{"title":"关于充分正则Gröbner基的二元多项式的快速约简","authors":"J. Hoeven, Robin Larrieu","doi":"10.1145/3208976.3209003","DOIUrl":null,"url":null,"abstract":"Let G be the reduced Grö bner basis of a zero-dimensional ideal I ⊆ K[X, Y] of bivariate polynomials over an effective field K. Modulo suitable regularity assumptions on G and suitable precomputations as a function of G , we prove the existence of a quasi-optimal algorithm for the reduction of polynomials in K [X, Y] with respect to G . Applications include fast algorithms for multiplication in the quotient algebra A=K[X, Y] / I and for conversions due to changes of the term ordering.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Fast Reduction of Bivariate Polynomials with Respect to Sufficiently Regular Gröbner Bases\",\"authors\":\"J. Hoeven, Robin Larrieu\",\"doi\":\"10.1145/3208976.3209003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be the reduced Grö bner basis of a zero-dimensional ideal I ⊆ K[X, Y] of bivariate polynomials over an effective field K. Modulo suitable regularity assumptions on G and suitable precomputations as a function of G , we prove the existence of a quasi-optimal algorithm for the reduction of polynomials in K [X, Y] with respect to G . Applications include fast algorithms for multiplication in the quotient algebra A=K[X, Y] / I and for conversions due to changes of the term ordering.\",\"PeriodicalId\":105762,\"journal\":{\"name\":\"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3208976.3209003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3208976.3209003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fast Reduction of Bivariate Polynomials with Respect to Sufficiently Regular Gröbner Bases
Let G be the reduced Grö bner basis of a zero-dimensional ideal I ⊆ K[X, Y] of bivariate polynomials over an effective field K. Modulo suitable regularity assumptions on G and suitable precomputations as a function of G , we prove the existence of a quasi-optimal algorithm for the reduction of polynomials in K [X, Y] with respect to G . Applications include fast algorithms for multiplication in the quotient algebra A=K[X, Y] / I and for conversions due to changes of the term ordering.
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