#8428: Problem with rational_points over plane curves AND addition of
rational_points_iterator function
----------------------------------+-----------------------------------------
Reporter: cturner | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone:
Component: algebraic geometry | Keywords:
Author: Charlie Turner | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
----------------------------------+-----------------------------------------
Description changed by cturner:
Old description:
> 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
> }}}
>
> A patch to improve this is on its way.
New description:
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 point. A patch to do all of this is on its way.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8428#comment:3>
Sage <http://www.sagemath.org>
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