MINIMAL GENERATING SETS FOR PARAMETRIC POLYNOMIAL IDEALS

Document Type : Original Manuscript

Author

1- Department of Mathematics, National University of Skills (NUS), Tehran, Iran 2- School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395- 5746, Tehran, Iran

10.22044/jas.2025.15366.1909

Abstract

This paper generalizes Schreyer’s syzygy theorem for polynomial ideals with parametric coefficients. It introduces an algorithm to compute the minimal generating set of homogeneous parametric polynomial ideals that form a Gr¨obner basis with respect to variables. By employing comprehensive Gr¨obner systems, we partition the parameter space into finite subspaces and identify the minimal generating set for each subspace. The algorithms are implemented in Maple, and we illustrate the main algorithm with a simple example.

Keywords

References

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Journal of Algebraic Systems
Volume 14, Issue 4
September 2026
Pages 801-821

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