Linear recurrences with polynomial coefficients and application to integer factorization and Cartier-Manin operator

被引：52

作者：

Bostan, Alin ^{[1
]}

Gaudry, Pierrick ^{[1
]}

Schost, Eric ^{[1
]}

机构：

[1] Ecole Polytech, Lab Informat LIX, F-91128 Palaiseau, France

来源：

SIAM JOURNAL ON COMPUTING | 2007年 / 36卷 / 06期

关键词：

linear recurrences; factorization; Cartier-Manin operator;

D O I：

10.1137/S0097539704443793

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. As applications, we improve the best currently known upper bounds for factoring integers deterministically and for computing the Cartier-Manin operator of hyperelliptic curves.

引用

页码：1777 / 1806

页数：30

共 11 条

[1] Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves
Bostan, A
Gaudry, P
Schost, É
FINITE FIELDS AND APPLICATIONS, 2004, 2948 : 40 - 58
[2] Linear recurrences with polynomial coefficients
Bronstein, M
Solé, P
JOURNAL OF COMPLEXITY, 2004, 20 (2-3) : 171 - 181
[3] HYPERGEOMETRIC SOLUTIONS OF LINEAR RECURRENCES WITH POLYNOMIAL COEFFICIENTS
PETKOVSEK, M
JOURNAL OF SYMBOLIC COMPUTATION, 1992, 14 (2-3) : 243 - 264
[4] Integral zeros of a polynomial with linear recurrences as coefficients
Fuchs, Clemens
Heintze, Sebastian
INDAGATIONES MATHEMATICAE-NEW SERIES, 2021, 32 (03): : 691 - 703
[5] Splitting a Linear System of Operator Equations with Constant Coefficients: A Matrix Polynomial Approach
Shayanfar, Nikta
Hadizadeh, Mahmoud
FILOMAT, 2013, 27 (08) : 1447 - 1454
[6] The regularized trace of a linear ordinary differential operator with polynomial coefficients on l 2(-∞, +∞)
Mikhaskiv D.N.
Journal of Mathematical Sciences, 2007, 147 (1) : 6447 - 6453
[7] The factorial-basis method for finding definite-sum solutions of linear recurrences with polynomial coefficients
Jimenez-Pastor, Antonio
Petkovsek, Marko
JOURNAL OF SYMBOLIC COMPUTATION, 2023, 117 : 15 - 50
[8] The regularized trace of an ordinary linear differential operator with polynomial coefficients in L2(-∞, plus ∞)
Mikhaskiv, DN
RUSSIAN MATHEMATICAL SURVEYS, 2005, 60 (02) : 361 - 362
[9] LINEAR-QUADRATIC AND POLYNOMIAL NON-NEGATIVE MATRIX FACTORIZATION; APPLICATION TO SPECTRAL UNMIXING
Meganem, Ines
Deville, Yannick
Hosseini, Shahram
Deliot, Philippe
Briottet, Xavier
Duarte, Leonardo T.
19TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO-2011), 2011, : 1859 - 1863
[10] GENERALIZED LAPLACIAN TRANSFORMATION FOR SPECIAL DIFFERENTIATION RINGS WITH APPLICATION TO LINEAR-DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS
PANKOKE, HJ
MATHEMATISCHE NACHRICHTEN, 1975, 65 : 83 - 104

← 1 2 →