The design of core 2: A library for exact numeric computation in geometry and algebra

Jihun Yu, Chee Yap, Zilin Du, Sylvain Pion, Hervé Brönnimann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationMathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings
Pages121-141
Number of pages21
Volume6327 LNCS
DOIs
StatePublished - 2010
Event3rd International Congress on Mathematical Software, ICMS 2010 - Kobe, Japan
Duration: Sep 13 2010Sep 17 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6327 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other3rd International Congress on Mathematical Software, ICMS 2010
CountryJapan
CityKobe
Period9/13/109/17/10

Fingerprint

Numerics
Algebra
Geometry
Computational geometry
Transcendental function
Algebraic number
Rapid Prototyping
Computer Algebra
Computational Geometry
Transcendental
Rapid prototyping
Modularity
Libraries
Design
Timing
Subsystem
Speedup
Integrate
Filter
Software

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Yu, J., Yap, C., Du, Z., Pion, S., & Brönnimann, H. (2010). The design of core 2: A library for exact numeric computation in geometry and algebra. In Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings (Vol. 6327 LNCS, pp. 121-141). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6327 LNCS). https://doi.org/10.1007/978-3-642-15582-6_24

The design of core 2 : A library for exact numeric computation in geometry and algebra. / Yu, Jihun; Yap, Chee; Du, Zilin; Pion, Sylvain; Brönnimann, Hervé.

Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings. Vol. 6327 LNCS 2010. p. 121-141 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6327 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yu, J, Yap, C, Du, Z, Pion, S & Brönnimann, H 2010, The design of core 2: A library for exact numeric computation in geometry and algebra. in Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings. vol. 6327 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6327 LNCS, pp. 121-141, 3rd International Congress on Mathematical Software, ICMS 2010, Kobe, Japan, 9/13/10. https://doi.org/10.1007/978-3-642-15582-6_24
Yu J, Yap C, Du Z, Pion S, Brönnimann H. The design of core 2: A library for exact numeric computation in geometry and algebra. In Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings. Vol. 6327 LNCS. 2010. p. 121-141. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-15582-6_24
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. Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings. Vol. 6327 LNCS 2010. pp. 121-141 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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