The diamond operator - Implementation of exact real algebraic numbers

Schmitt, Susanne; Ganzha, Victor G.; Mayr, Ernst W.; Vorozhtsov, Evgenii V.

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The diamond operator - Implementation of exact real algebraic numbers

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Schmitt, Susanne
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Schmitt, S. (2005). The diamond operator - Implementation of exact real algebraic numbers. In Computer Algebra in Scientific Computing, 8th International Workshop, CASC 2005 (pp. 355-366). Berlin, Germany: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-27F0-7

Abstract

The LEDA number type real is extended by the diamond operator, which allows to compute exactly with real algebraic numbers given as roots of polynomials. The coefficients of these polynomials can be arbitrary real algebraic numbers. The two important steps of the implementation (isolating interval computation and approximation) are described. Experiments with two other existing implementations of real algebraic numbers (CORE, EXACUS) show that the implementation is comparable with CORE and is more general than CORE or EXACUS.