mapToRNC -- Map plane rational curve to rational normal curve.

Synopsis

Usage:

mapToRNC(I)

mapToRNC(I,J)
Inputs:
- I, an ideal, defining the plane curve
- J, an ideal, the adjoint ideal of I.
Outputs:
- an ideal, of the rational normal curve.

Description

Maps a plane rational curve birationally to a rational normal curve by the adjoints of degree=degree(C)-2 Applied to a curve of genus >1 it uses the adjoints of degree=degree(C)-3.

If the second argument J is not specified and degree of C is bigger than 2 then J is being computed via the package AdjointIdeal.

i1 : K=QQ;

i2 : R=K[v,u,z];

i3 : I=ideal(v^8-u^3*(z+u)^5);

o3 : Ideal of R

i4 : betti mapToRNC(I)

            0  1
o4 = total: 1 15
         0: 1  .
         1: . 15

o4 : BettiTally

i5 : K=QQ;

i6 : R=K[v,u,z];

i7 : I=ideal(v^8-u^3*(z+u)^5);

o7 : Ideal of R

i8 : J=ideal(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);

o8 : Ideal of R

i9 : betti mapToRNC(I,J)

            0  1
o9 = total: 1 15
         0: 1  .
         1: . 15

o9 : BettiTally

Ways to use mapToRNC :

mapToRNC(Ideal)
mapToRNC(Ideal,Ideal)
mapToRNC(Ideal,Matrix)

For the programmer

The object mapToRNC is a method function.