Singular

D.8.7.3 getRelations

Usage:

getRelations(p,D,C); list p, int D, bigint C

Return:

list K: a list of ideals; the ideals contain homogeneous polynomial relations of degree <=D between the components of the point p

Note:

This procedure uses only the images of the one point p under the Veronese embeddings to find homogeneous polynomial relations.

LIB "recover.lib";
ring r=(complex,50),(x,y,z),dp;
list p=1,-1,0.5;
getRelations(p,2,10000);
==> [1]:
==>    _[1]=x+y
==>    _[2]=x-2*z
==> [2]:
==>    _[1]=xz+yz
==>    _[2]=xy+y2
==>    _[3]=x2-y2
==>    _[4]=-xy-xz+yz
==>    _[5]=-xz+2*z2