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Do you mean this?

sage: R.<x,y,z> = GF(127)[]
sage: p = R.random_element(degree=3)
sage: Q = [R.random_element() for _ in range(R.ngens())]
sage: r = p.reduce(Ideal(Q))
sage: M = (p - r).lift(Q)
sage: p -r == sum([M[i]*Q[i] for i in range(len(M))])
True