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Jan 24, 2023 at 18:38 comment added Michael Schindler Thank you, Max Alekseyev for your answer. Your argument is straightforward and clear. If I take the (consecutive) pairs of equations, I can expand them to polynomials of degree 4 which evaluate to zero. That makes them similar to what I has before. I would expect two sets of equations which encode the same ideal. A close look (and an implementation in sage) however shows me that these compatibility ideals are different. I included also the ideals from John Doyle's answer and found them also to be different. Am I wrong expecting the same compatibility ideals?
Jan 18, 2023 at 2:13 history answered Max Alekseyev CC BY-SA 4.0