{"title":"一种快速并行稀疏多项式GCD算法","authors":"Jiaxiong Hu, M. Monagan","doi":"10.1145/2930889.2930903","DOIUrl":null,"url":null,"abstract":"We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to determine the support of the GCD. We have implemented our algorithm in Cilk C. We compare it with Maple and Magma's implementations of Zippel's GCD algorithm.","PeriodicalId":169557,"journal":{"name":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","volume":"529 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"A Fast Parallel Sparse Polynomial GCD Algorithm\",\"authors\":\"Jiaxiong Hu, M. Monagan\",\"doi\":\"10.1145/2930889.2930903\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to determine the support of the GCD. We have implemented our algorithm in Cilk C. We compare it with Maple and Magma's implementations of Zippel's GCD algorithm.\",\"PeriodicalId\":169557,\"journal\":{\"name\":\"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"529 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2930889.2930903\",\"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 ACM on International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2930889.2930903","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to determine the support of the GCD. We have implemented our algorithm in Cilk C. We compare it with Maple and Magma's implementations of Zippel's GCD algorithm.
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