Ebook: Algebra, Geometry and Software Systems

The book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, GrÖ"obner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volumes other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

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The book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gr?"obner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volumes other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

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The book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gr?"obner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volumes other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.
Content:
Front Matter....Pages I-XIII
Beneath-and-Beyond Revisited....Pages 1-21
Some Algorithmic Problems in Polytope Theory....Pages 23-47
Computing Triangulations Using Oriented Matroids....Pages 49-75
Discrete Geometry for Algebraic Elimination....Pages 77-91
Sparse Resultant Perturbations....Pages 93-107
Numerical Irreducible Decomposition Using PHCpack....Pages 109-129
Generating Kummer Type Formulas for Hypergeometric Functions....Pages 131-145
A Computer Algebra System: Risa/Asir....Pages 147-162
Singular in a Framework for Polynomial Computations....Pages 163-176
Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms....Pages 177-206
The Geometry of ? n is Important for the Algebra of Elementary Functions....Pages 207-224
A Visual Introduction to Cubic Surfaces Using the Computer Software Spicy ....Pages 225-238
A Client-Server System for the Visualisation of Algebraic Surfaces on the Web....Pages 239-253
Visualizing Maple Plots with JavaViewLib....Pages 255-275
Automated Generation of Diagrams with Maple and Java....Pages 277-287
Interactive Mathematical Documents on the Web....Pages 289-307
Distributed Computing for Conglomerate Mathematical Systems....Pages 309-325
Back Matter....Pages 327-331

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The book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gr?"obner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volumes other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.
Content:
Front Matter....Pages I-XIII
Beneath-and-Beyond Revisited....Pages 1-21
Some Algorithmic Problems in Polytope Theory....Pages 23-47
Computing Triangulations Using Oriented Matroids....Pages 49-75
Discrete Geometry for Algebraic Elimination....Pages 77-91
Sparse Resultant Perturbations....Pages 93-107
Numerical Irreducible Decomposition Using PHCpack....Pages 109-129
Generating Kummer Type Formulas for Hypergeometric Functions....Pages 131-145
A Computer Algebra System: Risa/Asir....Pages 147-162
Singular in a Framework for Polynomial Computations....Pages 163-176
Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms....Pages 177-206
The Geometry of ? n is Important for the Algebra of Elementary Functions....Pages 207-224
A Visual Introduction to Cubic Surfaces Using the Computer Software Spicy ....Pages 225-238
A Client-Server System for the Visualisation of Algebraic Surfaces on the Web....Pages 239-253
Visualizing Maple Plots with JavaViewLib....Pages 255-275
Automated Generation of Diagrams with Maple and Java....Pages 277-287
Interactive Mathematical Documents on the Web....Pages 289-307
Distributed Computing for Conglomerate Mathematical Systems....Pages 309-325
Back Matter....Pages 327-331
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