Mathematical Aspects of Computer and Information Sciences

s of Invited Papers Current Challenges in Developing Open Source Computer Algebra Systems Janko Böhm, Wolfram Decker, Simon Keicher and Yue Ren 1 University of Kaiserslautern, 67663 Kaiserslautern, Germany {boehm,decker,ren}@mathematik.uni-kl.de 2 Universidad de Concepción, Casilla 160-C, Concepción, Chile simonkeicher@googlemail.com Abstract. This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Motivated by some of the work done within the Priority Programme SPP 1489 of the German Research Council DFG, we discuss a number of current challenges in the development of Open Source computer algebra systems. The main focus is on algebraic geometry and the system SINGULAR. This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Motivated by some of the work done within the Priority Programme SPP 1489 of the German Research Council DFG, we discuss a number of current challenges in the development of Open Source computer algebra systems. The main focus is on algebraic geometry and the system SINGULAR. The first author acknowledges support from the DFG projects DE 410/8-1 and -2, DE 410/9-1 and -2, and from the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541). The third author was supported partially by the DFG project HA 3094/8-1 and by proyecto FONDECYT postdoctorado no 3160016. Modeling Side-Channel Leakage

[1]  S. Tajima,et al.  Standard bases and algebraic local cohomology for zero dimensional ideals , 2009 .

[2]  Mathias Schulze,et al.  Algorithms for the Gauss-Manin Connection , 2001, J. Symb. Comput..

[3]  Avram Sidi,et al.  Extension of a class of periodizing variable transformations for numerical Integration , 2005, Math. Comput..

[4]  Craig Huneke,et al.  Integral closure of ideals, rings, and modules , 2006 .

[5]  Ian Robinson,et al.  d2lri: a nonadaptive algorithm for two-dimensional cubature , 1999 .

[6]  C. Schwartz,et al.  Numerical integration of analytic functions , 1969 .

[7]  Michael Hill,et al.  Algorithm 816: r2d2lri: an algorithm for automatic two-dimensional cubature , 2002, TOMS.

[8]  Knut Petras,et al.  Principles of verified numerical integration , 2007 .

[9]  Mathias Schulze.  Algorithmic Gauß-Manin Connection , 2002 .

[10]  Masatake Mori,et al.  Double exponential formulas for numerical indefinite integration , 2003 .

[11]  Masaaki Sugihara,et al.  Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration , 2013, Numerische Mathematik.

[12]  Masayuki Noro,et al.  Risa/Asir—a computer algebra system , 1992, ISSAC '92.

[13]  S. Tajima,et al.  Algebraic Local Cohomology Classes Attached to Quasi-Homogeneous Hypersurface Isolated Singularities , 2005 .

[14]  Volker Weispfenning,et al.  Comprehensive Gröbner Bases , 1992, J. Symb. Comput..

[15]  F. Stenger.  Summary of Sinc numerical methods , 2000 .

[16]  S. Tajima,et al.  Algebraic Local Cohomology Classes Attached to Unimodal Singularities , 2012 .

[17]  M. Mori,et al.  The double-exponential transformation in numerical analysis , 2001 .

[18]  Shinichi Tajima,et al.  Annihilating ideals for an algebraic local cohomology class , 2009, J. Symb. Comput..

[19]  Avram Sidi,et al.  A New Variable Transformation for Numerical Integration , 1993 .

[20]  Nicole Fruehauf.  Numerical Methods Based On Sinc And Analytic Functions , 2016 .

[21]  M. C. Eiermann.  Automatic, guaranteed integration of analytic functions , 1989 .

[22]  Akira Suzuki,et al.  A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases , 2006, ISSAC '06.

[23]  Automatic integration over a sphere , 1981 .

[24]  Masao Iri,et al.  On a certain quadrature formula , 1987 .

[25]  Masaaki Sugihara,et al.  Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind , 2010, J. Comput. Appl. Math..