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D.5.2.9 WitSet

Procedure from library numerDecom.lib (see numerDecom_lib).

Usage:
WitSet(ideal I); I ideal

Return:
lists W(0..d) of witness point sets of i-dimensional components of V(J) for i=0,...d respectively, where d the dimension of V(J), L list of generic linear polynomials

Note:
if W(i)=x, then V(J) has no component of dimension i

Example:
 
LIB "numerDecom.lib";
ring r=0,(x,y,z),dp;
poly f1=(x3+z)*(x2-y);
poly f2=(x3+y)*(x2-z);
poly f3=(x3+y)*(x3+z)*(z2-y);
ideal I=f1,f2,f3;
def W=WitSet(I);
setring W;
W(1);
// witness point  set of a pure 1-dimensional component of V(I)
W(0);
// witness point  set of a pure 0-dimensional component of V(I)
L;
// list of generic linear polynomials