as_witt_form addition works at least partially
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@ -15,6 +15,18 @@ class as_function:
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def __repr__(self):
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return str(self.function)
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def __eq__(self, other):
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AS = self.curve
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RxyzQ, Rxyz, x, y, z = AS.fct_field
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aux = self - other
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aux = RxyzQ(aux.function)
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aux = aux.numerator()
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aux = as_function(AS, aux)
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aux = aux.expansion_at_infty()
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if aux.valuation() >= 1:
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return True
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return False
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def __add__(self, other):
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C = self.curve
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@ -33,7 +45,7 @@ class as_function:
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g = self.function
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return as_function(C, constant*g)
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def __neg__(self, other):
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def __neg__(self):
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C = self.curve
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g = self.function
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return as_function(C, -g)
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@ -2,4 +2,18 @@ def teichmuller(self, n):
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AS = self.curve
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return as_witt([self] + n*[0*AS.x])
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as_function.teichmuller = teichmuller
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def Vd(self, n, m = 1):
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'''Return V^m([f] d[x]) in W_n Omega'''
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AS = self.curve
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if m == 0:
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return as_witt_form([self] + n*[0*AS.x], (n+1)*[0*AS.x])
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return as_witt_form(m*[0*AS.x] + [self] + (n-m)*[0*AS.x], (n+1)*[0*AS.x])
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def dV(self, n, m = 1):
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'''Return dV^m([f] d[x]) in W_n Omega'''
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AS = self.curve
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return as_witt_form((n+1)*[0*AS.x], m*[0*AS.x] + [self] + (n-m)*[0*AS.x])
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as_function.teichmuller = teichmuller
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as_function.Vd = Vd
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as_function.dV = dV
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@ -4,6 +4,10 @@ class as_witt_form:
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self.dVs = fcts2
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self.n = len(fcts1) - 1
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self.curve = fcts1[0].curve
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if self.dVs[0].function!=0:
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raise ValueError('First dV should be zero!')
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if len(fcts1) != len(fcts2):
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raise ValueError('Both lists should be of the same length!')
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def __repr__(self):
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result = ''
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@ -15,61 +19,74 @@ class as_witt_form:
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result += '[' + str(f) + '] d[x] +'
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i+=1
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i = 1
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for f in self.Vs:
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for f in self.dVs[1:]:
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result += 'dV^' + str(i) + '([' + str(f) + ']) +'
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i+=1
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return result
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def __add__(self, other):
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print(self, other)
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n = self.n
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AS = self.curve
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result = as_witt_form((n+1)*[0 * AS.x], (n+1)*[0 * AS.x])
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flag = 1
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for i in range(0, n+1):
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if self.Vs[i] != 0 and other.Vs[i] != 0:
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flag = 0
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if flag == 1:
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aux = [self.Vs[i] + other.Vs[i] for i in range(0, n+1)]
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aux = as_witt_form(aux, (n+1)*[0*AS.x])
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other1 = as_witt_form((n+1)*[0*AS.x], other.dVs)
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return aux + other1
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flag = 1
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for i in range(0, n+1):
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if self.dVs[i] != 0 and other.dVs[i] != 0:
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flag = 0
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if flag == 1:
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aux = [self.dVs[i] + other.dVs[i] for i in range(0, n+1)]
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aux = as_witt_form((n+1)*[0*AS.x], aux)
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other1 = as_witt_form(other.Vs, (n+1)*[0*AS.x])
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return aux + other1
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##################
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########
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i = 0
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while(self.Vs[i].function == 0 or other.Vs[i].function == 0):
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while(i <= n and self.Vs[i].function == 0 and other.Vs[i].function == 0):
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i+=1
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self1 = self.Vs[:i] + [0*AS.x] + self.Vs[i+1 : ]
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self1 = as_witt_form(self1, self.dVs)
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other1 = other.Vs[:i] + [0*AS.x] + other.Vs[i+1 : ]
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other1 = as_witt_form(other1, other.dVs)
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fct = self.Vs[i].teichmuller(n+1 - i) + other.Vs[i].teichmuller(n+1 - i)
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result = self1 + other1
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for j in range(0, n+1 - i):
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aux = as_witt_form((n+1)*[0*AS.x], (n+1)*[0*AS.x]) ####? write Verschiebung
