DeRhamComputation/as_drw/as_witt_form.sage

111 lines
4.0 KiB
Python

class as_witt_form:
def __init__(self, fcts1, fcts2):
self.Vs = fcts1
self.dVs = fcts2
self.n = len(fcts1) - 1
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):
result = ''
i = 0
for f in self.Vs:
if i != 0:
result += 'V^' + str(i) + '([' + str(f) + '] d[x]) +'
else:
result += '[' + str(f) + '] d[x] +'
i+=1
i = 1
for f in self.dVs[1:]:
result += 'dV^' + str(i) + '([' + str(f) + ']) +'
i+=1
return result
def __add__(self, other):
print(self, other)
n = self.n
AS = self.curve
########
i = 0
while(i <= n and self.Vs[i].function == 0 and other.Vs[i].function == 0):
i+=1
if i<=n:
print('a')
if (i <= n and self.Vs[i].function != 0 and other.Vs[i].function != 0):
self1 = self.cutVs(i)
other1 = other.cutVs(i)
result = self1 + other1
self_first = self.Vs[i].teichmuller(n)
other_first = other.Vs[i].teichmuller(n)
aux = self_first + other_first
for j in range(0, n+1 - i):
print(i, j)
result += aux.f[j].Vd(n, i+j)
return result
if (i <= n and self.Vs[i].function != 0 and other.Vs[i].function == 0):
self1 = self.cutVs(i)
other1 = other.cutVs(i)
result = self1 + other1
result.Vs[i] = self.Vs[i]
return result
if (i <= n and self.Vs[i].function == 0 and other.Vs[i].function != 0):
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):
AS = self.curve
p = AS.base_ring.characteristic()
n = self.n
if i == 1:
result_Vs = [0*AS.x] + self.Vs[1:]
result_dVs = 2*[0*AS.x] + self.Vs[2:]
result_dVs = [a^p for a in result_dVs]
return as_witt_form(result_Vs, result_dVs)
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)