{"title":"F[x, y]的Gröbner理想基的快速计算","authors":"Yindong Chen, Yao Lu, Peizhong Lu","doi":"10.1109/ISIT.2009.5205791","DOIUrl":null,"url":null,"abstract":"This paper provides a fast algorithm for Gröbner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing of a Gröbner bases of the ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. Although the complexity of the algorithm is hard to evaluated, it obviously has a great improvement from Buchberger's Algorithm.","PeriodicalId":412925,"journal":{"name":"2009 IEEE International Symposium on Information Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast computation of Gröbner bases of ideals of F[x, y]\",\"authors\":\"Yindong Chen, Yao Lu, Peizhong Lu\",\"doi\":\"10.1109/ISIT.2009.5205791\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper provides a fast algorithm for Gröbner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing of a Gröbner bases of the ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. Although the complexity of the algorithm is hard to evaluated, it obviously has a great improvement from Buchberger's Algorithm.\",\"PeriodicalId\":412925,\"journal\":{\"name\":\"2009 IEEE International Symposium on Information Theory\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 IEEE International Symposium on Information Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2009.5205791\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2009.5205791","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fast computation of Gröbner bases of ideals of F[x, y]
This paper provides a fast algorithm for Gröbner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing of a Gröbner bases of the ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. Although the complexity of the algorithm is hard to evaluated, it obviously has a great improvement from Buchberger's Algorithm.
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