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aux.Vs[i + j] = fct[j]
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result = result + aux
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#############
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if [a.function for a in other.Vs] == (n+1)*[0] and [a.function for a in other.dVs] == (n+1)*[0]:
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return self
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if [a.function for a in other.Vs] != (n+1)*[0]:
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f1 = self.f[i]
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f2 = other.f[i]
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f = f1.teichmuller(n) + f2.teichmuller(n)
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for j in range(i, i+1):
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result[i] += self.f[i] + other.f[i]
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if i<=n:
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print('a')
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if (i <= n and self.Vs[i].function != 0 and other.Vs[i].function != 0):
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self1 = self.cutVs(i)
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other1 = other.cutVs(i)
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result = self1 + other1
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self_first = self.Vs[i].teichmuller(n)
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other_first = other.Vs[i].teichmuller(n)
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aux = self_first + other_first
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for j in range(0, n+1 - i):
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print(i, j)
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result += aux.f[j].Vd(n, i+j)
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return result
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if (i <= n and self.Vs[i].function != 0 and other.Vs[i].function == 0):
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self1 = self.cutVs(i)
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other1 = other.cutVs(i)
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result = self1 + other1
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result.Vs[i] = self.Vs[i]
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return result
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if (i <= n and self.Vs[i].function == 0 and other.Vs[i].function != 0):
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self1 = self.cutVs(i)
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other1 = other.cutVs(i)
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result = self1 + other1
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result.Vs[i] = other.Vs[i]
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return result
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########
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i = 0
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while(i <= n and self.dVs[i].function == 0 and other.dVs[i].function == 0):
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i+=1
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if i<=n:
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print('b', i)
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if (i <= n and self.dVs[i].function != 0 and other.dVs[i].function != 0):
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self1 = self.cutdVs(i)
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other1 = other.cutdVs(i)
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result = self1 + other1
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self_first = self.dVs[i].teichmuller(n)
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other_first = other.dVs[i].teichmuller(n)
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aux = self_first + other_first
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for j in range(0, n+1 - i):
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result += aux.f[j].dV(n, i+j)
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return result
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if (i <= n and self.dVs[i].function != 0 and other.dVs[i].function == 0):
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self1 = self.cutdVs(i)
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other1 = other.cutdVs(i)
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result = self1 + other1
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result.dVs[i] = self.dVs[i]
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return result
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if (i <= n and self.dVs[i].function == 0 and other.dVs[i].function != 0):
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self1 = self.cutdVs(i)
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other1 = other.cutdVs(i)
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result = self1 + other1
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result.dVs[i] = other.dVs[i]
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return result
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return (0*AS.x).Vd(n)
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def verschiebung(self, i = 1):
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AS = self.curve
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p = AS.base_ring.characteristic()
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@ -79,4 +96,16 @@ class as_witt_form:
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result_dVs = 2*[0*AS.x] + self.Vs[2:]
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result_dVs = [a^p for a in result_dVs]
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return as_witt_form(result_Vs, result_dVs)
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return self.verschiebung().verschiebung(i = i-1)
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return self.verschiebung().verschiebung(i = i-1)
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def cutVs(self, i):
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n = self.n
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AS = self.curve
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result_Vs = self.Vs[:i] + (n+1 - i)*[0*AS.x]
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return as_witt_form(result_Vs, self.dVs)
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def cutdVs(self, i):
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n = self.n
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AS = self.curve
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result_dVs = self.dVs[:i] + (n+1 - i)*[0*AS.x]
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return as_witt_form(self.Vs, result_dVs)
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@ -26,6 +26,10 @@ load('auxilliaries/reverse.sage')
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load('auxilliaries/hensel.sage')
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load('auxilliaries/linear_combination_polynomials.sage')
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load('auxilliaries/laurent_analytic_part.sage')
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load('as_drw/witt_polynomials.sage')
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load('as_drw/as_witt.sage')
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load('as_drw/as_witt_form.sage')
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load('as_drw/as_compability.sage')
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##############
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##############
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def init(lista, tests = False, init=True):
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