-- Let I be the ideal generated by G_I={xy+z,yz+x}, and J be the ideal generated by G_J={yz+x, zx+y}.
-- We compute the intersection of I and J as follows.
Use QQ[t,x,y,z];
NC.SetOrdering("ELIM"); -- Choose an elimination word ordering for t
F1 := [[x,y], [z]]; -- xy+z
F2 := [[y,z], [x]]; -- yz+x
G1 := [[y,z], [x]]; -- yz+x
G2 := [[z,x], [y]]; -- zx+y
N:=[NC.Mul([[t]],F1), NC.Mul([[t]],F2)]; -- t*F1, t*F2
N:=Concat(N,[NC.Mul([[1],[-t]],G1), NC.Mul([[1],[-t]],G2)]); -- (1-t)*G1, (1-t)*G2
C:=[[[t,x],[-x,t]], [[t,y],[-y,t]], [[t,z],[-z,t]]]; -- set of commutators
G:=Concat(N,C);
Gb:=NC.GB(G,31,1,20,50);
-- Done.
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The following information printed by the ApCoCoAServer shows that Gb it is a partial Groebner basis.
the number of unselected generators: 0
the number of unselected obstructions: 81
the procedure is interrupted by loop bound!
the total number of obstructions: 293
the number of selected obstructions: 43
the number of obstructions detected by Criterion M: 128
the number of obstructions detected by Criterion F: 0
the number of obstructions detected by Tail Reduction: 0
the number of obstructions detected by Criterion Bk: 41
the number of redundant generators: 5
It is a partial Groebner basis.
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