Relative Gröbner and Involutive Bases For Ideals In Quotient Rings

Co-author(s): Amir Hashemi and Matthias Orth

Reference: Mathematics in Computer Science, 15 (2021) 453-482

Description: We introduce the concept of a relative Gröbner basis for ideals in the quotient of a polynomial ring. An algorithm for the computation is given and the corresponding syzygy theory is developed. Then we provide a relative version of involutive bases and an algorithm for them. Finally, for the case of relative Pommaret bases, the new notion of a relative quasi-stable ideal is introduced and used for the deterministic construction of coordinates such that a finite relative Pommaret basis exists.

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