82 lines
2.9 KiB
Python
82 lines
2.9 KiB
Python
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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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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.Vs:
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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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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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i = 0
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while(self.Vs[i].function == 0 or 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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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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