Algebra, Geometry and Software Systems

In many fields of modern mathematics specialised scientific software becomes increasingly important. Hence, tremendous effort is taken by numerous groups all over the world to develop appropriate solutions.
This 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, Gröbner 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 volume's 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 framework for modular systems.

Beneath-and-Beyond Revisited.- Some Algorithmic Problems in Polytope Theory.- Computing Triangulations Using Oriented Matroids.- Discrete Geometry for Algebraic Elimination.- Sparse Resultant Perturbations.- Numerical Irreducible Decomposition Using PHCpack.- Generating Kummer Type Formulas for Hypergeometric Functions.- A Computer Algebra System: Risa / Asir.- Singular in a Framework for Polynomial Computations.- Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms.- The Geometry of ?n is Important for the Algebra of Elementary Functions.- A Visual Introduction to Cubic Surfaces Using the Computer Software Spicy.- A Client-Server System for the Visualisation of Algebraic Surfaces on the Web.- Visualizing Maple Plots with JavaViewLib.- Automated Generation of Diagrams with Maple and Java.- Interactive Mathematical Documents on the Web.- Distributed Computing for Conglomerate Mathematical Systems.- Software Systems.