{"title":"关于词典学Gröbner基的w特征集","authors":"Chenqi Mou, Dongming Wang","doi":"10.1145/3338637.3338647","DOIUrl":null,"url":null,"abstract":"The structures of lexicographic (LEX) Gröbner bases were studied first by Lazard [4] for bivariate ideals and then extended to general zero-dimensional multivariate (radical) ideals [3, 6, 2]. Based on the structures of LEX Gröbner bases, algorithms have been proposed to compute triangular decompositions out of LEX Gröbner bases for zero-dimensional ideals [5, 2]. The relationships between LEX Gröbner bases and Ritt characteristic sets were explored in [1] and then made clearer in [8] with the concept of W-characteristic sets.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"41 1","pages":"142-144"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On W-characteristic sets of lexicographic Gröbner bases\",\"authors\":\"Chenqi Mou, Dongming Wang\",\"doi\":\"10.1145/3338637.3338647\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The structures of lexicographic (LEX) Gröbner bases were studied first by Lazard [4] for bivariate ideals and then extended to general zero-dimensional multivariate (radical) ideals [3, 6, 2]. Based on the structures of LEX Gröbner bases, algorithms have been proposed to compute triangular decompositions out of LEX Gröbner bases for zero-dimensional ideals [5, 2]. The relationships between LEX Gröbner bases and Ritt characteristic sets were explored in [1] and then made clearer in [8] with the concept of W-characteristic sets.\",\"PeriodicalId\":7093,\"journal\":{\"name\":\"ACM Commun. Comput. Algebra\",\"volume\":\"41 1\",\"pages\":\"142-144\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Commun. Comput. Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3338637.3338647\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Commun. Comput. Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3338637.3338647","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On W-characteristic sets of lexicographic Gröbner bases
The structures of lexicographic (LEX) Gröbner bases were studied first by Lazard [4] for bivariate ideals and then extended to general zero-dimensional multivariate (radical) ideals [3, 6, 2]. Based on the structures of LEX Gröbner bases, algorithms have been proposed to compute triangular decompositions out of LEX Gröbner bases for zero-dimensional ideals [5, 2]. The relationships between LEX Gröbner bases and Ritt characteristic sets were explored in [1] and then made clearer in [8] with the concept of W-characteristic sets.
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