Introduction to Rational Functions

• Autorzy: Christoph Schwarzweller
• 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

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2012
• Tom: 20
• Numer: 2
• Strony: 181-191

Daty

wydano

2012-12-01

online

2013-02-02

Twórcy

autor

Christoph Schwarzweller

• 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.

Identyfikatory

DOI

10.2478/v10037-012-0021-1