Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

The Evaluation of Polynomials


Robert Milewski
University of Bialystok

MML Identifier: POLYNOM4

The terminology and notation used in this paper have been introduced in the following articles [18] [25] [19] [1] [20] [26] [5] [6] [4] [2] [7] [24] [22] [9] [8] [14] [15] [16] [21] [10] [12] [27] [3] [23] [17] [13] [11]

Contents (PDF format)

  1. Preliminaries
  2. About Polynomials
  3. Leading Monomials
  4. Evaluation of Polynomials
  5. Evaluation Homomorphism

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[8] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[9] Jaroslaw Kotowicz. Functions and finite sequences of real numbers. Journal of Formalized Mathematics, 5, 1993.
[10] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[11] Robert Milewski. The ring of polynomials. Journal of Formalized Mathematics, 12, 2000.
[12] Michal Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Journal of Formalized Mathematics, 2, 1990.
[13] Michal Muzalewski and Leslaw W. Szczerba. Construction of finite sequence over ring and left-, right-, and bi-modules over a ring. Journal of Formalized Mathematics, 2, 1990.
[14] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[15] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[16] Jan Popiolek. Real normed space. Journal of Formalized Mathematics, 2, 1990.
[17] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Journal of Formalized Mathematics, 11, 1999.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[20] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.
[21] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[22] Wojciech A. Trybulec. Binary operations on finite sequences. Journal of Formalized Mathematics, 2, 1990.
[23] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[24] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[25] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[26] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[27] Katarzyna Zawadzka. Sum and product of finite sequences of elements of a field. Journal of Formalized Mathematics, 4, 1992.

Received June 7, 2000


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