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as_witt_form addition works at least partially

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jgarnek 2024-01-13 20:18:03 +00:00
parent 2face76a9e
commit c952ad5001
4 changed files with 108 additions and 49 deletions
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14
as_covers/as_function_class.sage
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@ -15,6 +15,18 @@ class as_function:
def __repr__(self): def __repr__(self):
return str(self.function) return str(self.function)
def __eq__(self, other):
AS = self.curve
RxyzQ, Rxyz, x, y, z = AS.fct_field
aux = self - other
aux = RxyzQ(aux.function)
aux = aux.numerator()
aux = as_function(AS, aux)
aux = aux.expansion_at_infty()
if aux.valuation() >= 1:
return True
return False
def __add__(self, other): def __add__(self, other):
C = self.curve C = self.curve
@ -33,7 +45,7 @@ class as_function:
g = self.function g = self.function
return as_function(C, constant*g) return as_function(C, constant*g)
def __neg__(self, other): def __neg__(self):
C = self.curve C = self.curve
g = self.function g = self.function
return as_function(C, -g) return as_function(C, -g)

16
as_drw/as_compability.sage
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@ -2,4 +2,18 @@ def teichmuller(self, n):
AS = self.curve AS = self.curve
return as_witt([self] + n*[0*AS.x]) return as_witt([self] + n*[0*AS.x])
as_function.teichmuller = teichmuller def Vd(self, n, m = 1):
'''Return V^m([f] d[x]) in W_n Omega'''
AS = self.curve
if m == 0:
return as_witt_form([self] + n*[0*AS.x], (n+1)*[0*AS.x])
return as_witt_form(m*[0*AS.x] + [self] + (n-m)*[0*AS.x], (n+1)*[0*AS.x])
def dV(self, n, m = 1):
'''Return dV^m([f] d[x]) in W_n Omega'''
AS = self.curve
return as_witt_form((n+1)*[0*AS.x], m*[0*AS.x] + [self] + (n-m)*[0*AS.x])
as_function.teichmuller = teichmuller
as_function.Vd = Vd
as_function.dV = dV

