restart R=QQ[t,x,y,MonomialOrder=>Lex] I=ideal(x^2*y) J=ideal(x*y^2) D=ideal(t)*I+ideal(1-t)*J GB=ideal groebnerBasis D --pick the only element that has no t's IcapJ=ideal(GB_0) --or IcapJ=eliminate(t,D) --or IcapJ=intersect(I,J)