Modular Algorithms in Symbolic Summation and Symbolic Integration

Jürgen Gerhard

ISBN 10: 3540240616 / ISBN 13: 9783540240617

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2004, 2004

About this Item

Neuware -This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms¿placedintothe limelightbyDonKnuth¿stalkat the 1970ICM ¿provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: ¿I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ¿ Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual ¿input size¿ parameters of computer science seem inadequate, and although some natural ¿geometric¿ parameters have been identi ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 240 pp. Englisch.

Seller Inventory # 9783540240617

Bibliographic Details

• Title: Modular Algorithms in Symbolic Summation and Symbolic Integration
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2004
• Publication Date: 2004
• Language: English
• ISBN 10: 3540240616
• ISBN 13: 9783540240617
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 14D millimeters 235 millimeters width by 155 millimeters height by 14 millimeters depth
• Weight: 371 grams

About this title

Synopsis

This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.