Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation最新文献_第2页

On Continuity of the Roots of a Parametric Zero Dimensional Multivariate Polynomial Ideal 参数零维多元多项式理想根的连续性

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209004

Yosuke Sato, Ryoya Fukasaku, Hiroshi Sekigawa

引用次数: 6

On Computing the Resultant of Generic Bivariate Polynomials 关于一般二元多项式结式的计算

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209020

G. Villard

{"title":"On Computing the Resultant of Generic Bivariate Polynomials","authors":"G. Villard","doi":"10.1145/3208976.3209020","DOIUrl":"https://doi.org/10.1145/3208976.3209020","url":null,"abstract":"An algorithm is presented for computing the resultant of two generic bivariate polynomials over a field K. For such p and q K[x,y] both of degree d in x and n in y , the algorithm computes the resultant with respect to y using (n2 - 1/ømega d) 1+o(1) arithmetic operations in K, where two n x n matrices are multiplied using O(nømega) operations. Previous algorithms required time (n2 d) 1+o(1). The resultant is the determinant of the Sylvester matrix S(x) of p and q , which is an n x n Toeplitz-like polynomial matrix of degree~ d . We use a blocking technique and exploit the structure of S(x) for reducing the determinant computation to the computation of a matrix fraction description R(x)Q(x)-1 of an m x m submatrix of the inverse S(x)-1, where młl n. We rely on fast algorithms for handling dense polynomial matrices: the fraction description is obtained from an x -adic expansion via matrix fraction reconstruction, and the resultant as the determinant of the denominator matrix. We also describe some extensions of the approach to the computation of generic Gröbner bases and of characteristic polynomials of generic structured matrices and in univariate quotient algebras.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124059463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 22

Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals.: The Case of One Translation 非自反素数微分理想的二元维多项式。:一个翻译的案例

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209008

A. Levin

引用次数: 2

Constructive Arithmetics in Ore Localizations with Enough Commutativity 具有足够交换性的局部化中的构造算法

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209021

Johannes Hoffmann, V. Levandovskyy

引用次数: 2

Volume of Alcoved Polyhedra and Mahler Conjecture 凹形多面体卷与马勒猜想

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3208990

M. J. Puente, Pedro L. Claveria

引用次数: 4

Computing Free Distances of Idempotent Convolutional Codes 幂等卷积码自由距离的计算

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3208985

J. Gómez-Torrecillas, F. J. Lobillo, G. Navarro

引用次数: 3

Fast Reduction of Bivariate Polynomials with Respect to Sufficiently Regular Gröbner Bases 关于充分正则Gröbner基的二元多项式的快速约简

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209003

J. Hoeven, Robin Larrieu

引用次数: 10

On the Complexity of Computing Real Radicals of Polynomial Systems 多项式系统实根计算的复杂性

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209002

M. S. E. Din, Zhi-Hong Yang, L. Zhi

引用次数: 10

Algorithmic Arithmetics with DD-Finite Functions 具有dd有限函数的算法算术

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209009

Antonio Jiménez-Pastor, V. Pillwein

引用次数: 11

A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations 一种基于多项式除法的线性递归关系计算算法

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209017

Jérémy Berthomieu, J. Faugère

{"title":"A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations","authors":"Jérémy Berthomieu, J. Faugère","doi":"10.1145/3208976.3209017","DOIUrl":"https://doi.org/10.1145/3208976.3209017","url":null,"abstract":"Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp--Massey algorithm. Likewise, sparse multivariate polynomial interpolation and multidimensional cyclic code decoding require guessing linear recurrence relations of a multivariate sequence. Several algorithms solve this problem. The so-called Berlekamp--Massey--Sakata algorithm (1988) uses polynomial additions and shifts by a monomial. The Scalar-FGLM algorithm (2015) relies on linear algebra operations on a multi-Hankel matrix, a multivariate generalization of a Hankel matrix. The Artinian Gorenstein border basis algorithm (2017) uses a Gram-Schmidt process. We propose a new algorithm for computing the Gröbner basis of the ideal of relations of a sequence based solely on multivariate polynomial arithmetic. This algorithm allows us to both revisit the Berlekamp--Massey--Sakata algorithm through the use of polynomial divisions and to completely revise the Scalar-FGLM algorithm without linear algebra operations. A key observation in the design of this algorithm is to work on the mirror of the truncated generating series allowing us to use polynomial arithmetic modulo a monomial ideal. It appears to have some similarities with Padé approximants of this mirror polynomial. Finally, we give a partial solution to the transformation of this algorithm into an adaptive one.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123205465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1