Re: [sage-support] integral points on ellipitc curves

Is any possibility to find on MAGMA of integral points on elliptic curve such type where coefficient by x^3 isn't equal 1 e.q.: A := AffineSpace(Rationals(),2); C := Curve(y^2-4*x^3+7*x+3); IntegralPoints(C); When I execute e.g. IntegralQuarticPoints([0, 4, 0, -7, -3]); output of Magma is: ) In

Re: [sage-support] integral points on ellipitc curves

A patch is up for review now at https://trac.sagemath.org/ticket/22063 On 15 December 2016 at 17:02, John Cremona wrote: > Without going so far as to use interval arithmetic (which leads to at > least one annoying problem: the RealIntervalField in Sage has no >

Re: [sage-support] integral points on ellipitc curves

Without going so far as to use interval arithmetic (which leads to at least one annoying problem: the RealIntervalField in Sage has no is_square() methods which is enough to make it hard to work with as far as creating points on elliptic curves is concerned) I came up with a better solution. I

Re: [sage-support] integral points on ellipitc curves

On 15 December 2016 at 14:52, wrote: > @John : Good point. The change in precision, at least seems to fix the > previous problems (at least in the specific examples). > I suppose, this is the precision that is used to bound the coefficients of > the linear form of elliptic

Re: [sage-support] integral points on ellipitc curves

@John : Good point. The change in precision, at least seems to fix the previous problems (at least in the specific examples). I suppose, this is the precision that is used to bound the coefficients of the linear form of elliptic logarithms (?) If this is the case, and I remember right, this

Re: [sage-support] integral points on ellipitc curves

On Thu, Dec 15, 2016 at 4:51 AM, Dima Pasechnik wrote: > > > On Thursday, December 15, 2016 at 12:23:15 PM UTC, John Cremona wrote: >> >> I just confirmed that if I change RealField(100) to RealField(200) in >> one place (line 6975 of ell_rational_field.py) then both the points

Re: [sage-support] integral points on ellipitc curves

On Thursday, December 15, 2016 at 12:23:15 PM UTC, John Cremona wrote: > > I just confirmed that if I change RealField(100) to RealField(200) in > one place (line 6975 of ell_rational_field.py) then both the points > Costas missed are found, so I was right that this is a stupid problem > of

Re: [sage-support] integral points on ellipitc curves

I just confirmed that if I change RealField(100) to RealField(200) in one place (line 6975 of ell_rational_field.py) then both the points Costas missed are found, so I was right that this is a stupid problem of precision rather than something more complicated. I can easily make a patch to make

Re: [sage-support] integral points on ellipitc curves

On 14 December 2016 at 21:34, wrote: > Thank you both for the answers, > > I found another problematic example > > sage:E1=EllipticCurve([0,0,0,37,18]);E1;S=E1.integral_points();S; > Elliptic Curve defined by y^2 = x^3 + 37*x + 18 > over Rational Field > [(2 : 10 : 1), (126 :

Re: [sage-support] integral points on ellipitc curves

Thank you both for the answers, I found another problematic example sage:E1=EllipticCurve([0,0,0,37,18]);E1;S=E1.integral_points();S; Elliptic Curve defined by y^2 = x^3 + 37*x + 18 over Rational Field [(2 : 10 : 1), (126 : 1416 : 1)] and R = E1(64039202,512470496030);M=E1(2,10 );3*M==R

Re: [sage-support] integral points on ellipitc curves

On Wednesday, December 14, 2016 at 12:09:36 PM UTC-8, John Cremona wrote: > > > Thanks for the bug report. As Nils pointed out there are known bugs > in the integral point code which cause solutions to be missed. Just to make clear: I wasn't taking a jibe at sage/or John on this, and I wasn't

Re: [sage-support] integral points on ellipitc curves

Dear Costas, Thanks for the bug report. As Nils pointed out there are known bugs in the integral point code which cause solutions to be missed. A lot of work has been spent on improving this, in part by me, and the main reason the fixes have not yet been approved and merged is that I still had

[sage-support] integral points on ellipitc curves

Hi all, I came across the following example... sage: E1=EllipticCurve([0,0,0,49,-64]);E1;S=E1.integral_points();S; Elliptic Curve defined by y^2 = x^3 + 49*x - 64 over Rational Field [(4 : 14 : 1), (464 : 9996 : 1)] but the following integer point Q belongs also to the curve