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Try:

ideal(*J)

This is standard python syntax: f(*[a1,a2,a3]) does the same thing as f(a1,a2,a3).

Try:

ideal(*J)

This is standard python syntax: f(*[a1,a2,a3]) does the same thing as f(a1,a2,a3).

Incidentally, I think you've hidden some of the commands. The code you suggest should produce:

sage: J.groebner_basis()
AttributeError: 'set' object has no attribute 'groebner_basis'

Finally, it seems you want to compute a Groebner basis of an ideal in a quotient ring. There is no such thing! Groebner bases are for ideals of polynomial rings. You should take the inverse image of that ideal in the polynomial ring (that's easy to do: just lift the generators and add the generators of the quotienting ideal to it) and compute a Groebner basis of that.