Arithmetic with real algebraic numbers is in NC

Bhubaneswar Mishra, Paul Pedersen

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

Abstract

We describe NC algorithms for doing exact arithmetic with real algebraic numbers in the signcoded representation introduced by Coste and Roy [CoR 1988]. We present polynomial sized circuits of depth O(log3 N) for the monadic operations -α, 1/α, as well as α + r, α · r, and sgn (α - r), where r is rational and α is real algebraic. We also present polynomial sized circuits of depth O(log7 N) for the dyadic operations α+β, α·β, and sgn(α-β), where α and β are both real algebraic. Our algorithms employ a strengthened form of the NC polynomial-consistency algorithm of Ben-Or, Kozen, and Reif [BKR 1986].

Original languageEnglish (US)
Title of host publicationISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation
EditorsShunro Watanabe, Morio Nagata
PublisherPubl by ACM
Pages120-126
Number of pages7
ISBN (Print)0201548925
StatePublished - 1990
EventISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation - Tokyo, Jpn
Duration: Aug 20 1990Aug 24 1990

Other

OtherISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation
CityTokyo, Jpn
Period8/20/908/24/90

Fingerprint

Polynomials
Networks (circuits)

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Mishra, B., & Pedersen, P. (1990). Arithmetic with real algebraic numbers is in NC. In S. Watanabe, & M. Nagata (Eds.), ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation (pp. 120-126). Publ by ACM.

Arithmetic with real algebraic numbers is in NC. / Mishra, Bhubaneswar; Pedersen, Paul.

ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation. ed. / Shunro Watanabe; Morio Nagata. Publ by ACM, 1990. p. 120-126.

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

Mishra, B & Pedersen, P 1990, Arithmetic with real algebraic numbers is in NC. in S Watanabe & M Nagata (eds), ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation. Publ by ACM, pp. 120-126, ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation, Tokyo, Jpn, 8/20/90.
Mishra B, Pedersen P. Arithmetic with real algebraic numbers is in NC. In Watanabe S, Nagata M, editors, ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation. Publ by ACM. 1990. p. 120-126
Mishra, Bhubaneswar ; Pedersen, Paul. / Arithmetic with real algebraic numbers is in NC. ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation. editor / Shunro Watanabe ; Morio Nagata. Publ by ACM, 1990. pp. 120-126
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