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diffn for arbitrary template should work

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jgarnek 2024-06-11 11:29:05 +00:00
parent bd1ecfbfae
commit 9aeee4993d
2 changed files with 61 additions and 56 deletions
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36
as_covers/as_cover_class.sage
View File

@ -1,6 +1,7 @@
class as_cover: class as_cover:
def __init__(self, C, cover_template, list_of_fcts, branch_points = [], prec = 10): def __init__(self, C, cover_template, list_of_fcts, branch_points = [], prec = 10):
self.quotient = C self.quotient = C
self.cover_template = cover_template
self.functions = list_of_fcts self.functions = list_of_fcts
print('a') print('a')
self.height = len(list_of_fcts) self.height = len(list_of_fcts)
@ -77,17 +78,38 @@ class as_cover:
self.z = [as_function(self, z[j]) for j in range(n)] self.z = [as_function(self, z[j]) for j in range(n)]
self.dx = as_form(self, 1) self.dx = as_form(self, 1)
self.one = as_function(self, 1) self.one = as_function(self, 1)
Rzf, zgen, fgen = cover_template.fct_field
subs_fs = {zgen[i] : z[i]}| {fgen[i] : RxyzQ(list_of_fcts[i].function) for i in range(n)}
self.rhs = [RxyzQ(cover_template.fcts[i].subs(subs_fs)) for i in range(n)]
#####
##### We compute now the differentials dz[i]
y_super = superelliptic_function(C, y)
dy_super = y_super.diffn().form
dz = []
for i in range(n):
aux_fct = self.rhs[i]
result = 0
for j in range(i):
result += aux_fct.derivative(z[j])*dz[j]
result += aux_fct.derivative(x)
result += aux_fct.derivative(y)*dy_super
dz += [-result]
self.dz = dz
def __repr__(self): def __repr__(self):
n = self.height n = self.height
p = self.characteristic p = self.characteristic
if n==1: result = str(self.group)
return "(Z/p)-cover of " + str(self.quotient)+" with the equation:\n z^" + str(p) + " - z = " + str(self.functions[0]) result += "-cover of " + str(self.quotient)+" with the equations: \n"
result = "(Z/p)^"+str(self.height)+ "-cover of " + str(self.quotient)+" with the equations:\n"
for i in range(n): for i in range(n):
result += 'z' + str(i) + "^" + str(p) + " - z" + str(i) + " = " + str(self.functions[i]) + "\n" result += 'z'+str(i)+'^p - z'+str(i) + ' = '
aux = str(self.cover_template.fcts[i])
for t in range(n):
aux = aux.replace("f"+str(t), "(" + str(self.functions[t]) + ")")
result += aux + '\n'
return result return result
def genus(self): def genus(self):
@ -289,7 +311,7 @@ class as_cover:
def ith_ramification_gp(self, i, place = 0): def ith_ramification_gp(self, i, place = 0):
'''Find ith ramification group at place at infty of nb place.''' '''Find ith ramification group at place at infty of nb place.'''
G = self.group G = self.group.elts
t = self.uniformizer(place) t = self.uniformizer(place)
Gi = [G[0]] Gi = [G[0]]
for g in G: for g in G:
@ -302,7 +324,7 @@ class as_cover:
def ramification_jumps(self, place = 0): def ramification_jumps(self, place = 0):
'''Return list of lower ramification jumps at at place at infty of nb place.''' '''Return list of lower ramification jumps at at place at infty of nb place.'''
G = self.group G = self.group.elts
ramification_jps = [] ramification_jps = []
i = 0 i = 0
while len(G) > 1: while len(G) > 1:

