#5269: coordinate ring of an affine patch on a hyperelliptic curve is broken
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Reporter: AlexGhitza | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: algebraic geometry | Keywords:
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When taking an affine patch of a hyperelliptic curve, the defining
polynomial (sometimes?) has the wrong parent:
{{{
sage: P.<x> = QQ[]
sage: f = 4*x^5 - 30*x^3 + 45*x - 22
sage: C = HyperellipticCurve(f)
sage: D = C.affine_patch(0); D
Closed subscheme of Affine Space of dimension 2 over Rational Field
defined by:
x0^2*x1^3 + 22*x1^5 - 45*x1^4 + 30*x1^2 - 4
sage: f = D.defining_polynomials()[0]; f
x0^2*x1^3 + 22*x1^5 - 45*x1^4 + 30*x1^2 - 4
sage: f.parent()
Multivariate Polynomial Ring in x0, x1, x2 over Rational Field
}}}
Everything is fine except the last line: the parent of f should be a
multivariate polynomial ring in two variables, not three.
This might be a more generic problem and not necessarily related to
hyperelliptic curves.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5269>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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