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Applications of Computer Algebra

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Applications of Computer Algebra 22nd Conference on Applications of Computer Algebra ACA 2016 Kassel (Germany) st th August 1 – 4 Chairs Wolfram Koepf and Werner Seiler (general) Georg Regensburger Winfried Neun Michael Wester (program) Advisory Committee: Eugenio Roanes-Lozano Stanly Steinberg Michael Wester Contact: [email protected] Deadline for submissions: March 31st, 2016 submission of session proposals May 29th, 2016 submission of talks Notification of acceptance: 1 July 13th, 2016 http://www.mathematik.uni-kassel.de/ACA2016 Contents Sponsors vi Schedule vii Plenary Talks 1 Computer Algebra Systems and the Lambert W Function D. Jeffrey .........................................2 Real Problems over the Reals: From Complete Elimination Procedures to Subtropical Decisions T. Sturm .........................................2 Exploring a Homotopy Approach to the Science of Data: Huge Scenarios, Topological Scintigraphy and Flagellate Structures P. Real ..........................................2 Sponsor Talks 3 What's New in Mathematica? S. Szurmant ........................................4 What's New in Maple 2016? J. Gerhard ........................................4 S1 Computer Algebra for Modeling in Science and Engineering 5 Application of Computer Algebra System and the Mean-Value Theory for Evaluating Electrostatic Potential and its Associated Field for Nontrivial Configurations H. Sarafian ........................................6 Experimental and Finite Elements Stress Analysis of a Double Edge Notched Specimen A. Bilek, M. Beldi, T. Cherfi, S. Djebali and S. Larbi ................ 12 Modelling and Simulation of Solid Particle Sidementation in an Incompressible Newtonian Fluid S. Zouaoui, H. Djebouri, A. Bilek and K. Mohammedi ................ 18 Interfacing KetCindy and CASs, and its Applications to Scientific Problems Modeling S. Takato, J. A. Vallejo and M. Kaneko ........................ 23 On the Visualization of Random Fibonacci-Padovan Sequences T. Myll¨ari,A. Myll¨ari,A. Anckar and G. H¨ogn¨as .................. 28 Symbolic Contour Integration in Mathematica (Part 2): Some Special Topics to be In- vestigated R. Kragler ......................................... 33 Motion of a Swinging Atwood's Machine: Simulation and Analysis A. N. Prokopenya .................................... 35 Construction of Analytical Solutions to Nonlinear Evolution Equations Using the Gener- alized Differential Operator Method T. Telksnys, Z. Navickas and M. Ragulskis ...................... 40 On Degenerate Central Configurations in the N-Body Problem A. Siluszyk ........................................ 41 i Secular Perturbations in the Two-Planetary Three-Body Problem with the Masses Vary- ing Anisotropically with Different Rates M. Zh. Minglibayev, A. N. Prokopenya, G. M. Mayemerova and Zh. U. Imanova . 46 S2 Computer Algebra in Education 51 Developing Competences in Higher Mathematics in a CAS Supported Learning Environ- ment E. Varbanova and M. Durcheva ............................. 52 Improving mathematical competences by using modern technology J. Weitendorf ....................................... 55 Applications of CAS in the Teaching and Learning of Discrete Mathematics M. Durcheva and E. Varbanova ............................. 59 A Transparent Rule Based CAS to support Formalization of Knowledge R. Oldenburg ....................................... 61 The GUI CATO { how natural usage of CAS with CATO modified the mathematical lectures and the interface itself H.-D. Janetzko ...................................... 64 Collaborative Use of KeTCindy and Free CASs for Making Materials S. Takato, A. McAndrew and M. Kaneko ....................... 69 Visualization of simplex method with Mathematica W. Wojas and J. Krupa ................................. 74 Real-time animated dynamic geometry in the classrooms by using fast Gr¨obner basis computations Z. Kov´acs ......................................... 82 Familiarizing students with definition of Lebesgue integral - examples of calculation di- rectly from its definition using Mathematica W. Wojas and J. Krupa ................................. 86 A framework for an ICT-based study of parametric integrals Th. Dana-Picard and D. Zeitoun ........................... 91 S3 Human-Computer Algebra Interaction 93 MathCheck2: Combining SAT and CAS C. Bright, V. Ganesh, A. Heinle, I. Kotsireas, S. Nejati and K. Czarnecki ..... 94 Conservative conversion between LATEX and TEXmacs J. van der Hoeven and F. Poulain ........................... 96 Math Web Search Interfaces and the Generation Gap of Mathematicians A. Kohlhase ........................................ 114 Collaborative Computer Algebra Shell M. Minimair ....................................... 