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2008 | 62 | 1 | 81-90
Tytuł artykułu

Smith normal form of a matrix of generalized polynomials with rational exponents

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.
Rocznik
Tom
62
Numer
1
Strony
81-90
Opis fizyczny
Daty
wydano
2008-01-01
online
2009-02-09
Twórcy
  • Institute of Mathematics, Brno University of Technology, Technická 2, 61669 Brno Czech Republic
  • Institute of Mathematics, Brno University of Technology, Technická 2, 61669 Brno Czech Republic
Bibliografia
  • Brown, W. C., Matrices over Commutative Rings, Marcel Dekker, 1993.[WoS]
  • Cohen, H., Hermite and Smith normal form algorithms over Dedekind domains, Math. Comp. 65 (1996), 1681-1699.
  • Cohn, P. M., On the structure of GL2 of a ring, Publications Mathématiques de l'I. H.É. S. 30 (1966), 5-53.
  • Delzell, C. N., Extension of Pólya's theorems to signomials with rational exponents, Preprint available on
  • Gantmacher, F. R., The Theory of Matrices, Vol. 1, AMS Chelsea Publishing, Providence, RI, 1998.
  • Gillman, L., Henriksen, M., Some remarks about elementary divisor rings, Trans. Am. Math. Soc. 82 (1956), 362-365.
  • Helmer, O., The elementary divisor theorem for certain rings without chain condition, Bull. Am. Math. Soc. 49 (1943), 225-236.
  • Kannan, A., Bachem, A., Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix, SIAM J. Comput. 8 (1979), 499-507.
  • Kaplansky, I., Elementary divisors and modules, Trans. Am. Math. Soc. 66 (1949), 464-491.
  • Karásek, J., Šlapal, J., Polynomials and Generalized Polynomials in Control Theory, (Czech), CERM Academic Publishing Brno, 2007.
  • Kureš, M., On the computation of Smith normal form of a matrix of generalized polynomials with rational exponents, in: Aplimat 2007, Proceedings of the International Conference Aplimat, Bratislava, Slovakia, February 6-9, 2007, Slovak University of Technology, 2007, pp. 103-108.
  • Pascolletti, A.: SmithForm.m, version 1.0 (2005). The Mathematica package available on
  • Suslin, A. A., On the structure of the special linear group over polynomial rings, Math. USSR, Izv. 11 (1977), 221-238.
  • Villard, G., Computation of the Smith normal form of polynomial matrices, in: ISSAC '93, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, Kiev, Ukraine, July 6-8, 1993, ACM Press Baltimore, 1993, pp. 209-217.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10062-008-0010-6
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