書誌事項
- タイトル別名
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- Comprehensive structural Gröbner basis detection (Computer Algebra : Foundations and Applications)
- パラメータを伴ったGrobner基底の構造的な検出について
- パラメータ オ トモナッタ Grobner キテイ ノ コウゾウテキ ナ ケンシュツ ニ ツイテ
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抄録
In this talk, we introduce a method to find a term order such that the given F, a set of polynomials with parameters is a Gröbner basis for the ideal〈F〉.This problem without parameters is called the Gröbner basis detection (GBD) and there is also its simpler problem called the structural Gröbner basis detection (SGBD). GBD can be solved by the equivalent classes of term orders computed by the affine Newton polyhedron of F, and SGBD can be reduced to the maximum matching problem of bipartite graph and linear-inequality feasibility problem. Especially for SGBD with parameters, our method divides the parameter space comprehensively, and then solves each SGBD without parameters. Moreover, we also introduce some improvements using affine Newton polyhedron and comprehensive Gröbner system over modules.
収録刊行物
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- 数理解析研究所講究録
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数理解析研究所講究録 2224 79-94, 2022-06
京都大学数理解析研究所
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詳細情報 詳細情報について
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- CRID
- 1050576966671363712
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- NII書誌ID
- AN00061013
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- HANDLE
- 2433/279674
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- NDL書誌ID
- 032427804
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- ISSN
- 18802818
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- 本文言語コード
- ja
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
- NDL