Singular

D.6.6.7 HHnormalForm

Usage:

HHnormalForm(I), I=<x(t),y(t)> an ideal, # optional, a bound for the conductor

Compute:

computes the Hefez-Hernandez normal form of the ideal I=<x(t),y(t)>

Return:

a list L with 5 entries
L[1] the Hefei-Hernandez normal form of the ideal I=<x(t),y(t)> L[2] the semi group Gamma
L[3] the semi module Lambda
L[4] 0 if Lambda=Gamma or lambda=min(Lambda-Gamma) -n, the Zariski number L[5] the integers i, i>lambda, i+n not in Lambda, 0 if this set is empty

LIB "classify_aeq.lib";
ring r=0,t,Ds;
ideal I=t6+3t7,t8+t13+t19;
HHnormalForm(I);
==> [1]:
==>    _[1]=t6
==>    _[2]=t8-4t9+425/6t11-823/32t13
==> [2]:
==>    0,6,8,12,14,16,18,20,22,24,25,26,28,30,31,32,33,34,36
==> [3]:
==>    0,6,8,12,14,15,16,18,20
==> [4]:
==>    9
==> [5]:
==>    11,13