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The modulo N extended GCD problem for polynomials

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Published:01 August 1998Publication History
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  1. 1.AHO, A. V., HOPCROFT, J. E., AND ULLMAN, J. D. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2.DOMICH, P. D., KANNAN, R., AND TROTTER, JR., L. E. Hermite normal form computation using modulo determinant arithmetic. Mathematics of Operations Research 12, 1 (1987), 50-59.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.GIESBRECHT, M. Fast computation of the Smith normal form of an integer matrix. In Proc. Int'l. Syrup. on Symbolic and Algebraic Computation: ISSAC '95 (1995), A. H. M. Levelt, Ed., pp. 110-118.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.IWANIEC, H. On the problem of Jacobsthal. Demonstratio Mathematica 11, 1 (1978), 225--231.]]Google ScholarGoogle ScholarCross RefCross Ref
  5. 5.JACOBSTHAL, E. /Jber Sequenzen ganzer Zahlen, von denen keine zu n teilerfremd ist I-III. Norske Vid. Selsk. Forhdl. 33 (1960), 117-124, 125-131, 132-139.]]Google ScholarGoogle Scholar
  6. 6.KALTOFEN, E., KRISHNAMOORTHY, M. S., AND SAUN- DERS, B. D. Fast parallel computation of Hermite and Smith forms of polynomial matrices. SIAM Journal of Algebraic and Discrete Methods 8 (1987), 683-690.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7.KALTOFEN, E., KRISHNAMOORTHY, M. S., AND SAUN- DERS, B. D. Parallel algorithms for matrix normal forms. Linear Algebra and its Applications 136 (1990), 189-208.]]Google ScholarGoogle ScholarCross RefCross Ref
  8. 8.KANOLD, H.-J. /Jber eine zahlentheoretische Funktion von Jacobsthal. Math. Annalen 170 (1967), 314-326.]]Google ScholarGoogle ScholarCross RefCross Ref
  9. 9.STORJOHANN, A. A solution to the extended gcd problem with applications. In Proc. Int'l. Syrup. on Symbolic and Algebraic Computation: ISSAC '97 (1997).]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10.STORJOHANN, A., AND LABAHN, G. A fast Las Vegas algorithm for computing the Smith normal form of a polynomial matrix. Linear Algebra and its Applications 253 (1997), 155--173.]]Google ScholarGoogle ScholarCross RefCross Ref
  11. 11.STORJOHANN, A., AND MULDERS, T. Fast algorithms for linear algebra modulo N. To appear in Proc. of Sixth Ann. Europ. Symp. on Algorithms: ESA '98.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.VILLARD, G. Generalized subresultants for computing the Smith normal form of polynomial matrices. Journal of Symbolic Computation 20, 3 (1995), 269--286.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13.VILLARD, G. Fast parallel algorithms for matrix reduction to normal forms. Applicable Algebra in Engineering, Communication and Control 8 (1997), 511--537.]]Google ScholarGoogle Scholar

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        cover image ACM Conferences
        ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation
        August 1998
        330 pages
        ISBN:1581130023
        DOI:10.1145/281508

        Copyright © 1998 ACM

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        • Published: 1 August 1998

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