----- Original Message -----
From: Luis Finotti <[EMAIL PROTECTED]>
Date: Wednesday, February 7, 2007 9:50 pm
Subject: [sage-support] Real points on elliptic curves
To: [email protected]
> sage: E=EllipticCurve(RR,[0,-1])
> sage: x0=RR(4)^(1/3)
> sage: y0=sqrt(RR(3))
> sage: E([x0,y0])
> --------------------------------------------------------------------
> -------
> <type 'exceptions.TypeError'> Traceback (most recent
> call last)
> I can implement the addition formula and work with the approximations
> instead of using Sage to add the points (or call Pari, which I think
> does it), but I thought I should see if I am missing something and/or
> if this is the expected behavior.
Is there a way to coerce an elliptic curve Pari object to a SAGE elliptic curve
object? Perhaps this will circumvent he above problem(?)
sage: E=EllipticCurve(RR,[0,-1])
sage: x0=RR(4)^(1/3)
sage: e = gp(E)
sage: type(e)
<class 'sage.interfaces.gp.GpElement'>
sage: type(E)
<class 'sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic'>
sage: e.ellordinate(x0)
[1.732050807568856617276384369, -1.732050807568856617276384369]
sage: y0 = e.ellordinate(x0)[1]
sage: e.ellisoncurve([x0,y0])
1
sage: E([x0,y0])
---------------------------------------------------------------------------
<type 'exceptions.TypeError'> Traceback (most recent call last)
/Users/weirdalerdos/Documents/sage-2.0/<ipython console> in <module>()
/Users/weirdalerdos/Documents/sage-2.0/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_generic.py
in __call__(self, *args)
300 R = self.base_ring()
301 return self.point([R(0),R(1),R(0)], check=False)
--> 302 return plane_curve.ProjectiveCurve_generic.__call__(self, *args)
303
304 def _homset_class(self, *args, **kwds):
/Users/weirdalerdos/Documents/sage-2.0/local/lib/python2.5/site-packages/sage/schemes/generic/scheme.py
in __call__(self, *args)
124 if S.codomain() == self:
125 return S
--> 126 return self.point(args)
127
128 def point_homset(self, R=None):
/Users/weirdalerdos/Documents/sage-2.0/local/lib/python2.5/site-packages/sage/schemes/generic/scheme.py
in point(self, v, check)
140
141 def point(self, v, check=True):
--> 142 return self._point_class(self, v, check=check)
143
144 def _point_class(self):
/Users/weirdalerdos/Documents/sage-2.0/local/lib/python2.5/site-packages/sage/schemes/generic/morphism.py
in __init__(self, X, v, check)
372 raise ValueError, "%s does not define a valid point
since all entries are 0"%v
373
--> 374 X.codomain()._check_satisfies_equations(v)
375
376 self._coords = v
/Users/weirdalerdos/Documents/sage-2.0/local/lib/python2.5/site-packages/sage/schemes/generic/algebraic_scheme.py
in _check_satisfies_equations(self, v)
226 for f in self.defining_polynomials():
227 if f(v) != 0:
--> 228 self._error_bad_coords(v)
229
230 def base_extend(self, R):
/Users/weirdalerdos/Documents/sage-2.0/local/lib/python2.5/site-packages/sage/schemes/generic/algebraic_scheme.py
in _error_bad_coords(self, v)
217
218 def _error_bad_coords(self, v):
--> 219 raise TypeError, "coordinates %s do not define a point on
%s"%(v,self)
220
221 def _check_satisfies_equations(self, v):
<type 'exceptions.TypeError'>: coordinates [1.58740105196819, 1.73205080756885,
1.00000000000000] do not define a point on Elliptic Curve defined by y^2 +
0.000000000000000*x*y + 0.000000000000000*y = x^3 + 0.000000000000000*x^2 +
0.000000000000000*x - 1.00000000000000 over Real Field with 53 bits of precision
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/
-~----------~----~----~----~------~----~------~--~---
