The design of core 2: A library for exact numeric computation in geometry and algebra. There is a growing interest in numeric-algebraic techniques in the computer algebra community as such techniques can speed up many applications. This paper is concerned with one such approach called Exact Numeric Computation (ENC). The ENC approach to algebraic number computation is based on iterative verified approximations, combined with constructive zero bounds. This paper describes Core 2, the latest version of the Core Library, a package designed for applications such as non-linear computational geometry. The adaptive complexity of ENC combined with filters makes such libraries practical. Core 2 smoothly integrates our algebraic ENC subsystem with transcendental functions with ϵ-accurate comparisons. This paper describes how the design of Core 2 addresses key software issues such as modularity, extensibility, efficiency in a setting that combines algebraic and transcendental elements. Our redesign preserves the original goals of the Core Library, namely, to provide a simple and natural interface for ENC computation to support rapid prototyping and exploration. We present examples, experimental results, and timings for our new system, released as Core Library 2.0
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References in zbMATH (referenced in 4 articles , 1 standard article )
Showing results 1 to 4 of 4.
- Lien, Jyh-Ming; Sharma, Vikram; Vegter, Gert; Yap, Chee: Isotopic arrangement of simple curves: an exact numerical approach based on subdivision (2014)
- Mörig, Marc: Deferring dag construction by storing sums of floats speeds-up exact decision computations based on expression dags (2010)
- Mörig, Marc; Rössling, Ivo; Schirra, Stefan: On design and implementation of a generic number type for real algebraic number computations based on expression dags (2010)
- Yu, Jihun; Yap, Chee; Du, Zilin; Pion, Sylvain; Brönnimann, Hervé: The design of Core 2: a library for exact numeric computation in geometry and algebra (2010)