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Bernstein--Sato ideals might not be linear
Let $F=(f_1,\dots,f_r)$ be a family of nonzero polynomials on $\mathbb C^n$. More than ten years ago, Budur conjectured that $B_F$, the Bernstein--Sato ideal of $F$, is generated by products of linear polynomials with rational coefficients. With the aid of AI, we construct two counterexamples to Bud
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