
|
Rxy.<x, y> = PolynomialRing(F, 2)
|
||
|
|
Qxy = FractionField(Rxy)
|
||
|
|
return superelliptic_function(C_super, Qxy(result))
|