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Computations On Polynomials (F.2.1...)
Exact transversal hypergraphs and application to Boolean
Eiter T. Journal of Symbolic Computation 17(3): 215-225, 1994. Type: Article, Reviews: (2 of 2)
A hypergraph is a generalized structure of a graph in which an edge, called a hyperedge, can have more than two vertices. A subset
is said to be a transversal of a given hypergraph if it intersects every (non-empty) set of ver...
Nov 26 2020
The Gröbner cover
Montes A., Springer International Publishing, New York, NY, 2018. 276 pp. Type: Book (978-3-030039-03-5)
The Gröbner basis provides a canonical representation of ordinary polynomial systems. This development allowed computers to solve polynomial equations across mathematics, engineering, and other sciences; however, the ability to tackle polynom...
Dec 20 2019
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 wish more were publ...
Oct 10 2018
Computing highly oscillatory integrals
Deaño A., Huybrechs D., Iserles A., SIAM-Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017. 190 pp. Type: Book (978-1-611975-11-6)
Even though the numerical computation of integrals is a topic that has been investigated for many centuries, current textbooks have failed to describe certain facets in detail. One of these missing areas is the special case of when the integrand o...
Jul 10 2018
Some new results on permutation polynomials over finite fields
Ma J., Zhang T., Feng T., Ge G. Designs, Codes and Cryptography 83(2): 425-443, 2017. Type: Article
A permutation polynomial (PP) over a finite field
is a polynomial over
onto itself, that is, permutes the elements of
Jun 28 2017
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 polynomials
Jan 13 2017
On the Newton bivariate polynomial interpolation with applications
Varsamis D., Karampetakis N. Multidimensional Systems and Signal Processing 25(1): 179-209, 2014. Type: Article
Readers interested in numerical methods and systems theory will find a significant contribution to bivariate interpolation in this paper....
Jun 13 2014
Deciding polynomial-transcendental problems
McCallum S., Weispfenning V. Journal of Symbolic Computation 47(1): 16-31, 2012. Type: Article
The theory of quantifier elimination over real closed fields goes back to Tarski , though practical methods had to wait for Collins in 1975 . Given a formula
May 14 2013
Deterministic extraction from weak random sources
Gabizon A., Springer-Verlag New York, Inc., New York, NY, 2010. 148 pp. Type: Book (978-3-642149-02-3)
Before sketching important elements of this book, it may be useful to potential readers for me to make a few general observations. This monograph is in the European Association for Theoretical Computer Science (EATCS) monograph series. It is an ed...
Nov 17 2011
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
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