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Computer Algebra Handbook Foundations · Applications · Systems

Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec­ ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berli...

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Bibliographic Details
Other Authors: Grabmeier, Johannes (Editor), Kaltofen, Erich (Editor), Weispfenning, Volker (Editor)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2003, 2003
Edition:1st ed. 2003
Subjects:
Computer Science—mathematics
Symbolic And Algebraic Manipulation
Algorithms
Algebra
Computer Software
Mathematical Software
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Development, Characterization, Prospects
  • 1.1 Historical Remarks
  • 1.2 General Characterization
  • 1.3 Impact on Education
  • 1.4 Impact on Research
  • 1.5 Computer Algebra — Today and Tomorrow
  • 2 Topics of Computer Algebra
  • 2.1 Exact Arithmetic
  • 2.2 Algorithms for Polynomials and Power Series
  • 2.3 Linear Algebra
  • 2.4 Constructive Methods of Number Theory
  • 2.5 Algorithms of Commutative Algebra and Algebraic Geometry
  • 2.6 Algorithmic Aspects of the Theory of Algebras
  • 2.7 Computational Group Theory
  • 2.8 Algorithms of Representation Theory
  • 2.9 Algebraic Methods for Constructing Discrete Structures
  • 2.10 Summation and Integration
  • 2.11 Symbohc Methods for DiflFerential Equations
  • 2.12 Symbolic/Numeric Methods
  • 2.13 Algebraic Complexity Theory
  • 2.14 Coding Theory and Cryptography
  • 2.15 Algorithmic Methods inUniversal Algebra and Logic
  • 2.16 Knowledge Representation and Abstract Data Types
  • 2.17 On the Design of Computer Algebra Systems
  • 2.18 Parahel Computer Algebra Systems
  • 2.19 Interfaces and Standardization
  • 2.20 Hardware Implementation of Computer Algebra Algorithms
  • 3 Applications of Computer Algebra
  • 3.1 Physics
  • 3.2 Mathematics
  • 3.3 Computer Science
  • 3.4 Engineering
  • 3.5 Chemistry
  • 3.6 Computer Algebra in Education
  • 4 Computer Algebra Systems
  • 4.1 General Purpose Systems
  • 4.2 Special Purpose Systems
  • 4.3 Packages
  • 5 Meetings and Publications
  • 5.1 Conferences and Proceedings
  • 5.2 Books on Computer Algebra
  • Cited References
  • Index for Authors’ Contributions

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