2.4.8 Module intersection 1

Lemma 2..20   Let $(F) \subseteq R$ and $(G) \subseteq R$.
Then $std((F) \cap (G))=std(y(F)+(1-y)(G)) \cap R$ in R[y].

Remark 2..21   For $std(H) \cap R$ use lemma 2.7.

SINGULAR example:

ring r1 = 32003,(x,y,z),(c,ds);
poly s1=x2y3+45x6y3+68x4z5+80y6x8;
poly s2=6x5+3y6+8z6;
poly s3=12xyz3+2y3z6;
ideal i1=s1,s2,s3;
ideal i2=s1+s2,s2,s1;
intersect(i1,i2);