## Mathematical Software - ICMS 2006: Second International Congress on Mathematical Software, Castro Urdiales, Spain, September 1-3, 2006, ProceedingsAndres Iglesias, Nobuki Takayama 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. |

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### Contents

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

Efficient Implementation of Polynomial Arithmetic in a MultipleLevel Programming Environment | 12 |

Development of a Maple Macro Package Suitable for Drawing Fine TEXPictures | 24 |

MatlabBased ProblemSolving Environment for Geometric Processing of Surfaces | 35 |

A Mathematica Notebook for Computing the Homology of Iterated Products of Groups | 47 |

GCLC A Tool for Constructive Euclidean Geometry and More Than That | 58 |

jReality jtem and Oorange A Way to Do Math with Computers | 74 |

MuPADs Graphics System | 86 |

PrimalDual Enumeration for Multiparametric Linear Programming | 248 |

A Parallel Asynchronous Method for DerivativeFree Nonlinear Programs | 260 |

Convergent SDPRelaxations for Polynomial Optimization with Sparsity | 263 |

Algorithm and Software for Integration over a Convex Polyhedron | 273 |

A Matlab Implementation of an Algorithm for Computing Integrals of Products of Bessel Functions | 284 |

Computation of the Real Zeros of the Kummer Function Macx | 296 |

Towards Reliable Software for the Evaluation of a Class of Special Functions | 308 |

An Implementation of a Mathematics Learning Framework | 320 |

An Efficient Implementation for Computing Gröbner Bases over Algebraic Number Fields | 99 |

Tree Checking for Sparse Complexes | 110 |

Some Algorithms in Real Algebraic Geometry | 122 |

Algebraic Computation of Some Intersection DModules | 132 |

Past Present and Future | 144 |

Development of NZMATH | 158 |

Recent Developments | 170 |

Balancing a Knapsack | 182 |

Robust HGCD with No Backup Steps | 194 |

The Design of CoCoALib | 205 |

Generation of Oriented Matroids Using Satisfiability Solvers | 216 |

Flexible Object Hierarchies in Polymake Extended Abstract | 219 |

A Presentation of the Gfan Software | 222 |

Parallel Homotopy Algorithms to Solve Polynomial Systems | 225 |

DEpthLAUNAY | 235 |

A Software Framework for Parametrizing Specialized LP Problems | 245 |

Methods to Access and Retrieve Mathematical Content in ActiveMath | 331 |

Logiweb A System for Web Publication of Mathematics | 343 |

Interfacing with the Numerical Homotopy Algorithms in PHCpack | 354 |

Computational Construction of a Maximum Equilateral Triangle Inscribed in an Origami | 361 |

A System for Interfacing MATLAB with External Software Geared Toward Automatic Differentiation | 373 |

Portable and Distributable Collection of Mathematical Software and Free Documents | 385 |

Stability of Parametric Decomposition | 391 |

On the GAP Package sgpviz | 403 |

Making Research on Symmetric Functions with MuPADCombinat | 407 |

Exhaustive and Heuristic Searches | 419 |

An Interactive User Interface for Division Algorithms and the Buchberger Algorithm | 423 |

Experiment of Multithreading Symbolic and Algebraic Computations with OpenMP | 426 |

Links to Projects Mathematical Software icms2006Developers Meeting | 438 |

451 | |

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ActiveMath algebraic number algorithm applications bases Berlin Heidelberg 2006 Buchberger algorithm called CoCoALib coeﬃcients computer algebra system constraints construction continued fraction curves decomposition deﬁned deﬁnition diﬀerent diﬀerential eﬀective eﬃcient elements equations example facet complex ﬁelds ﬁgures ﬁle ﬁnd ﬁnite ﬁrst function G–algebras gclc geometry Gr¨obner basis graphical homotopy ICMS Iglesias implementation incomplete Gamma function inequalities input integral interactive interface irreducible KASH KETpic Kostka polynomials language Lemma linear LNCS Logiweb Maple Math mathematical Matlab matrix method minimal polynomial module monomial multiple MuPAD nilpotent nilpotent orbits number ﬁelds number theory NZMATH objects oﬀers OMDoc OpenMath OpenMP optimization oriented matroids origami package parallel parameters PHCpack polynomial systems polytope problem proof queries recursive representation ring satisﬁes Scientiﬁc sequence solution solving speciﬁc Springer-Verlag Berlin Heidelberg square-free stable structure Takayama Eds theorem University of Cantabria values variables vector