#15340: Bug in chord_and_tangent
-------------------------------+-----------------------------
Reporter: vbraun | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The `chord_and_tangent` method fails to treat one special case: the
`t`-family of points
{{{
(dy*t+P[0], (-dx-dz)*t+P[1], dy*t+P[2])
}}}
might fail to parametrize a line if `(dy,-dx-dz,dy)` is projectively
equivalent to P. One needs to try two independent normal directions...
This leads to the following failure (reported by Pierre Vanhove):
{{{
sage: R.<x,y,z> = QQ[]
sage: cubic = x^2*y + 4*x*y^2 + x^2*z + 8*x*y*z + 4*y^2*z + 9*x*z^2 +
9*y*z^2
sage: EllipticCurve_from_cubic(cubic, [1,-1,1], morphism=False)
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
<ipython-input-3-67b6e7c68a76> in <module>()
----> 1 EllipticCurve_from_cubic(cubic,
[Integer(1),-Integer(1),Integer(1)], morphism=False)
/home/vbraun/Code/sage.git/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in
EllipticCurve_from_cubic(F, P, morphism)
774 X, Y, Z = S.gen(0), S.gen(1), S(-1/b)*S.gen(2)
775 F4 = F3(X, Y, Z)
--> 776 E = EllipticCurve(F4.subs(z=1))
777 if not morphism:
778 return E
/home/vbraun/Code/sage.git/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in EllipticCurve(x,
y, j, minimal_twist)
313 if is_MPolynomial(x):
314 if y is None:
--> 315 return EllipticCurve_from_Weierstrass_polynomial(x)
316 else:
317 return EllipticCurve_from_cubic(x, y, morphism=False)
/home/vbraun/Code/sage.git/local/lib/python2.7/site-
packages/sage/schemes/elliptic_curves/constructor.pyc in
EllipticCurve_from_Weierstrass_polynomial(f)
433 a3 = -coeff
434 else:
--> 435 raise ValueError('polynomial is not in long
Weierstrass form')
436
437 if x3 != y2:
ValueError: polynomial is not in long Weierstrass form
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15340>
Sage <http://www.sagemath.org>
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