#16068: Use base_ring in chord_and_tangent
-------------------------------+------------------------------
Reporter: jkeitel | Owner:
Type: PLEASE CHANGE | Status: new
Priority: minor | Milestone: sage-6.2
Component: elliptic curves | Keywords:
Merged in: | Authors: Jan Keitel
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Right now, the following fails:
{{{
sage: from sage.schemes.elliptic_curves.constructor import
chord_and_tangent
sage: R = PolynomialRing(QQ, 'x,y,z')
sage: x,y,z = R.gens()
sage: cubic = x**3 - 4*x**2*y - 65*x*y**2 + 3*x*y*z - 76*y*z**2
sage: f0 = (0, 1, 0)
sage: chord_and_tangent(cubic, f0)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
<ipython-input-9-05d9ab02db04> in <module>()
----> 1 chord_and_tangent(cubic, f0)
/home/pcl337b/jkeitel/sage/sage/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in
chord_and_tangent(F, P)
898 g = F.substitute({x:y, y:x})
899 Q = [P[1], P[0], P[2]]
--> 900 R = chord_and_tangent(g, Q)
901 return [R[1], R[0], R[2]]
902 elif dz != 0:
/home/pcl337b/jkeitel/sage/sage/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in
chord_and_tangent(F, P)
917 g = F.substitute({x:z, z:x})
918 Q = [P[2], P[1], P[0]]
--> 919 R = chord_and_tangent(g, Q)
920 return [R[2], R[1], R[0]]
921 # Ft has a double zero at t=0 by construction, which we now
remove
/home/pcl337b/jkeitel/sage/sage/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in
chord_and_tangent(F, P)
924 # first case: the third point is at t=infinity
925 if Ft.is_constant():
--> 926 return projective_point([dy, -dx, 0])
927 # second case: the third point is at finite t
928 else:
/home/pcl337b/jkeitel/sage/sage/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in
projective_point(p)
955 from sage.rings.integer import GCD_list, LCM_list
956 try:
--> 957 p_gcd = GCD_list([x.numerator() for x in p])
958 p_lcm = LCM_list([x.denominator() for x in p])
959 except AttributeError:
TypeError: 'int' object is not callable
}}}
This is very simple to fix - convert a 0 into an element of the base ring
of the curve and I've attached a branch that does that.
--
Ticket URL: <http://trac.sagemath.org/ticket/16068>
Sage <http://www.sagemath.org>
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