Unhandled case in EllipticCurve_from_cubic

[Robin Houston]

I ran into an unexpected error in EllipticCurve_from_cubic, with the following cubic and rational point:

R.<x,y,z> = QQ[]

cubic = -3*x^2*y + 3*x*y^2 + 4*x^2*z + 4*y^2*z - 3*x*z^2 + 3*y*z^2 - 8*z^3

EllipticCurve_from_cubic(cubic, (-4/5, 4/5, 3/5))

Note that it works as expected using instead the different rational point (1, 1, 0).

On investigation, I found there is a case that isn’t handled correctly. The code computes

P2 = chord_and_tangent(F, P)

and if P2 is projectively equivalent to P then it uses a different algorithm. If they’re different, it then computes

P3 = chord_and_tangent(F, P2)

and uses an algorithm that fails if P3 is equivalent to P2.

I think the attached patch fixes this problem. At least, with this patch it now works for my examples.

Best wishes,

Robin

[John Cremona]

Can someone make a trac ticket for this please?

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[Jeroen Demeyer]

On 2016-07-25 13:07, John Cremona wrote:
> Can someone make a trac ticket for this please?

Done: https://trac.sagemath.org/ticket/21092

[leif]

Ooops, race condition (I did look at the trac timeline!).

On behalf of John (Forgot your password?):

https://trac.sagemath.org/ticket/21093



-leif

[John Cremona]

On 25 Jul 2016 17:03, "leif" <not.r...@online.de> wrote:
>
> Jeroen Demeyer wrote:
> > On 2016-07-25 13:07, John Cremona wrote:
> >> Can someone make a trac ticket for this please?
> >
> > Done: https://trac.sagemath.org/ticket/21092
>
> Ooops, race condition (I did look at the trac timeline!).
>
> On behalf of John (Forgot your password?):

No just away from home with only a phone.

>
> https://trac.sagemath.org/ticket/21093
>
>
>
> -leif

[Robin Houston]

I think there’s another case that isn’t handled correctly, exemplified by:

R.<x,y,z> = QQ[]

T = EllipticCurve_from_cubic(y^2*z - x^3 - z^3, (0,1,0))

A simple change that fixes this problem is to make the projective_point() method not blow up when given (0,0,0), e.g.:

--- a/src/sage/schemes/elliptic_curves/constructor.py

+++ b/src/sage/schemes/elliptic_curves/constructor.py

@@ -1127,6 +1127,8 @@ def projective_point(p):

         p_lcm = LCM_list([x.denominator() for x in p])

     except AttributeError:

         return p

+    if p_gcd == 0:

+        return p

     scale = p_lcm / p_gcd

     return [scale * x for x in p]

 

This change may be undesirable for other reasons, though.

Robin

[John Cremona]

I think that an error should be raised if the projective point constructor is called with (0,0,0). 

[Robin Houston]

Okay, that’s reasonable. How about the attached, then?

Robin

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