94 lines
2.8 KiB
Python
94 lines
2.8 KiB
Python
class superelliptic_drw_form:
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def __init__(self, h1, omega, h2):
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'''Form [h1] d[x] + V(omega) + dV([h2])'''
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self.curve = h1.curve
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self.h1 = h1
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self.omega = omega
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self.h2 = h2
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def r(self):
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C = self.curve
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h1 = self.h1
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return superelliptic_form(C, h1.function)
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def __eq__(self, other):
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eq1 = (self.h1 == self.h1)
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try:
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H = (self.h2 - other.h2).pth_root()
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except:
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return False
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eq2 = ((other.omega - self.omega).cartier() - H.diffn()) == 0*self.curve.dx
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if eq1 and eq2:
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return True
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return False
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def __repr__(self):
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C = self.curve
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h1 = self.h1
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omega = self.omega
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h2 = self.h2
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result = ""
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if h1.function != 0:
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result += "[" + str(h1) + "] d[x]"
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if (h1.function !=0 and omega.form != 0) or (h2.function !=0 and omega.form != 0):
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result += " + "
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if omega.form != 0:
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result += "V(" + str(omega) + ")"
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if h2.function !=0 and omega.form != 0:
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result += " + "
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if h2.function != 0:
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result += "dV([" + str(h2) +"])"
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if result == "":
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result += "0"
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return result
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def __rmul__(self, other):
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h1 = self.h1
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h2 = self.h2
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omega = self.omega
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p = self.curve.characteristic
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if other in ZZ:
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if other == 0:
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return superelliptic_drw_form(0*C.x, 0*C.dx, 0*C.x)
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if other > 0:
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return self + (other-1)*self
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if other < 0:
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return (-other)*(-self)
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if other in QQ:
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other_integer = Integers(p^2)(other)
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return other_integer*self
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t = other.t
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f = other.f
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aux_form = t^p*omega - h2*t^(p-1)*t.diffn() + f*h1^p*(C.x)^(p-1)*C.dx
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return superelliptic_drw_form(t*h1, aux_form, t^p*h2)
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def __neg__(self):
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C = self.curve
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h1 = self.h1
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h2 = self.h2
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omega = self.omega
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return superelliptic_drw_form(-h1, -omega, -h2)
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def __sub__(self, other):
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return self + (-other)
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def __add__(self, other):
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C = self.curve
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h1 = self.h1
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h2 = self.h2
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omega = self.omega
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H1 = other.h1
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H2 = other.h2
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OMEGA = other.omega
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aux = (teichmuller(h1) + teichmuller(H1))*superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)
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h1_aux = aux.h1
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h2_aux = aux.h2
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omega_aux = aux.omega
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return superelliptic_drw_form(h1_aux, omega + OMEGA + omega_aux, h2 + H2 + h2_aux)
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def frobenius(self):
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C = self.curve
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h1 = self.h1
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h2 = self.h2
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p = C.characteristic
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return h1^p*C.x^(p-1)*C.dx + h2.diffn() |