NDLI: Modular dynamic evaluation

Content Provider	ACM Digital Library
Author	Noro, Masayuki
Abstract	In this paper we propose an efficient modular method for Dynamic Evaluation (DE) [2][3][5]. For efficient computation over algebraic number fields, we have to design algorithms very carefully. For example, over algebraic number fields, the polynomial factorization is harder and the coefficient swell is more serious than those over the rationals. In DE, the defining polynomial of an algebraic number to be added to a ring L need not to be irreducible, which avoids expensive irreducible factorizations. Instead, the obtained extension may have zero-divisors in general. Such a zero-divisor can be detected dynamically during a computation of the inverse or a zero-recognition of an element and the ring is then decomposed into several components. The known method simply applies the Euclid algorithm to detect zero-divisors, but it often causes coefficient swell. In this paper we give a new formulation of DE by using the notion of ideal quotient, which enables us to apply efficient modular methods to decompose the ring.
Starting Page	262
Ending Page	268
Page Count	7
File Format	PDF
ISBN	1595932763
DOI	10.1145/1145768.1145812
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-07-09
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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Modular dynamic evaluation