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You can do the following:

R.ideal([f.reduce(J) for f in I.gens()])

That is basically what singular does: reduce the generators of I w.r.t. J.

You can do the following:

R.ideal([f.reduce(J) R.ideal([f.reduce(J.groebner_basis()) for f in I.gens()])

That is basically what singular does: reduce the generators of I w.r.t. J.