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I am interested in computing the "top-degree homogenization of an ideal", the ideal generated by the top-degree homogeneous components of every element in a polynomial ideal $I$.

I had previously been (mistakenly) doing:

ideal([f(list(R.gens()) + [0]) for f in I.homogenize().gens()])

which gives the ideal generated by the top-degree homogeneous components of the given generators of $I$.

This is not the same: consider $I = (x^2 + x, x^2 + y)$. The above code would produce $(x^2)$, but the top-degree homogenization should contain $x-y$ (as the top-degree component of $(x^2+x) - (x^2 + y)$).

Are there known techniques for doing this?

I am interested in computing the "top-degree homogenization of an ideal", the ideal generated by the top-degree homogeneous components of every element in a polynomial ideal $I$.

I had previously been (mistakenly) doing:

ideal([f(list(R.gens()) + [0]) for f in I.homogenize().gens()])
I.homogenize().gens()])