{"title":"仿射幂和的多项式等价问题","authors":"Ignacio García-Marco, P. Koiran, Timothée Pecatte","doi":"10.1145/3208976.3208993","DOIUrl":null,"url":null,"abstract":"A sum of affine powers is an expression of the form [f(x1,...,xn) = ∑i=1s αi li(x1,...,xn)ei] where li is an affine form. We propose polynomial time black-box algorithms that find the decomposition with the smallest value of s for an input polynomial f . Our algorithms work in situations where s is small enough compared to the number of variables or to the exponents ei. Although quite simple, this model is a generalization of Waring decomposition. This paper extends previous work on Waring decomposition as well as our work on univariate sums of affine powers (ISSAC'17).","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"102 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Polynomial Equivalence Problems for Sum of Affine Powers\",\"authors\":\"Ignacio García-Marco, P. Koiran, Timothée Pecatte\",\"doi\":\"10.1145/3208976.3208993\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A sum of affine powers is an expression of the form [f(x1,...,xn) = ∑i=1s αi li(x1,...,xn)ei] where li is an affine form. We propose polynomial time black-box algorithms that find the decomposition with the smallest value of s for an input polynomial f . Our algorithms work in situations where s is small enough compared to the number of variables or to the exponents ei. Although quite simple, this model is a generalization of Waring decomposition. This paper extends previous work on Waring decomposition as well as our work on univariate sums of affine powers (ISSAC'17).\",\"PeriodicalId\":105762,\"journal\":{\"name\":\"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"102 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"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/10.1145/3208976.3208993\",\"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/10.1145/3208976.3208993","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Polynomial Equivalence Problems for Sum of Affine Powers
A sum of affine powers is an expression of the form [f(x1,...,xn) = ∑i=1s αi li(x1,...,xn)ei] where li is an affine form. We propose polynomial time black-box algorithms that find the decomposition with the smallest value of s for an input polynomial f . Our algorithms work in situations where s is small enough compared to the number of variables or to the exponents ei. Although quite simple, this model is a generalization of Waring decomposition. This paper extends previous work on Waring decomposition as well as our work on univariate sums of affine powers (ISSAC'17).
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