Interaction Between Computer Algebra and Interval Computations

Special Session at
16th International Conference on Applications of Computer Algebra (ACA 2010)
June 24-27, 2010, Vlora, Albania

Session Organizers:

  • Walter Kraemer, Bergische Universitaet, Wuppertal
    email: <>
  • Markus Neher, University of Karlsruhe
    email: <>
  • Evgenija D. Popova, Inst.of Maths & Informatics, Bulgarian Academy of Sciences
    email: <>


For many years there is a considerable interaction between symbolic-algebraic and result-verification methods. The usage of validated computations at critical points of some algebraic algorithms improves the stability of the complete solution. Several hybrid algorithms using floating-point and/or interval arithmetic in intermediate computations combine the speed of numerical computations with the exactness of symbolic methods providing still guaranteed correct results and a dramatic speed up of the corresponding algebraic algorithm. Embedding of interval data structures, hybrid and result-verification methods in computer algebra systems turn the latter into valuable tool for reliable scientific computing while by applying symbolic-algebraic methods interval computations expand the methodology tools and get an increased efficiency.

This special session continues the tradition established by previous conferences and special sessions (including e.g. the conferences Interval-xx, ACA 2000, 2003, 2006, 2008 and 2009 sessions) on interval and computer-algebraic methods in science and engineering. The aim is to bring together participants from diverse areas of mathematics, computer science, various life & engineering/science disciplines that will demonstrate the progress in the interaction between symbolic-algebraic and result-verification methods. The meeting goal is to stimulate the communication, coordination, integration, and cross-fertilization of ideas capable to meet the emerging challenges.


For this special session, we invite survey papers, presentations of some recent developments, application case studies and research challenges. The topics include but are not limited to:

  • Algebraic approach to interval mathematics; theoretical foundations for combining interval and symbolic-algebraic techniques; formalisms for presentation of interval knowledge in CA; usage of analytical transformations and other techniques from computer algebra in interval computations;

  • Exact methods, computer aided proofs, computational complexity analysis of symbolic computation problems with interval uncertainty;

  • Verified multiple-precision computation of special functions;

  • Bugs in current CA systems;

  • Development and implementation of symbolic-numeric methods for problems involving interval data;

  • (Interval) Taylor models;

  • Embedding of interval data structures, hybrid and result-verification algorithms in CA systems and specialized software;

  • Applications of combined interval-analytical techniques in science, biology, engineering, control and other areas;

  • Interval mathematics on the Internet: the use of web and grid service infrastructures, and semantic web technologies for identifying and describing web-based interval resources;

  • Interval Software Interoperability: interoperability between computing systems (like Mathematica, Maple, Matlab, etc.) and languages for dynamic applications ( C, C++, Fortran, Java, JavaScript, ...) that support interval computations aiming at an increased functionality and effectiveness;

  • CA in interval education and online interval knowledge (e-Learning).

TALKS   scheduled for Saturday ,   June 26, 2010,   The abstracts are available here.

  • 8:00-8:25 Walter Kraemer (University of Wuppertal, Germany)
    Computer-Assisted Proofs and Symbolic Computations

  • 8:30-8:55 Ines Ferrer-Mallorqui, Josep Vehi (Univeritat de Girona, Spain)
    Combining symbolic tools with interval analysis. An application to solve robust control problems.

  • 9:00-8:25 Neli Dimitrova (Bulgarian Academy of Sciences)
    Investigation of a model of plasmid-bearing, plasmid-free competition in a chemostat under uncertainties

  • 9:30-9:55 Juergen Garloff, Andrew P. Smith, Horst Werkle (University of Applied Sciences/HTWG Konstanz, Germany)
    Truss Models with Uncertain Node Locations and Their Verified Finite Element Solution

  • 10:30-10:55 Joris Van der Hoeven (CNRS, France)
    Ball arithmetic

  • 11:00-11:25 Milen Borisov (Bulgarian Academy of Sciences)
    Symbolic and verification software tools for bifurcation analysis of bioprocess models

  • 11:30-11:55 Evgenija D. Popova (Bulgarian Academy of Sciences), W. Kraemer, M. Russev
    Embedding C-XSC Automatic Differentiation in Mathematica


A special issue of the Albanian Journal of Mathematics is dedicated to the conference.