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from sage.all import *
from ..utilities.supersingular import compute_linearly_independent_point
from .montgomery_theta import (
montgomery_point_to_theta_point,
theta_point_to_montgomery_point,
torsion_to_theta_null_point,
)
class ThetaStructureDim1:
def __init__(self,E,P=None,Q=None):
self.E=E
a_inv=E.a_invariants()
A =a_inv[1]
if a_inv != (0,A,0,1,0):
raise ValueError("The elliptic curve E is not in the Montgomery model.")
if Q==None:
y2=A-2
y=y2.sqrt()
Q=E([-1,y,1])
P=compute_linearly_independent_point(E,Q,4)
else:
if Q[0]!=-1:
raise ValueError("You should enter a canonical 4-torsion basis. Q[0] should be -1.")
self.P=P
self.Q=Q
self._base_ring=E.base_ring()
self._point=ThetaPointDim1
self._null_point=self._point(self,torsion_to_theta_null_point(P))
def null_point(self):
"""
"""
return self._null_point
def base_ring(self):
"""
"""
return self._base_ring
def zero(self):
"""
"""
return self.null_point()
def elliptic_curve(self):
return self.E
def torsion_basis(self):
return (self.P,self.Q)
def __call__(self,coords):
r"""
Input: either a tuple or list of 2 coordinates or an elliptic curve point.
Output: the corresponding theta point for the self theta structure.
"""
if isinstance(coords,tuple):
return self._point(self,coords)
elif isinstance(coords,list):
return self._point(self,coords)
else:
return self._point(self,montgomery_point_to_theta_point(self.null_point().coords(),coords))
def __repr__(self):
return f"Theta structure on {self.elliptic_curve()} with null point: {self.null_point()} induced by the 4-torsion basis {self.torsion_basis()}"
def to_montgomery_point(self,P):
return theta_point_to_montgomery_point(self.E,self.null_point().coords(),P.coords())
class ThetaPointDim1:
def __init__(self, parent, coords):
"""
"""
if not isinstance(parent, ThetaStructureDim1):
raise ValueError("Entry parent should be a ThetaStructureDim1 object.")
self._parent = parent
self._coords = tuple(coords)
def coords(self):
return self._coords
def __repr__(self):
return f"Theta point with coordinates: {self.coords()}"
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