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Does this do what you want? GroebnerReduce[L_, order_: Lexicographic] := Module[{G, V}, G = Union[L, SameTest -> (PolynomialMod[MonomialList[#1, order][[1]], MonomialList[#2, order][[1]]] === 0 &)]; V = Union@Flatten@(Variables /@ G); #[[2]] & /@ (PolynomialReduce[#, Complement[G, {#}], V] & /@ G) ]



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