Field Theory

Computational Methods

12-04

  1. Gregory V. Bard, Nicolas T. Courtois, and Chris Jefferson, Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF(2) via SAT-solvers, IACR (2007), 14 pages.[eprint]
  2. Cristina Bertone, Guillaume Chéze, and André Galligo, Modular Las Vegas algorithms for polynomial absolute factorization, J. Symbolic Comput. 45 (2010), no. 12, 1280–1295.[arXiv]
  3. Thomas Beth, Jörn Müller-Quade, and Rainer Steinwandt, Computing restrictions of ideals in finitely generated k-algebras by means of Buchberger's algorithm, J. Symbolic Comput. 41 (2006), no. 3-4, 372–380.[MR]
  4. A. Bostan, G. Lecerf, B. Salvy, É. Schost, and B. Wiebelt, Complexity issues in bivariate polynomial factorization, in ISSAC '04: Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, NY, USA, 2004, pp. 42–49.[doi]
  5. Guillaume Chèze and Grégoire Lecerf, Lifting and recombination techniques for absolute factorization, J. Complexity 23 (2007), no. 3, 380–420.[MR]
  6. Akpodigha Filatei, Xin Li, Marc Moreno Maza, and Éric Schost, Implementation techniques for fast polynomial arithmetic in a high-level programming environment, in ISSAC '06: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, NY, USA, 2006, pp. 93–100.[doi]
  7. Katharina Geißler and Jürgen Klüners, Galois group computation for rational polynomials, J. Symbolic Comput. 30 (2000), no. 6, 653–674.[MR]
  8. Kiran S. Kedlaya, Search techniques for root-unitary polynomials, Computational arithmetic geometry, Contemp. Math., vol. 463, Amer. Math. Soc., Providence, RI, 2008, pp. 71–81.[MR/arXiv]
  9. Sara Khodadad and Michael Monagan, Fast rational function reconstruction, ISSAC 2006, ACM, New York, 2006, pp. 184–190.[MR]
  10. Grégoire Lecerf, New recombination algorithms for bivariate polynomial factorization based on Hensel lifting, Appl. Algebra Engrg. Comm. Comput. 21 (2010), no. 2, 151–176.[MR/doi]
  11. Hsin-Chao Liao and Richard J. Fateman, Evaluation of the heuristic polynomial GCD, in ISSAC '95: Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, NY, USA, 1995, pp. 240–247.[doi]
  12. Michael Monagan, Maximal quotient rational reconstruction: An almost optimal algorithm for rational reconstruction, ISSAC 2004, ACM, New York, 2004, pp. 243–249.[MR]
  13. Jörn Müller-Quade and Rainer Steinwandt, Basic algorithms for rational function fields, J. Symbolic Comput. 27 (1999), no. 2, 143–170.[MR]
  14. Jörn Müller-Quade and Rainer Steinwandt, Gröbner bases applied to finitely generated field extensions, J. Symbolic Comput. 30 (2000), no. 4, 469–490.[MR]
  15. Fatima K. Abu Salem and Rawan N. Soudah, An empirical study of cache-oblivious polygon indecomposability testing, Computing 88 (2010), no. 8, 55–78.[doi]
  16. Leonard Soicher and John McKay, Computing Galois groups over the rationals, J. Number Theory 20 (1985), no. 3, 273–281.[MR]
  17. Allan Steel, A new scheme for computing with algebraically closed fields, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 491–505.[MR]
  18. Allan K. Steel, Computing with algebraically closed fields, J. Symbolic Comput. 45 (2010), no. 3, 342–372.
  19. Rainer Steinwandt, On computing a separating transcendence basis, SIGSAM Bulletin 34 (2000), no. 4.