Compute a rational parametrization of a rational normal curve C defined by I.
phi contains the rational parametrization of C over ℙ1 if the degree of C is odd or over a conic if the degree of C is even.
Ic is the 0-ideal for odd degree or the ideal of the conic for even degree.
i1 : K=QQ; |
i2 : R=K[v,u,z]; |
i3 : I0=ideal(v^8-u^3*(z+u)^5); o3 : Ideal of R |
i4 : J=ideal matrix {{u^6+4*u^5*z+6*u^4*z^2+4*u^3*z^3+u^2*z^4,v*u^5+3*v*u^4*z+3*v*u^3*z^2+v*u^2*z^3,v^2*u^4+3*v^2*u^3*z+3*v^2*u^2*z^2+v^2*u*z^3,v^3*u^3+2*v^3*u^2*z+v^3*u*z^2,v^4*u^2+v^4*u*z,v^5*u+v^5*z,v^6}};
o4 : Ideal of R
|
i5 : I=mapToRNC(I0,J)
o5 = ideal (x x - x x , x x - x x , x x - x x , x x - x x , x x - x x ,
4 5 3 6 3 5 2 6 1 5 0 6 3 4 1 6 2 4 0 6
------------------------------------------------------------------------
2 2 2
x x - x , x - x x , x x - x x , x x - x , x x - x x , x x - x x ,
0 4 6 3 0 6 2 3 0 5 1 3 6 0 3 5 6 1 2 5 6
------------------------------------------------------------------------
2 2 2
x x - x , x - x x , x x - x x , x - x x )
0 2 5 1 4 6 0 1 3 6 0 2 6
o5 : Ideal of QQ[x , x , x , x , x , x , x ]
0 1 2 3 4 5 6
|
i6 : rParametrizeRNC(I)
2
o6 = {| t_0^2t_2 |, ideal(t - t t )}
| -t_1t_2^2 | 1 0 2
| t_0^3 |
| -t_0t_1t_2 |
| t_2^3 |
| -t_0^2t_1 |
| t_0t_2^2 |
o6 : List
|