# Singular

#### D.5.4.6 mapToRatNormCurve

Procedure from library `paraplanecurves.lib` (see paraplanecurves_lib).

Usage:
mapToRatNormCurve(f, AI); f polynomial, AI ideal

Assume:
The polynomial f is homogeneous in three variables and absolutely irreducible.
The plane curve C defined by f is rational.
The ideal AI is the adjoint ideal of C.

Return:
ring with an ideal RNC.

Example:
 ```LIB "paraplanecurves.lib"; ring R = 0,(x,y,z),dp; poly f = y^8-x^3*(z+x)^5; ideal adj = adjointIdeal(f); def Rn = mapToRatNormCurve(f,adj); ==> //'mapToRatNorm' created a ring together with an ideal RNC. ==> // Supposing you typed, say, def RPn = mapToRatNorm(f,AI); ==> // you may access the ideal by typing ==> // setring RPn; RNC; setring(Rn); RNC; ==> RNC[1]=y(5)*y(6)-y(4)*y(7) ==> RNC[2]=y(4)*y(6)-y(3)*y(7) ==> RNC[3]=y(2)*y(6)-y(1)*y(7) ==> RNC[4]=y(4)*y(5)-y(2)*y(7) ==> RNC[5]=y(3)*y(5)-y(1)*y(7) ==> RNC[6]=y(1)*y(5)-y(7)^2 ==> RNC[7]=y(4)^2-y(1)*y(7) ==> RNC[8]=y(3)*y(4)-y(1)*y(6) ==> RNC[9]=y(2)*y(4)-y(1)*y(5) ==> RNC[10]=y(1)*y(4)-y(6)*y(7) ==> RNC[11]=y(2)*y(3)-y(6)*y(7) ==> RNC[12]=y(1)*y(3)-y(6)^2 ==> RNC[13]=y(2)^2-y(5)*y(7) ==> RNC[14]=y(1)*y(2)-y(4)*y(7) ==> RNC[15]=y(1)^2-y(3)*y(7) ==> RNC[16]=y(1)*y(6)^2-y(3)^2*y(7) ==> RNC[17]=y(6)^4-y(3)^3*y(7) ```