# 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 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)