Problem with rational_points over plane curves AND addition of rational_points_iterator function

[sagetrac-cturner]

The newly "improved" rational_points function for projective plane curves (#8193) has a bug; if for some (Y,Z) the polynomial defining the curve becomes identically 0, it returns a ValueError caused by the function trying to factorise 0 as a polynomial.

Here is an example

sage: F = GF(2)
sage: P2.<X,Y,Z> = ProjectiveSpace(F,2)
sage: C = Curve(X*Y)
sage: a = C.rational_points_iterator()
sage: a.next()
(1 : 0 : 0)
sage: a.next()
(0 : 1 : 0)
sage: a.next()
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)

/home/charlie/<ipython console> in <module>()

/home/charlie/sage-current/local/lib/python2.6/site-packages/sage/schemes/plane_curves/projective_curve.pyc
in rational_points_iterator(self)
   353         # points with Z = 1
   354         for y in K:
--> 355             for x in R(g(X,y,one)).roots(multiplicities=False):
   356                 yield(self.point([x,y,one]))
   357

/home/charlie/sage-current/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_element.so
in sage.rings.polynomial.polynomial_element.Polynomial.roots
(sage/rings/polynomial/polynomial_element.c:30111)()

/home/charlie/sage-current/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_element.so
in sage.rings.polynomial.polynomial_element.Polynomial.factor
(sage/rings/polynomial/polynomial_element.c:18463)()
ValueError: factorization of 0 not defined

I propose to write new rational_points_iterator function that will return an iterator over the set of rational points of the projective plane curve. It will avoid this bug. It will be called by rational_points to return a list of all these rational points. A patch to do all of this is on its way.

CC: @JohnCremona

Component: algebraic geometry

Author: Charlie Turner

Reviewer: David Roe

Merged: sage-4.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8428

[sagetrac-cturner]

Applies to 4.3.3

[sagetrac-cturner]

Attachment: trac_8428_rational_points_iterator.2.patch.gz

Applies to 4.3.3

[sagetrac-cturner]

comment:5

Attachment: trac_8428_rational_points_iterator.patch.gz

[sagetrac-cturner]

comment:6

Apologies; both copies of the patch are the same, I double-clicked and am unable to remove the 2nd copy.

[roed314]

comment:8

Fixes the bug, doctested and doctests pass. Positive review.

[roed314]

Reviewer: David Roe

[jhpalmieri]

Merged: sage-4.4.alpha0

[jhpalmieri]

comment:9

Merged "trac_8428_rational_points_iterator.patch" into 4.4.alpha0.