Interaction Between Computer Algebra and Interval Computations

Special Session at
18th International Conference on Applications of Computer Algebra (ACA 2012)
June 2528, 2012, Sofia, Bulgaria

Session Organizers:

  • Walter Kraemer, Bergische Universitaet, Wuppertal
    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, 2009, and 2010 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 Wednesday,   June 27, 2012.   The abstracts are available here.