111 lines
4.0 KiB
Python
111 lines
4.0 KiB
Python
class as_witt_form:
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def __init__(self, fcts1, fcts2):
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self.Vs = fcts1
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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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i = 0
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for f in self.Vs:
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if i != 0:
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result += 'V^' + str(i) + '([' + str(f) + '] d[x]) +'
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else:
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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.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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########
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i = 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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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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n = self.n
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if i == 1:
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result_Vs = [0*AS.x] + self.Vs[1:]
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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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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) |