Mathematical Software - ICMS 2006

1. Front Matter

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2. New Developments on Computer Algebra Packages (Andr´es Iglesias, Tetsuo Ida)

   1. A General Computational Scheme for Testing Admissibility of Nilpotent Orbits of Real Lie Groups of Inner Type

      • Alfred G. Noël

      Pages 1-11

   2. Efficient Implementation of Polynomial Arithmetic in a Multiple-Level Programming Environment

      • Xin Li, Marc Moreno Maza

      Pages 12-23

   3. Development of a Maple Macro Package Suitable for Drawing Fine \({\rm\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}\)-Pictures

      • Masayoshi Sekiguchi, Satoshi Yamashita, Setsuo Takato

      Pages 24-34

   4. Matlab-Based Problem-Solving Environment for Geometric Processing of Surfaces

      • A. Gálvez, A. Iglesias

      Pages 35-46

   5. A Mathematica Notebook for Computing the Homology of Iterated Products of Groups

      • V. Álvarez, J. A. Armario, M. D. Frau, P. Real

      Pages 47-57

3. Interfacing Computer Algebra and Mathematical Visualization (Konrad Polthier)

   1. GCLC — A Tool for Constructive Euclidean Geometry and More Than That

      • Predrag Janičić

      Pages 58-73

   2. jReality, jtem, and Oorange — A Way to Do Math with Computers

      • Tim Hoffmann, Markus Schmies

      Pages 74-85

   3. MuPAD’s Graphics System

      • Christopher Creutzig

      Pages 86-98

4. Software for Algebraic Geometry and Related Topics (Nobuki Takayama, Gert-Martin Greuel)

   1. An Efficient Implementation for Computing Gröbner Bases over Algebraic Number Fields

      • Masayuki Noro

      Pages 99-109

   2. Tree Checking for Sparse Complexes

      • Massimo Caboara, Sara Faridi, Peter Selinger

      Pages 110-121

   3. The SARAG Library: Some Algorithms in Real Algebraic Geometry

      • Fabrizio Caruso

      Pages 122-131

   4. Algebraic Computation of Some Intersection D-Modules

      • F. J. Calderón Moreno, L. Narváez Macarro

      Pages 132-143

   5. Plural, a Non–commutative Extension of Singular: Past, Present and Future

      • Viktor Levandovskyy

      Pages 144-157

5. Number Theoretical Software (Ken Nakamula, Michael Pohst)

   1. Development of NZMATH

      • Matsui Tetsushi

      Pages 158-169

   2. KASH: Recent Developments

      • Sebastian Freundt, Aneesh Karve, Anita Krahmann, Sebastian Pauli

      Pages 170-181

6. Methods in Computational Number Theory (David Sevilla, Jaime Gutierrez)

   1. Making Change and Finding Repfigits: Balancing a Knapsack

      • Daniel Lichtblau

      Pages 182-193

   2. Robust HGCD with No Backup Steps

      • Niels Möller

      Pages 194-204

7. Free Software for Computer Algebra (Joris Van Der Hoeven)

   1. The Design of CoCoALib

      • J. Abbott

      Pages 205-215

8. Software for Optimization and Geometric Computation (Komei Fukuda, Michael Joswig)

   1. Generation of Oriented Matroids Using Satisfiability Solvers

      • Lars Schewe

      Pages 216-218

This volume contains the outstanding collection of invited papers and refereed papers selected for the Second International Congress on Mathematical Software, ICMS 2006, held in Castro Urdiales, Spain, September 1-3, 2006. We cordially invite you to visit the ICMS 2006 website http://www.icms2006.unican.es where you can find all relevant information about this interesting event. ICMS 2006 was the second edition of this congress, which follows up the successful ICMS 2002 held in Beijing, China. Since its inception, this congress has been a satellite event of the International Congress of Mathematicians - ICM, the world’s largest conference on mathematics, celebrated every four years since the edition of 1900 in Paris, where David Hilbert presented his 23 famous problems. For the first time, this 2006 edition of ICM is held in Spain (see: http://www.icm2006.org for details), and so is ICMS 2006. This congress was devoted to all aspects of mathematical software, whose appearance is — in our opinion — one of the most important events in mathematics. Mathematical software systems are used to construct examples, to prove theorems, and to find new mathematical phenomena. Conversely, mathematical research often motivates developments of new algorithms and new systems. Beyond mathematics, mathematical software systems are becoming indispensable tools in many branches of science and technology.

• Mathematica
• computer
• computer algebra
• mathematical software
• number theory
• optimization
• visualization
• algorithm analysis and problem complexity

• Department of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain

  Andrés Iglesias

• Faculty of Science Department of Mathematics, Kobe University, Kobe, Japan

  Nobuki Takayama

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