It looks as if Sage blindly runs is_homogeneous() - and this is not needed.
Namely, after I get rid of these checks:
-- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
@@ -3025,8 +3025,8 @@ class MPolynomialIdeal_singular_repr(
On Tue, Jul 4, 2023 at 12:26 PM Kwankyu Lee wrote:
>
> Also, as far as I understand, Sage can compute the minimal free resolution of
> the module of syzygies of S, and from the resolution the presentation can be
> assembled.
>
>
> Yes. It's here:
> https://doc.sagemath.org/html/en/reference/resol