123
as_drw/as_witt_form.sage
View File

@ -4,6 +4,10 @@ class as_witt_form:
self.dVs = fcts2 self.dVs = fcts2
self.n = len(fcts1) - 1 self.n = len(fcts1) - 1
self.curve = fcts1[0].curve self.curve = fcts1[0].curve
if self.dVs[0].function!=0:
raise ValueError('First dV should be zero!')
if len(fcts1) != len(fcts2):
raise ValueError('Both lists should be of the same length!')
def __repr__(self): def __repr__(self):
result = '' result = ''
@ -15,61 +19,74 @@ class as_witt_form:
result += '[' + str(f) + '] d[x] +' result += '[' + str(f) + '] d[x] +'
i+=1 i+=1
i = 1 i = 1
for f in self.Vs: for f in self.dVs[1:]:
result += 'dV^' + str(i) + '([' + str(f) + ']) +' result += 'dV^' + str(i) + '([' + str(f) + ']) +'
i+=1 i+=1
return result return result
def __add__(self, other): def __add__(self, other):
print(self, other)
n = self.n n = self.n
AS = self.curve AS = self.curve
result = as_witt_form((n+1)*[0 * AS.x], (n+1)*[0 * AS.x]) ########
flag = 1
for i in range(0, n+1):
if self.Vs[i] != 0 and other.Vs[i] != 0:
flag = 0
if flag == 1:
aux = [self.Vs[i] + other.Vs[i] for i in range(0, n+1)]
aux = as_witt_form(aux, (n+1)*[0*AS.x])
other1 = as_witt_form((n+1)*[0*AS.x], other.dVs)
return aux + other1
flag = 1
for i in range(0, n+1):
if self.dVs[i] != 0 and other.dVs[i] != 0:
flag = 0
if flag == 1:
aux = [self.dVs[i] + other.dVs[i] for i in range(0, n+1)]
aux = as_witt_form((n+1)*[0*AS.x], aux)
other1 = as_witt_form(other.Vs, (n+1)*[0*AS.x])
return aux + other1
##################
i = 0 i = 0
while(self.Vs[i].function == 0 or other.Vs[i].function == 0): while(i <= n and self.Vs[i].function == 0 and other.Vs[i].function == 0):
i+=1 i+=1
self1 = self.Vs[:i] + [0*AS.x] + self.Vs[i+1 : ] if i<=n:
self1 = as_witt_form(self1, self.dVs) print('a')
other1 = other.Vs[:i] + [0*AS.x] + other.Vs[i+1 : ] if (i <= n and self.Vs[i].function != 0 and other.Vs[i].function != 0):
other1 = as_witt_form(other1, other.dVs) self1 = self.cutVs(i)
fct = self.Vs[i].teichmuller(n+1 - i) + other.Vs[i].teichmuller(n+1 - i) other1 = other.cutVs(i)
result = self1 + other1 result = self1 + other1
for j in range(0, n+1 - i): self_first = self.Vs[i].teichmuller(n)
aux = as_witt_form((n+1)*[0*AS.x], (n+1)*[0*AS.x]) ####? write Verschiebung other_first = other.Vs[i].teichmuller(n)
aux.Vs[i + j] = fct[j] aux = self_first + other_first
result = result + aux for j in range(0, n+1 - i):
print(i, j)
############# result += aux.f[j].Vd(n, i+j)
if [a.function for a in other.Vs] == (n+1)*[0] and [a.function for a in other.dVs] == (n+1)*[0]: return result
return self if (i <= n and self.Vs[i].function != 0 and other.Vs[i].function == 0):
if [a.function for a in other.Vs] != (n+1)*[0]: self1 = self.cutVs(i)
other1 = other.cutVs(i)
f1 = self.f[i] result = self1 + other1
f2 = other.f[i] result.Vs[i] = self.Vs[i]
f = f1.teichmuller(n) + f2.teichmuller(n) return result
for j in range(i, i+1): if (i <= n and self.Vs[i].function == 0 and other.Vs[i].function != 0):
result[i] += self.f[i] + other.f[i] self1 = self.cutVs(i)
other1 = other.cutVs(i)
result = self1 + other1
result.Vs[i] = other.Vs[i]
return result
########
i = 0
while(i <= n and self.dVs[i].function == 0 and other.dVs[i].function == 0):
i+=1
if i<=n:
print('b', i)
if (i <= n and self.dVs[i].function != 0 and other.dVs[i].function != 0):
self1 = self.cutdVs(i)
other1 = other.cutdVs(i)
result = self1 + other1
self_first = self.dVs[i].teichmuller(n)
other_first = other.dVs[i].teichmuller(n)
aux = self_first + other_first
for j in range(0, n+1 - i):
result += aux.f[j].dV(n, i+j)
return result
if (i <= n and self.dVs[i].function != 0 and other.dVs[i].function == 0):
self1 = self.cutdVs(i)
other1 = other.cutdVs(i)
result = self1 + other1
result.dVs[i] = self.dVs[i]
return result
if (i <= n and self.dVs[i].function == 0 and other.dVs[i].function != 0):
self1 = self.cutdVs(i)
other1 = other.cutdVs(i)
result = self1 + other1
result.dVs[i] = other.dVs[i]
return result
return (0*AS.x).Vd(n)
def verschiebung(self, i = 1): def verschiebung(self, i = 1):
AS = self.curve AS = self.curve
p = AS.base_ring.characteristic() p = AS.base_ring.characteristic()
@ -79,4 +96,16 @@ class as_witt_form:
result_dVs = 2*[0*AS.x] + self.Vs[2:] result_dVs = 2*[0*AS.x] + self.Vs[2:]
result_dVs = [a^p for a in result_dVs] result_dVs = [a^p for a in result_dVs]
return as_witt_form(result_Vs, result_dVs) return as_witt_form(result_Vs, result_dVs)
return self.verschiebung().verschiebung(i = i-1) return self.verschiebung().verschiebung(i = i-1)
def cutVs(self, i):
n = self.n
AS = self.curve
result_Vs = self.Vs[:i] + (n+1 - i)*[0*AS.x]
return as_witt_form(result_Vs, self.dVs)
def cutdVs(self, i):
n = self.n
AS = self.curve
result_dVs = self.dVs[:i] + (n+1 - i)*[0*AS.x]
return as_witt_form(self.Vs, result_dVs)

4
init.sage
View File

@ -26,6 +26,10 @@ load('auxilliaries/reverse.sage')
load('auxilliaries/hensel.sage') load('auxilliaries/hensel.sage')
load('auxilliaries/linear_combination_polynomials.sage') load('auxilliaries/linear_combination_polynomials.sage')
load('auxilliaries/laurent_analytic_part.sage') load('auxilliaries/laurent_analytic_part.sage')
load('as_drw/witt_polynomials.sage')
load('as_drw/as_witt.sage')
load('as_drw/as_witt_form.sage')
load('as_drw/as_compability.sage')
############## ##############
############## ##############
def init(lista, tests = False, init=True): def init(lista, tests = False, init=True):