About the book
This project is intended to outline some recent trends, and to share results in the field of polynomials and applications. Polynomials are a basic field of both classic and modern algebra. They have multiple connections with all mathematical areas. The book covers both scholar and research approaches of this mathematical area.
One basic topic is that of expression manipulation: combining, expanding etc, and the applications of this scholar topic needs focusing on.
The general topic of "polynomials" is very large, and here the focus is both on scholar/student basics of it, and on applications of some special polynomials in science and research.
An important topic of the book is "algebraic curve". Here the approaches are multiple: basic/scholar on one hand, and applications on the other hand. It must be noticed the use of algebraic curves properties in the field of differential equations, for example for finding the singularities.
Grobner basis is a very modern and applied topic of algebra. Here we must outline the great importance of Grobner basis and polynomial ideals manipulation, in the differential equations field, an example being in fast finding normal forms of differential systems.
Related to this last topic of the book, but applying to all specified topics, it must be noticed the importance of numeric algorithms. The importance of software algorithms in all fields of science is continuously increasing. Therefore, computational approach of the specified algebraic topics is very useful, with applications in other mathematical and scientific fields.