{"title":"稀疏多项式的快速并行多点求值","authors":"M. Monagan, Alan Wong","doi":"10.1145/3096730.3096732","DOIUrl":null,"url":null,"abstract":"In [3] the following polynomial evaluation problem arises. Let <i>A</i> be a sparse polynomial with <i>s</i> terms in <i>Z<sup>p</sup></i>[<i>x<sup>0</sup>,x<sup>1</sup>,...,x<sup>n</sup></i>]. Suppose we seek evaluations of <i>A</i> into <i>t</i> bivariate images in <i>Z<sup>p</sup></i>[<i>x<sup>0</sup>,x<sup>1</sup></i>], for some <i>t</i> ≪ <i>s</i>. We do not know <i>a priori</i> the exact number of images <i>t</i> needed. This will be determined by using a trial value <i>T</i> for <i>t</i>, and increasing <i>T</i> as required.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"16 1","pages":"12-14"},"PeriodicalIF":0.0000,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Fast parallel multi-point evaluation of sparse polynomials\",\"authors\":\"M. Monagan, Alan Wong\",\"doi\":\"10.1145/3096730.3096732\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In [3] the following polynomial evaluation problem arises. Let <i>A</i> be a sparse polynomial with <i>s</i> terms in <i>Z<sup>p</sup></i>[<i>x<sup>0</sup>,x<sup>1</sup>,...,x<sup>n</sup></i>]. Suppose we seek evaluations of <i>A</i> into <i>t</i> bivariate images in <i>Z<sup>p</sup></i>[<i>x<sup>0</sup>,x<sup>1</sup></i>], for some <i>t</i> ≪ <i>s</i>. We do not know <i>a priori</i> the exact number of images <i>t</i> needed. This will be determined by using a trial value <i>T</i> for <i>t</i>, and increasing <i>T</i> as required.\",\"PeriodicalId\":7093,\"journal\":{\"name\":\"ACM Commun. Comput. Algebra\",\"volume\":\"16 1\",\"pages\":\"12-14\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Commun. Comput. Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3096730.3096732\",\"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/10.1145/3096730.3096732","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fast parallel multi-point evaluation of sparse polynomials
In [3] the following polynomial evaluation problem arises. Let A be a sparse polynomial with s terms in Zp[x0,x1,...,xn]. Suppose we seek evaluations of A into t bivariate images in Zp[x0,x1], for some t ≪ s. We do not know a priori the exact number of images t needed. This will be determined by using a trial value T for t, and increasing T as required.
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