TY - GEN
T1 - The design of core 2
T2 - 3rd International Congress on Mathematical Software, ICMS 2010
AU - Yu, Jihun
AU - Yap, Chee
AU - Du, Zilin
AU - Pion, Sylvain
AU - Brönnimann, Hervé
N1 - Funding Information:
Yap, Du and Yu are supported by NSF Grants CCF-043836, CCF-0728977 and CCF-0917093, and with partial support from Korea Institute of Advance Studies (KIAS). Brönnimann is supported by NSF Career Grant 0133599. Brönnimann, Pion, and Yap are supported by an Collaborative Action GENEPI grant at INRIA and an NSF International Collaboration Grant NSF-04-036, providing travel support for Du and Yu to INRIA.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=78149261787&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78149261787&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-15582-6_24
DO - 10.1007/978-3-642-15582-6_24
M3 - Conference contribution
AN - SCOPUS:78149261787
SN - 3642155812
SN - 9783642155819
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 121
EP - 141
BT - Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings
Y2 - 13 September 2010 through 17 September 2010
ER -