Ticket #1785 (closed defect: fixed)
[with patch, with positive review] bug in creating points on elliptic curves over extension fields
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On Jan 15, 2008 10:25 AM, John Cremona <email@example.com> wrote: > > I like Robert's suggestion. If the user wants n independent generic > points, construct a large enough field (transcendence degree n) to > contain them. > > A useful change Magma made relatively recently (a couple of years or > so ago) was to aloow points on an elliptic curve to have coordinates > in an extension of the base field of the curve -- as one would when > working mathematically. e.g. given a curve defined over QQ you can > define points on E(K) for e.g. K=a number field, or K=a function field > (such as the function field of E, to get a generic point). Of course, > these points "know" what their curve is so you can do point arithmetic > on them and so on. > > I don't see why this should be workable in Sage too (maybe it is > already? if so I will retire shame-faced from the discussion...) It's sort of half-way there. You can do: sage: K.<a> = NumberField(x^2 + x - (3^3-3)) sage: E = EllipticCurve('37a') sage: X = E(K) but stupidly X is wrong: sage: X Abelian group of points on Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field though: sage: X.domain() Spectrum of Number Field in a with defining polynomial x^2 + x - 24 However, sage: P = X([3,a]); boom with a TypeError So this obviously needs work. In fact, this counts as a bug.
- Summary changed from bug in creating points on elliptic curves over extension fields to [with patch, needs review] bug in creating points on elliptic curves over extension fields
- Summary changed from [with patch, needs review] bug in creating points on elliptic curves over extension fields to [with patch, with positive review] bug in creating points on elliptic curves over extension fields
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