Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language

Conference object, Preprint English OPEN
Fieker, Claus ; Hart, William ; Hofmann, Tommy ; Johansson, Fredrik (2017)
  • Publisher: HAL CCSD
  • Related identifiers: doi: 10.1145/3087604.3087611
  • Subject: [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT] | Computer Science - Mathematical Software | [ INFO.INFO-MS ] Computer Science [cs]/Mathematical Software [cs.MS] | Computer Science - Symbolic Computation | [ INFO.INFO-SC ] Computer Science [cs]/Symbolic Computation [cs.SC]

International audience; We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort to a low-level C implementation. For specialised algorithms, we use Julia's efficient native C interface to wrap existing C/C++ libraries such as Flint, Arb, Antic and Singular. We give examples of how to use Hecke and Nemo and discuss some algorithms that we have implemented to provide high performance basic arithmetic.
  • References (29)
    29 references, page 1 of 3

    [1] E. Bach, Improved approximations for Euler products, Number theory (Halifax, NS, 1994), vol. 15, CMS Conference Proceedings, pages 13-28. Amer. Math. Soc., Providence, RI, 1995.

    [2] K. Belabas, Topics in computational algebraic number theory, J. Théor. Nombres Bordeaux, 16(1):19-63, 2004.

    [3] K. Belabas, E. Friedman. Computing the residue of the Dedekind zeta function, Math. Comp., 84(291):357-369, 2015.

    [4] J. Bezanson, A. Edelman, S. Karpinski, V. B. Shah, Julia: A fresh approach to numerical computing,

    [5] J.-F. Biasse, C. Fieker, Subexponential class group and unit group computation in large degree number fields , LMS J. Comput. Math., 17(suppl. A):385-403, 2014.

    [6] W. Bosma, J. J. Cannon, C. Fieker, A. Steel (Eds.), Handbook of Magma Functions, Edition 2.22 (2016).

    [7] W. Brown, Null ideals and spanning ranks of matrices, Comm. Algebra 26, (1998), pp. 2401-2417.

    [8] H. Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, vol. 138, Springer-Verlag, Berlin, 1993.

    [9] A. Danilevsky, The numerical solution of the secular equation, (Russian), Matem. Sbornik, 44(2), 1937. pp. 169-171.

    [10] W. Decker, G. M. Greuel, G. Pfister and H. Schönemann, Singular - A computer algebra system for polynomial computations,

  • Metrics
    No metrics available
Share - Bookmark