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An Algorithm for Computing Comprehensive Order Basis Systems of Parametric Polynomial Matrices
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DOI：10.1007/s11424-026-4233-9.png)
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Abstract
En 中文
An algorithm for computing parametric order bases for univariate polynomial matrices with parameters is first presented in this paper. Starting from the non-parametric univariate polynomial matrix, the proposed key idea is to construct a special module and module order. Then based on Gröbner basis theory for modules, the authors present that the order basis can be obtained by computing a minimal Gröbner basis for this module under this order. Further, the authors extend the definition of the order basis to the parametric polynomial matrix, and give the concept of comprehensive order basis systems. More importantly, the method based on Gröbner bases for modules can be naturally generalized to the parametric case by means of comprehensive Gröbner systems for modules. As a consequence, the authors design a new algorithm for computing comprehensive order basis systems. The proposed algorithm has been implemented on the computer algebra system Singular and Maple.
Keywords:
Comprehensive Gröbner system
comprehensive order basis system
Gröbner basis
order basis
Journal
IF:
2.8
Papers:
212
Citations:
2.1K
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