Exact Computation

 

 

Reports

  • Final report: Domain-theoretic Solution of Differential Equations [report.pdf].

  • Final report: Exact Real Arithmetic Using Linear Fractional Transformations [report.ps.gz].
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Papers

Domain-theoretic Solution of Differential Equations

Domain-theoretic Solution of Differential Equations (Scalar Fields) (A. Edalat and M. Krznaric and A. Lieutier) Electronic Notes in Theoretical Computer Science volume 83, 2003.
A domain theoretic account of Picard's theorem (A. Edalat and D. Pattinson)
In Proceedings of ICALP 2004. Full paper to appear in the London Mathematical Society Journal of Computation and Mathematics.
A domain theoretic account of Euler's method for Solving Initial Value Problems (A. Edalat and D. Pattinson) In Proceedings of PARA 2004
Domain Theoretic Solutions of Initial Value Problems for Unbounded Vector Fields (A. Edalat and D. Pattinson) In Proceedings of MFPS XXI, ENTCS volume 155, 2005.
A Computational Model for Multi-Variable Differential Calculus (A. Edalat and A. Lieutier and D. Pattinson) In Proceedings of FOSSACS 2005.
Denotational Semantics of Hybrid Automata (A. Edalat with D. Pattinson) Proceedings of Foundations of Software Science and Computation Structures: 9th International Conference, FOSSACS 2006 Lecture Notes in Computer Science Volume 3921 pp.231-245 March, 2006
Inverse and Implicit Functions in Domain Theory (A. Edalat and D. Pattinson) In Proceedings of LICS 2005.
A continuous derivative for real-valued functions (A. Edalat) Invited paper for New Computational Paradigms
Domain Theory and Differential Calculus (Functions of one variable) (A. Edalat and A.Lieutier).
Mathematical Structures in Computer Science, Volume 14, Issue 06, Dec 2004, pp 771-802. (Extended abstract in Proceedings of IEEE Symposium on Logic in Computer Science (LICS) 2002.)

 

Exact Real Arithmetic, Computational Geometry and Solid Modelling

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Implementations

  • IC-ODE-solvers: C library for Solving Initial value Problems. [complete package in tar.gz format]

    IC-ODE-solvers is a C package, which solves initial value problems, using interval arithmetic and rational arithmetic packages. The package contains programs based on domian-theoretic versions of Picard's and Euler's methods to solve initial value problems.

    The installation method and a few examples are provided in this package in order to help the user. All feedbacks and comments should be sent to the email provided in the package.

  • IC-Reals: C library for Exact Real Computation. [complete package in tar.gz format] [manual in ps.gz format] [manual in pdf format][copy right]

    The Imperial College Exact Real Arithmetic Library is a collection of C types and functions which implement exact real arithmetic. The functions allow one to construct objects representing real numbers and then to demand information, for example some number of decimal digits, from those objects. The user need not specify a precision in advance. All the digits retrieved are correct and further digits can be demanded.

    The library includes arithmetic operations as well as a suite of analytic functions on reals. In addition to a real type, the library also includes a lazy boolean type and a collection of predicates on reals, boolean operations and a conditional construct.

  • iRRAM with Continued Fractions: C++ library for Exact Real Computation. [complete package in tar.gz format]

    This C++ package combines Norbert Muller's approach to real computation, iRRAM, with the Continued Fraction algorithms for elementary functions developed at IC.

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Ali Khanban
Last modified: Tuesday, 15 January 2002.