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Computations On Polynomials (F.2.1...)
What can (and can’t) we do with sparse polynomials?
Roche D. ISSAC 2018 (Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, New York, NY, Jul 16-19, 2018) 25-30, 2018. Type: Proceedings
This is the paper version of Roche’s ISSAC 2018 tutorial, which serves as an update to my work . It is an excellent tutorial, written in a clear and accessible style. ISSAC is to be commended for these tutorials, and I wis...
Oct 10 2018
A new faster algorithm for factoring skew polynomials over finite fields
Caruso X., Le Borgne J. Journal of Symbolic Computation 79, Part 2, 411-443, 2017. Type: Article
be a finite field of characteristic
, and let σ be an automorphism of
. The ring of skew...
Jan 13 2017
Local Bernstein-Sato ideals: algorithm and examples
Bahloul R., Oaku T. Journal of Symbolic Computation 45(1): 46-59, 2010. Type: Article
For a single polynomial
(in several variables), we can define the Bernstein-Sato polynomial
as the least-degree, monic polynomial, such that there exists a differential operator
Feb 9 2010
Artin automorphisms, cyclotomic function fields, and folded list-decodable codes
Guruswami V. STOC 2009 (Proceedings of the 41st Annual ACM Symposium on Theory of Computing, Bethesda, MD, May 31-Jun 2, 2009) 23-32, 2009. Type: Proceedings
Guruswami and several collaborators have developed the idea of list decoding of linear codes, focusing on folded Reed-Solomon codes. “Folded” means that one regards a sequence of
symbols, from t...
Aug 18 2009
Algorithm for defining the distribution of zeros of random polynomials
Shmerling E. Computers (Proceedings of the 11th WSEAS International Conference on Computers, Agios Nikolaos, Crete Island, Greece, Jul 26-28, 2007) 659-662, 2007. Type: Proceedings
be a random polynomial of degree
; namely, the
coefficients are random variables, not necessarily independent. Let
May 20 2008
The Berlekamp-Massey algorithm revisited
Atti N., Diaz–Toca G., Lombardi H. Applicable Algebra in Engineering, Communication and Computing 17(1): 75-82, 2006. Type: Article
The authors of this paper “propose a slight modification of the Berlekamp-Massey algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence.”...
Jan 22 2008
Complexity of real root isolation using continued fractions
Sharma V. Symbolic and algebraic computation (Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, Waterloo, Ontario, Canada, 339-346, 2007. Type: Proceedings
Sharma’s algorithm for finding the list of isolating intervals for the roots of a square-free polynomial (with real coefficients) uses a Möbius transformation, which in turn can be associated with a finite continued ...
Oct 10 2007
Numerical polynomial algebra
Stetter H., Society for Industrial & Applied Mathematics, 2004. Type: Book (9780898715576)
This book offers an interesting approach, combining numerical analysis and polynomial algebra. The emphasis is on multivariate polynomial systems arising in problems from scientific computing, and their solution with methods adopted fr...
Oct 18 2004
Asymptotics of the best constant in a certain Markov-type inequality
Dörfler P. Journal of Approximation Theory 114(1): 84-97, 2002. Type: Article
This is an interesting and well-written paper on a highly theoretical subject: deriving an estimate for
, which is defined as follows:
Mar 6 2003
When are two numerical polynomials relatively prime?
Beckermann B., Labahn G. Journal of Symbolic Computation 26(6): 677-689, 1998. Type: Article
The authors discuss testing the relative primality of twopolynomials that are given with inexact coefficients or, in other words,testing whether two polynomials will always remain relatively prime (orcoprime) even if their coefficients...
Jul 1 1999
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