The Evaluation of Multivariate Polynomials

Christoph Schwarzweller

University of T\"ubingen

Andrzej Trybulec

University of Bialystok

MML Identifier: POLYNOM2

Contents (PDF format)

1. Preliminaries
2. About Finite Sequences and the Functor SgmX
3. Evaluation of Bags
4. Evaluation of Polynomials
5. Evaluation Homomorphism

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[3] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[5] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[9] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[10] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[11] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.

[12] Czeslaw Bylinski. Some properties of restrictions of finite sequences. Journal of Formalized Mathematics, 7, 1995.

[13] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.

[14] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.

[15] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

[16] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.

[17] Beata Madras. On the concept of the triangulation. Journal of Formalized Mathematics, 7, 1995.

[18] Michal Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Journal of Formalized Mathematics, 2, 1990.

[19] Michal Muzalewski and Wojciech Skaba. From loops to abelian multiplicative groups with zero. Journal of Formalized Mathematics, 2, 1990.

[20] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Journal of Formalized Mathematics, 11, 1999.

[21] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[22] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[23] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.

[24] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.

[25] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.

[26] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Journal of Formalized Mathematics, 2, 1990.

[27] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.

[28] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Journal of Formalized Mathematics, 1, 1989.

[29] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[30] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[31] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

[32] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.