Degree Upper Bounds for Involutive Bases

Co-author(s): Amir Hashemi and Hossein Parnian

Reference: Mathematics in Computer Science, 15 (2021) 233-254

Description: We show that the maximal degree of a Pommaret basis can be bounded by the same doubly exponential bound as that of a general Gröbner basis. For Janet bases one obtains the same bound only in generic position (we explicitly characterise two such positions), in "bad" positions the bound is worse. We exhibit an explicit example demonstrating that the degree of a Janet basis can be arbitrarily higher than that of a Pommaret basis.

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