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Computer Algebra and Symbolic Computation: Mathematical Methods [Pehme köide]

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  • Formaat: Paperback / softback, 466 pages, kõrgus x laius: 229x152 mm, kaal: 870 g
  • Ilmumisaeg: 30-Sep-2020
  • Kirjastus: CRC Press
  • ISBN-10: 0367659476
  • ISBN-13: 9780367659479
Teised raamatud teemal:
Computer Algebra and Symbolic Computation: Mathematical MethodsSuurem pilt
  • Formaat: Paperback / softback, 466 pages, kõrgus x laius: 229x152 mm, kaal: 870 g
  • Ilmumisaeg: 30-Sep-2020
  • Kirjastus: CRC Press
  • ISBN-10: 0367659476
  • ISBN-13: 9780367659479
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367659479.html
Märksõnad:
Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial factorization. This book includes complexity analysis of algorithms and other recent developments. It is well-suited for self-study and can be used as the basis for a graduate course. Maintaining the style set by Elementary Algorithms, the author explains mathematical methods as needed while introducing advanced methods to treat complex operations.

Arvustused

" ""There is no doubt that this book is a labour of love. It grew out of the author's lectures on computer algebra . . . and was perfected over the years, as one can see from the careful choice of topics, and the smoothness with which the text flows . . . this is not just a wonderful book to teach from, but one that can be read profitably by any bright undergraduate student."" -S. C. Coutinho, The Mathematical Gazette, July 2004 ""A readable introduction to computer algebra . . . useful to undergraduate students of mathematics and computer science. The text is also accessible to a more general audience interested in computer algebra and its applications."" -EMS Newsletter, June 2004"

Preface ix
1 Background Concepts
1(16)
1.1 Computer Algebra Systems
1(1)
1.2 Mathematical Pseudo-Language (MPL)
2(3)
1.3 Automatic Simplification and Expression Structure
5(6)
1.4 General Polynomial Expressions
11(1)
1.5 Miscellaneous Operators
12(5)
2 Integers, Rational Numbers, And Fields
17(46)
2.1 The Integers
17(20)
2.2 Rational Number Arithmetic
37(7)
2.3 Fields
44(19)
3 Automatic Simplification
63(48)
3.1 The Goal of Automatic Simplification
63(28)
3.2 An Automatic Simplification Algorithm
91(20)
4 Single Variable Polynomials
111(68)
4.1 Elementary Concepts and Polynomial Division
111(15)
4.2 Greatest Common Divisors in F[ x]
126(20)
4.3 Computations in Elementary Algebraic Number Fields
146(20)
4.4 Partial Fraction Expansion in F(x)
166(13)
5 Polynomial Decomposition
179(22)
5.1 Theoretical Background
180(8)
5.2 A Decomposition Algorithm
188(13)
6 Multivariate Polynomials
201(64)
6.1 Multivariate Polynomials and Integral Domains
201(6)
6.2 Polynomial Division and Expansion
207(22)
6.3 Greatest Common Divisors
229(36)
7 The Resultant
265(32)
7.1 The Resultant Concept
265(24)
7.2 Polynomial Relations for Explicit Algebraic Numbers
289(8)
8 Polynomial Simplification With Side Relations
297(52)
8.1 Multiple Division and Reduction
297(21)
8.2 Equivalence, Simplification, and Ideals
318(16)
8.3 A Simplification Algorithm
334(15)
9 Polynomial Factorization
349(82)
9.1 Square-Free Polynomials and Factorization
350(10)
9.2 Irreducible Factorization: The Classical Approach
360(10)
9.3 Factorization in Zp[ x]
370(29)
9.4 Irreducible Factorization: A Modern Approach
399(32)
Bibliography 431(10)
Index 441
Joel S. Cohen