73
as_covers/as_function_class.sage
View File

@ -3,13 +3,7 @@ class as_function:
self.curve = C self.curve = C
F = C.base_ring F = C.base_ring
n = C.height n = C.height
variable_names = 'x, y' RxyzQ, Rxyz, x, y, z = C.fct_field
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 = RxyzQ(g)
#self.function = as_reduction(AS, RxyzQ(g)) #self.function = as_reduction(AS, RxyzQ(g))
@ -81,13 +75,7 @@ class as_function:
y_series = C.y_series[place] y_series = C.y_series[place]
z_series = C.z_series[place] z_series = C.z_series[place]
n = C.height n = C.height
variable_names = 'x, y' RxyzQ, Rxyz, x, y, z = C.fct_field
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 prec = C.prec
Rt.<t> = LaurentSeriesRing(F, default_prec=prec) Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
g = self.function g = self.function
@ -103,13 +91,7 @@ class as_function:
y_series = C.y_series[pt] y_series = C.y_series[pt]
z_series = C.z_series[pt] z_series = C.z_series[pt]
n = C.height n = C.height
variable_names = 'x, y' RxyzQ, Rxyz, x, y, z = C.fct_field
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 prec = C.prec
Rt.<t> = LaurentSeriesRing(F, default_prec=prec) Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
g = self.function g = self.function
@ -117,37 +99,39 @@ class as_function:
sub_list = {x : x_series, y : y_series} | {z[j] : z_series[j] for j in range(n)} sub_list = {x : x_series, y : y_series} | {z[j] : z_series[j] for j in range(n)}
return g.substitute(sub_list) return g.substitute(sub_list)
def group_action(self, ZN_tuple): def group_action(self, elt):
C = self.curve C = self.curve
n = C.height RxyzQ, Rxyz, x, y, z = C.fct_field
F = C.base_ring Rzf, zgen, fgen = C.cover_template.fct_field
variable_names = 'x, y' if isinstance(elt, group_elt):
for j in range(n): elt = elt.as_tuple
variable_names += ', z' + str(j) AS = self.curve
Rxyz = PolynomialRing(F, n+2, variable_names) n = AS.height
x, y = Rxyz.gens()[:2] G = AS.group
z = Rxyz.gens()[2:]
RxyzQ = FractionField(Rxyz) if elt in G.gens:
sub_list = {x : x, y : y} | {z[j] : z[j]+ZN_tuple[j] for j in range(n)} ind = G.gens.index(elt)
gp_action_list = C.cover_template.gp_action[ind]
sub_list = {x : x, y : y} | {z[j] : Rxyz(gp_action_list[j].subs({zgen[i] : z[i] for i in range(n)})) for j in range(n)}
g = self.function g = self.function
return as_function(C, g.substitute(sub_list)) return as_function(C, g.substitute(sub_list))
result = self
for i in range(n):
for j in range(elt[i]):
result = result.group_action(G.gens[i])
return result
def reduce(self): def reduce(self):
aux = as_reduction(self.curve, self.function) aux = as_reduction(self.curve, self.function)
return as_function(self.curve, aux) return as_function(self.curve, aux)
def trace(self): def trace(self, super=True):
C = self.curve C = self.curve
C_super = C.quotient C_super = C.quotient
n = C.height n = C.height
F = C.base_ring F = C.base_ring
variable_names = 'x, y' RxyzQ, Rxyz, x, y, z = C.fct_field
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) result = as_function(C, 0)
G = C.group G = C.group
for a in G: for a in G:
@ -156,7 +140,10 @@ class as_function:
Rxy.<x, y> = PolynomialRing(F, 2) Rxy.<x, y> = PolynomialRing(F, 2)
Qxy = FractionField(Rxy) Qxy = FractionField(Rxy)
result = as_reduction(C, result) result = as_reduction(C, result)
if super:
return superelliptic_function(C_super, Qxy(result)) return superelliptic_function(C_super, Qxy(result))
return as_function(AS, Qxy(result))
def coordinates(self, prec = 100, basis = 0): def coordinates(self, prec = 100, basis = 0):
"Return coordinates in H^1(X, OX)." "Return coordinates in H^1(X, OX)."
@ -180,14 +167,10 @@ class as_function:
C_super = C.quotient C_super = C.quotient
n = C.height n = C.height
RxyzQ, Rxyz, x, y, z = C.fct_field RxyzQ, Rxyz, x, y, z = C.fct_field
fcts = C.functions
f = self.function f = self.function
y_super = superelliptic_function(C_super, y) y_super = superelliptic_function(C_super, y)
dy_super = y_super.diffn().form dy_super = y_super.diffn().form
dz = [] dz = C.dz
for i in range(n):
dfct = fcts[i].diffn().form
dz += [-dfct]
result = f.derivative(x) result = f.derivative(x)
result += f.derivative(y)*dy_super result += f.derivative(y)*dy_super
for i in range(n): for i in range(n):