Algebraic aspects of linear differential and difference equations

Algebraic aspects of linear differential and difference equations
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Hendriks, Peter Anne

Algebraic aspects of linear differential and difference equations.
Korte beschrijving: Dit proefschrift behandelt enkele algebraische en algorithmische aspecten van differentiaal-, differentie- en q-dlfferentievergelijkingen. Het grootste gedeelte van dit proefschrift gaat over algoritmes die nagaan of een gegeven tweede orde differentiaal-, differeritie- of g-differentievergelijking elementaire oplossingen heeft en als eventueel resultaat deze oplossingen bepaalt. Dit noemt men het symbolisch oplossen van vergelijkingen Het begrip elementaire oplossing is hierbij zeer precies gedefinieerd. ...

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An Introduction to Computational Combinatorics (Cambridge Computer Science Texts - 9)

An Introduction to Computational Combinatorics (Cambridge Computer Science Texts - 9)
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Page E.S., Wilson L.B.

Product Description
By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.


Book Description
Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.
Product Details

* Paperback: 228 pages
* Publisher: Cambridge University Press (May 31, 1979)
* Language: English
* ISBN-10: 0521294924
* ISBN-13: 978-0521294928

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Algorithmic Algebra (Texts and Monographs in Computer Science)

Algorithmic Algebra (Texts and Monographs in Computer Science)
by: Bhubaneswar Mishra

Details

# Hardcover: 416 pages
# Publisher: Springer; 1 edition (September 29, 1993)
# Language: English
# ISBN-10: 0387940901
# ISBN-13: 978-0387940908

Description

Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

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Algorithms for Computer Algebra

Algorithms for Computer Algebra
by: Keith O. Geddes, Stephen R. Czapor, George Labahn

Details

# Hardcover: 608 pages
# Publisher: Springer; 1 edition (September 30, 1992)
# Language: English
# ISBN-10: 0792392590
# ISBN-13: 978-0792392590

Description

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

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Computational Algebra (Lecture Notes in Pure and Applied Mathematics)

Computational Algebra (Lecture Notes in Pure and Applied Mathematics)
by: Klaus G. Fischer, Philippe Loustaunau, Jay Shapiro, Edward Green, David Farkas

Details

* Publisher: CRC
* Number Of Pages: 272
* Publication Date: 1993-10-18
* ISBN-10 / ASIN: 0824790707
* ISBN-13 / EAN: 9780824790707

Description

Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.

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The Center and Cyclicity Problems: A Computational Algebra Approach

The Center and Cyclicity Problems: A Computational Algebra Approach
by: Valery G. Romanovski, Douglas S. Shafer

Details

* Publisher: Birkhäuser Boston
* Number Of Pages: 330
* Publication Date: 2009-04-16
* ISBN-10 / ASIN: 0817647260
* ISBN-13 / EAN: 9780817647261

Description

In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincaré center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories).

Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The text first lays the groundwork for computational algebra and gives the main properties of ideals in polynomial rings and their affine varieties; this is followed by a discussion regarding the theory of normal forms and stability of differential equations. The center and cyclicity problems are then explored in detail.

The book contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography. Completely self-contained, it is thus suitable mainly as a textbook for a graduate course in the subject but also as a reference for researchers.

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