.
A.<x,y> = AffineSpace(QQ, 2)
C = Curve([(x^2+y^2)^4 - 3*(x^2+y^2)^2 - 2*(x^2-y^2)], A)
C.genus()
C.genus() is zero, but C.parameterization() give error.
The given curve resamble (but differ) with "Durer-folium" and I study a family of these curves. How to get a (rational) parametrization for it? Thanks!
First off, the method is called .rational_parameterization() not just .parameterization(), but nevertheless it gives an error.
You can try to start with
P2.<x,y,z> = ProjectiveSpace(QQ, 2)
f = (x^2+y^2)^4 - 3*(x^2+y^2)^2 - 2*(x^2-y^2)
C = Curve( f.homogenize(z) )
and then proceed as in this answer.
Asked: 2026-03-11 05:14:30 +0100
Seen: 22 times
Last updated: Mar 23
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