{"title":"Buchberger算法和交错线性基","authors":"Rudiger Gebauer","doi":"10.1145/32439.32482","DOIUrl":null,"url":null,"abstract":"The most time consuming part is the S-polynomial reduction. Consequently Buchbergcr developed criteria for predicting that certain reductions lead to the zero polynomial, hence allowing the elimination of these reductions [Bu79]. A new interpretation of these criteria and an efficient implcmcntation of them is given in [GM861 and installed in Reduce 3.2 and in Scratchpad II. However there arc still many instances of s~~pcrfluous zero reductions not covered by these criteria.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"36","resultStr":"{\"title\":\"Buchberger's algorithm and staggered linear bases\",\"authors\":\"Rudiger Gebauer\",\"doi\":\"10.1145/32439.32482\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The most time consuming part is the S-polynomial reduction. Consequently Buchbergcr developed criteria for predicting that certain reductions lead to the zero polynomial, hence allowing the elimination of these reductions [Bu79]. A new interpretation of these criteria and an efficient implcmcntation of them is given in [GM861 and installed in Reduce 3.2 and in Scratchpad II. However there arc still many instances of s~~pcrfluous zero reductions not covered by these criteria.\",\"PeriodicalId\":314618,\"journal\":{\"name\":\"Symposium on Symbolic and Algebraic Manipulation\",\"volume\":\"28 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"36\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symposium on Symbolic and Algebraic Manipulation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/32439.32482\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Symbolic and Algebraic Manipulation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/32439.32482","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The most time consuming part is the S-polynomial reduction. Consequently Buchbergcr developed criteria for predicting that certain reductions lead to the zero polynomial, hence allowing the elimination of these reductions [Bu79]. A new interpretation of these criteria and an efficient implcmcntation of them is given in [GM861 and installed in Reduce 3.2 and in Scratchpad II. However there arc still many instances of s~~pcrfluous zero reductions not covered by these criteria.
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