jgarnek/DeRhamComputation
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

first version of template works

Browse Source
This commit is contained in:
jgarnek 2024-06-10 19:50:09 +00:00
parent 6fe120b690
commit bd1ecfbfae
4 changed files with 45 additions and 24 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

23
as_covers/as_cover_class.sage
View File

@ -1,21 +1,18 @@
class as_cover:
def __init__(self, C, list_of_fcts, branch_points = [], prec = 10):
def __init__(self, C, cover_template, list_of_fcts, branch_points = [], prec = 10):
self.quotient = C
self.functions = list_of_fcts
print('a')
self.height = len(list_of_fcts)
print('b')
F = C.base_ring
self.base_ring = F
p = C.characteristic
self.characteristic = p
self.prec = prec
#group acting
n = self.height
from itertools import product
pr = [list(GF(p)) for _ in range(n)]
group = []
for a in product(*pr):
group += [a]
self.group = group
self.height = cover_template.height
self.group = cover_template.group
#########
f = C.polynomial
m = C.exponent
@ -25,7 +22,7 @@ class as_cover:
self.branch_points = list(range(delta)) + branch_points
Rxy.<x, y> = PolynomialRing(F, 2)
Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
Rzf, zgen, fgen = cover_template.fct_field
all_x_series = {}
all_y_series = {}
all_z_series = {}
@ -40,7 +37,13 @@ class as_cover:
n = len(list_of_fcts)
list_of_power_series = [g.expansion(pt=pt, prec=prec) for g in list_of_fcts]
for j in range(n):
power_series = list_of_power_series[j]
####
#TUTAJ WSTAWIĆ ZMIANĘ
print(cover_template.fcts[j], {zgen[i] : z_series[i] for i in range(j)} | {zgen[i] : 0 for i in range(j, n)} | {fgen[i] : list_of_power_series[i] for i in range(n)})
power_series = Rzf(cover_template.fcts[j]).subs({zgen[i] : z_series[i] for i in range(j)} | {zgen[i] : 0 for i in range(j, n)} | {fgen[i] : list_of_power_series[i] for i in range(n)})
####
#power_series = list_of_power_series[j]
jump, correction, t_old, z = artin_schreier_transform(power_series, prec = prec)
x_series = x_series(t = t_old)
y_series = y_series(t = t_old)

15
as_covers/group.sage
View File

@ -1,5 +1,5 @@
class group:
def __init__(self, name, elts, one, mult, inv, gens, as_gens):
def __init__(self, name, elts, one, mult, inv, gens):
self.name = name
self.elts = elts
self.one = one
@ -7,7 +7,6 @@ class group:
self.inv = inv
self.order = len(self.elts)
self.gens = gens
self.as_gens = as_gens
def __repr__(self):
return self.name
@ -25,7 +24,6 @@ class group_elt:
def __init__(self, as_tuple, group):
self.group = group
self.as_tuple = as_tuple
self.as_gens = self.group.as_gens(as_tuple)
def __repr__(self):
return str(self.as_tuple)
@ -62,8 +60,7 @@ def cyclic_gp(p, n):
mult = lambda i1, i2: (i1 + i2) % (p ** n)
inv = lambda i: (-i) % (p ** n)
gens = [1]
as_gens = lambda i : [[0, i]]
gp = group(name, elts, one, mult, inv, gens, as_gens)
gp = group(name, elts, one, mult, inv, gens)
return gp
def elementary_gp(p, n):
@ -81,8 +78,7 @@ def elementary_gp(p, n):
e = n*[0]
e[i] = 1
gens += [tuple(e)]
as_gens = lambda i : [[j, i[j]] for j in range(n)]
gp = group(name, elts, one, mult, inv, gens, as_gens)
gp = group(name, elts, one, mult, inv, gens)
return gp
@ -91,9 +87,8 @@ def heisenberg(p):
name = "Heisenberg group E(" + str(p) + "^3)"
elts = [(i, j, k) for i in range(p) for j in range(p) for k in range(p)]
one = 0
mult = lambda elt1, elt2 : ((elt1[0] + elt2[0])%p, (elt1[1] + elt2[1])%p, (-elt1[0]*elt2[1] + elt1[2] + elt2[2])%p)
mult = lambda elt1, elt2 : ((elt1[0] + elt2[0])%p, (elt1[1] + elt2[1])%p, (-elt1[1]*elt2[0] + elt1[2] + elt2[2])%p)
inv = lambda elt : (p-elt[0], p-elt[1], (p - elt[2] - (p-elt[0])*(p-elt[1]))%p)
gens = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
as_gens = lambda elt : [[0, elt[0]], [1, elt[1]], [2, elt[2]]]
gp = group(name, elts, one, mult, inv, gens, as_gens)
gp = group(name, elts, one, mult, inv, gens)
return gp

29
as_covers/template.sage
View File

@ -3,7 +3,6 @@ class template:
def __init__(self, height, field, group, fcts, gp_action):
self.height = height
self.group = group
self.fcts = fcts #RHSs of the Artin-Schreier equations
self.gp_action = gp_action #action of the generators of the group on z[i]'s
self.field = field
n = height
@ -14,9 +13,11 @@ class template:
variable_names += 'f'+str(i)
if i!=n-1:
variable_names += ','
R = PolynomialRing(field, 2*n, variable_names)
z = R.gens()[:n]
f = R.gens()[n:]
Rzf = PolynomialRing(field, 2*n, variable_names)
z = Rzf.gens()[:n]
f = Rzf.gens()[n:]
self.fct_field = Rzf, z, f
self.fcts = [Rzf(ff) for ff in fcts] #RHSs of the Artin-Schreier equations
def elementary_template(p, n):
group = elementary_gp(p, n)
@ -34,4 +35,24 @@ def elementary_template(p, n):
height = n
fcts = [f[i] for i in range(n)]
gp_action = [[z[j] + (i == j) for j in range(n)] for i in range(n)]
return template(height, field, group, fcts, gp_action)
def heisenberg_template(p):
group = heisenberg(p)
field = GF(p)
variable_names = ''
n = 3
for i in range(n):
variable_names += 'z'+str(i)+','
for i in range(n):
variable_names += 'f'+str(i)
if i!=n-1:
variable_names += ','
R = PolynomialRing(field, 2*n, variable_names)
z = R.gens()[:n]
f = R.gens()[n:]
height = n
fcts = [f[i] for i in range(n)]
fcts[2] += (z[0] - z[1])*f[1]
gp_action = [[z[0] + 1, z[1], z[2] + z[1]], [z[0] + 1, z[1] + 1, z[2]], [z[0], z[1], z[2] - 1]]
return template(height, field, group, fcts, gp_action)

2
init.sage
View File

@ -3,6 +3,8 @@ load('superelliptic/superelliptic_function_class.sage')
load('superelliptic/superelliptic_form_class.sage')
load('superelliptic/superelliptic_cech_class.sage')
load('superelliptic/frobenius_kernel.sage')
load('as_covers/group.sage')
load('as_covers/template.sage')
load('as_covers/as_transform.sage')
load('as_covers/holomorphic_combinations.sage')
load('as_covers/as_cover_class.sage')