Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree \((1,1)\): algorithms and complexity
The authors analyze the structure of ideals generated by generic bilinear equations. They describe very explicitly the syzygy module of these ideals. They propose a powerful extension of the well-known \(\mathbb{F}_5\) criterion in the case of bilinear systems. Furthermore, using the combinatorics of the syzygy module they derive an explicit, but complicated formula for the Hilbert bi-series. This helps them to understand the complexity analysis of a multihomogeneous variant of the \(F_5\) Algorithm. Finally, they analyze the complexity of computation of Gröbner bases of affine bilinear systems. They prove that the generic bilinear systems are regular, and they give an upper bound for the degree of regularity of these systems.
scientific article; zbMATH DE number 5862849
scientific article