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Volumn 45, Issue 9, 2010, Pages 902-917

Algorithms for solving linear systems over cyclotomic fields

Author keywords

Cyclotomic fields; Cyclotomic polynomials; Linear systems; Modular algorithms

Indexed keywords


EID: 77954310200     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2010.05.001     Document Type: Article
Times cited : (2)

References (17)
  • 1
    • 85061079172 scopus 로고
    • Exact solution of linear equations
    • ACM Press
    • Cabay S. Exact solution of linear equations. Proc. SYMSAC '71 1971, 392-398. ACM Press.
    • (1971) Proc. SYMSAC '71 , pp. 392-398
    • Cabay, S.1
  • 3
    • 21844436353 scopus 로고    scopus 로고
    • A BLAS based C library for exact linear algebra on integer matrices
    • ACM Press
    • Chen Z., Storjohann A. A BLAS based C library for exact linear algebra on integer matrices. Proc. ISSAC '05 2005, 92-99. ACM Press.
    • (2005) Proc. ISSAC '05 , pp. 92-99
    • Chen, Z.1    Storjohann, A.2
  • 5
    • 0001380055 scopus 로고
    • Exact solution of linear equations using p-adic expansions
    • Dixon J.D. Exact solution of linear equations using p-adic expansions. Numer. Math. 1982, 40:137-141.
    • (1982) Numer. Math. , vol.40 , pp. 137-141
    • Dixon, J.D.1
  • 6
    • 36349009278 scopus 로고    scopus 로고
    • Faster inversion and other black box matrix computation using efficient block projections
    • ACM Press
    • Eberly W., Giesbrecht M., Giorgi P., Storjohann A., Villard G. Faster inversion and other black box matrix computation using efficient block projections. Proc. ISSAC '07 2007, 143-150. ACM Press.
    • (2007) Proc. ISSAC '07 , pp. 143-150
    • Eberly, W.1    Giesbrecht, M.2    Giorgi, P.3    Storjohann, A.4    Villard, G.5
  • 7
    • 84966229077 scopus 로고
    • On the coefficients of the cyclotomic polynomials
    • Erdos P., Vaughn R.C. On the coefficients of the cyclotomic polynomials. Bull. Amer. Math. Soc. 1946, 52:179-184.
    • (1946) Bull. Amer. Math. Soc. , vol.52 , pp. 179-184
    • Erdos, P.1    Vaughn, R.C.2
  • 10
    • 11844262962 scopus 로고
    • A Hadamard-type bound on the coefficients of a determinant of polynomials
    • Goldstein A., Graham G. A Hadamard-type bound on the coefficients of a determinant of polynomials. SIAM Rev. 1974, 1:394-395.
    • (1974) SIAM Rev. , vol.1 , pp. 394-395
    • Goldstein, A.1    Graham, G.2
  • 11
    • 85008373567 scopus 로고
    • Factorization of polynomials over finite fields and factorization of primes in algebraic number fields
    • ACM Press
    • Huang M.A. Factorization of polynomials over finite fields and factorization of primes in algebraic number fields. Proc. STOC '84 1984, 175-182. ACM Press.
    • (1984) Proc. STOC '84 , pp. 175-182
    • Huang, M.A.1
  • 12
    • 77954312041 scopus 로고    scopus 로고
    • On the calculations of the coefficients of the cyclotomic polynomials. Kagoshima Univ. Faculty of Science Report No. 31, 31-44.
    • Koshiba, Y., 1998 On the calculations of the coefficients of the cyclotomic polynomials. Kagoshima Univ. Faculty of Science Report No. 31, 31-44.
    • (1998)
    • Koshiba, Y.1
  • 13
    • 31744446524 scopus 로고    scopus 로고
    • The size of the coefficients of cyclotomic polynomials
    • Birkhäuser
    • Maier H. The size of the coefficients of cyclotomic polynomials. Analytic Number Theory 1996, vol. 2:633-639. Birkhäuser.
    • (1996) Analytic Number Theory , vol.vol. 2 , pp. 633-639
    • Maier, H.1
  • 14
    • 84945708089 scopus 로고
    • Approximate algorithms to drive exact solutions to systems of linear equations
    • Springer Verlag, Proc. EUROSAM '79
    • Moenck R., Carter J. Approximate algorithms to drive exact solutions to systems of linear equations. LNCS 1979, vol. 72:65-72. Springer Verlag.
    • (1979) LNCS , vol.vol. 72 , pp. 65-72
    • Moenck, R.1    Carter, J.2
  • 15
    • 27644457134 scopus 로고    scopus 로고
    • Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction
    • ACM Press
    • Monagan M.B. Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction. Proc. ISSAC '04 2004, 243-249. ACM Press.
    • (2004) Proc. ISSAC '04 , pp. 243-249
    • Monagan, M.B.1
  • 16
    • 21844458687 scopus 로고    scopus 로고
    • The shifted number system for fast linear algebra on integer matrices
    • Storjohann A. The shifted number system for fast linear algebra on integer matrices. J. Complexity 2005, 21:605-650.
    • (2005) J. Complexity , vol.21 , pp. 605-650
    • Storjohann, A.1
  • 17
    • 85034427792 scopus 로고
    • A p-adic algorithm for univariate partial fractions
    • ACM Press
    • Wang P. A p-adic algorithm for univariate partial fractions. Proc. SYMSAC '81 1981, 212-217. ACM Press.
    • (1981) Proc. SYMSAC '81 , pp. 212-217
    • Wang, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.