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2012 | 20 | 2 | 181-191
Tytuł artykułu

Introduction to Rational Functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
2
Strony
181-191
Opis fizyczny
Daty
wydano
2012-12-01
online
2013-02-02
Twórcy
  • Institute of Computer Science, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [8] H. Heuser. Lehrbuch der Analysis. B.G. Teubner Stuttgart, 1990.
  • [9] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • [10] Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391-395, 2001.
  • [11] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001.
  • [12] Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339-346, 2001.
  • [13] Michał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3-11, 1991.
  • [14] Michał Muzalewski and Lesław W. Szczerba. Construction of finite sequences over ring and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):97-104, 1991.
  • [15] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [16] Christoph Schwarzweller and Agnieszka Rowinska-Schwarzweller. Schur’s theorem on the stability of networks. Formalized Mathematics, 14(4):135-142, 2006, doi:10.2478/v10037-006-0017-9.[Crossref]
  • [17] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [18] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • [19] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [20] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. FormalizedMathematics, 2(1):41-47, 1991.
  • [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [22] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [23] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0021-1
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