Conditional GrÖbner Basis: GrÖbner Basis Detection with Parameters

For a given finite polynomial set, finding a monomial order such that the given set is already a GrÖbner basis for the ideal generated by the given set with respect to the found monomial order is called GrÖbner basis detection (GBD) problem and there is also its simpler version, called structural Gr...

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Bibliographic Details
Published in:ACM communications in computer algebra 2023-12, Vol.57 (3), p.160-164
Main Authors: Nagasaka, Kosaku, Oshimatani, Ryo
Format: Article
Language:English
Subjects:
Computing methodologies
Computing methodologies / Symbolic and algebraic manipulation
Computing methodologies / Symbolic and algebraic manipulation / Symbolic and algebraic algorithms
Computing methodologies / Symbolic and algebraic manipulation / Symbolic and algebraic algorithms / Algebraic algorithms
Mathematics of computing
Mathematics of computing / Mathematical analysis
Mathematics of computing / Mathematical analysis / Numerical analysis
Mathematics of computing / Mathematical analysis / Numerical analysis / Computations on polynomials
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Summary:For a given finite polynomial set, finding a monomial order such that the given set is already a GrÖbner basis for the ideal generated by the given set with respect to the found monomial order is called GrÖbner basis detection (GBD) problem and there is also its simpler version, called structural GrÖbner basis detection (SGBD) problem. In this short communication, we give algorithms to solve these problems for polynomials with parameters on their coefficients.
ISSN:1932-2240
1932-2240
DOI:10.1145/3637529.3637540