115 S4 Applied and Computational Algebraic Topology 116 Computing Betti numbers of Veronese subrings with Pommaret bases M. Fetzer ......................................... 117 Some computational elements of fractal topology based on HSF structures C. Alem´an,F. Cappelli and P. Real .......................... 118 An implementation of effective homotopy of fibrations A. Romero, J. Rubio and F. Sergeraert ........................ 119 Motion planning of robot arms with combinatorial restrictions J. Gonz´alez,B. Guti´errez and S. Yuzvinsky ...................... 125 Computing a new topological feature for grey-level 2D digital images: the topological hole tree F. D´ıazdel R´ıo,D. Onchis and P. Real ........................ 126 S5 Difference Computer Algebra and its Applications 127 Bases for Modules of Difference-Operators by Gr¨obnerReduction C. F¨urstand G. Landsmann .............................. 128 ii Difference algebra aided discretization of quasilinear evolution equations V. P. Gerdt, Yu. A. Blinkov and K. B. Marinov ................... 130 Difference Dimension Quasi-polynomials A. Levin .......................................... 134 Gr¨obnerbasis driven construction of a new s-consistent difference approximation to Navier-Stokes equations P. Amodio, Yu.A. Blinkov, V. P. Gerdt and R. La Scala ............... 137 Binomial partial difference ideals C. M. Yuan ........................................ 141 Order Bounds for a Difference Decomposition Algorithm E. Amzallag and R. Gustavson ............................. 144 Maple packages for the analysis of linear systems of partial difference equations and applications D. Robertz ........................................ 145 On Computing Rational Generating Function of a Solution to the Cauchy Problem of Difference Equation A. A. Kytmanov and A. P. Lyapin ........................... 147 Computing difference algebraic relations among solutions of linear differential equations M. Wibmer ........................................ 152 S6 Computer Algebra for Dynamical Systems and Celestial Mechanics 153 A Case Study on the Parametric Occurrence of Multiple Steady States H. Errami, V. Gerdt, D. Grigoriev, M. Koˇsta,O. Radulescu, T. Sturm and A. Weber 154 Quantitative analysis of competition models C. Chiralt, A. Ferragut, A. Gasull and P. Vindel ................... 159 Greedy trajectories of Plancherel processes on two dimensional Young and Schur graphs N. Vasilyev and V. Duzhin ............................... 160 Symbolic Dynamics, Mixing and Entropy in the Three-Body Problem A. Myll¨ari,V. Orlov, A. Chernin and T. Myll¨ari ................... 162 Global dynamics of Planar Quintic Quasi{homogeneous Polynomial Differential Systems Y. Tang .......................................... 165 P4 and desingularization of vector fields in the plane J. C. Artes, P. De Maesschalck, F. Dumortier, C. Herssens and J. Llibre ..... 166 Local invariant sets of analytic vector fields N. Kruff .......................................... 167 Invariant varieties for rational control systems C. Schilli, E. Zerz and V. Levandovskyy ........................ 168 Elementary and Darboux first integrals for planar polynomial vector fields J. Llibre, C. Pantazi and S. Walcher .......................... 169 Limit cycles in planar polynomial systems J. Torregrosa ....................................... 170 A Geometric Approach for Invariant Algebraic Curves in 2D Lotka Volterra Systems I C. J. Christopher and W. M. A. Hussein ....................... 171 A Geometric Approach for Invariant Algebraic Curves in 2D Lotka Volterra Systems II C. J. Christopher and W. M. A. Hussein ....................... 172 A Dynamical Systems Approach to Singularities of Ordinary Differential Equations W. M. Seiler ....................................... 173 Singular Initial Value Problems for Quasi-Linear Ordinary Differential Equations M. Seiß .......................................... 174 S7 Information Services for Mathematical Software, Models, and Research Data 176 Information services for mathematical research data W. Sperber ........................................ 177 The swMATH service for mathematical software - state of the art and perspectives H. Chrapary and W. Neun ................................ 178 iii The SymbolicData Project { a Community Driven Project for the CA Community H.-G. Gr¨abe ........................................ 179 Benchmarks for and Quality Evaluation of CAS A. Heinle ......................................... 184 S8 Algebraic and Algorithmic Aspects of Differential and Integral Operator Session185 Algebraic Theory of Linear Partial Differential Algebraic Equations W. M. Seiler ....................................... 186 Desingularization of First Order Linear Difference Systems with Rational Function Co- efficients M. A. Barkatou and M. Jaroschek ..........................
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