Advertisement

KASH: Recent Developments

  • Sebastian Freundt
  • Aneesh Karve
  • Anita Krahmann
  • Sebastian Pauli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4151)

Abstract

In recent years the computer algebra system KASH/KANT for number theory has evolved considerably. We present its new features and introduce the related components, QaoS (Querying Algebraic Objects System) and GiANT (Graphical Algebraic Number Theory).

Keywords

Type System Galois Group Computer Algebra System Algebraic Number Theory Full Text Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AED05]
    Assmann, B., Eick, B., Distler, A.: GAP package Alnuth: an interface to KANT, http://www.gap-system.org/Packages/alnuth.html
  2. [BB+05]
    Batut, C., Belabas, K., Benardi, D., Cohen, H., