Fast Library for Number Theory: An Introduction

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)


We discuss FLINT (Fast Library for Number Theory), a library to support computations in number theory, including highly optimised routines for polynomial arithmetic and linear algebra in exact rings.


Number Theory Polynomial Multiplication High Level Language Theta Series Exact Ring 
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  1. 1.
    Behnel, S., Bradshaw, R., Seljebotn, D.: Cython: C extensions for Python,
  2. 2.
    Belabas, K.: Pari/GP,
  3. 3.
    Cannon, J., Steel, A., et al.: Magma Computational Algebra System,
  4. 4.
    Erocal, B., Stein, W.: The Sage Project: Unifying Free Mathematical Software to Create a Viable Alternative to Magma, Maple, Mathematica and Matlab,,
  5. 5.
    Granlund, T.: GNU MP Bignum Library,
  6. 6.
    Hart, W., Harvey, D., et al.: Fast Library for Number Theory,
  7. 7.
    Hart, W., Novocin, A.: A practical univariate polynomial composition algorithm (2010) (preprint)Google Scholar
  8. 8.
    Hart, W., Novocin, A., van Hoeij, M.: Improved polynomial factorisation (2010) (preprint)Google Scholar
  9. 9.
    Hart, W., Tornaria, G., Watkins, M.: Congruent number theta coefficients to 1012. In: Gaudry, et al. (eds.) Proceedings of the Algorithmic Number Theory Symposium (ANTS IX). Springer, Heidelberg (to appear 2010)Google Scholar
  10. 10.
    Hart, W.: A One Line Factoring Algorithm (2010) (preprint)Google Scholar
  11. 11.
    Hart, W.: A refinement of Mulders’ polynomial short division algorithm (2007) (unpublished report)Google Scholar
  12. 12.
    Harvey, D.: A cache–friendly truncated FFT. Theor. Comput. Sci. 410, 2649–2658 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Harvey, D.: Faster polynomial multiplication via multipoint Kronecker substitution. J. Symb. Comp. 44, 1502–1510 (2009), zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Mulders, T.: On short multiplication and division. AAECC 11(1), 69–88 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Nguyen, P., Stehlé, D.: An LLL algorithm with quadratic complexity. SIAM Journal of Computation 39(3), 874–903 (2009), zbMATHCrossRefGoogle Scholar
  16. 16.
    Shoup, V.: NTL: A Library for doing Number Theory,

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Mathematics InstituteWarwick UniversityCoventryUnited Kingdom

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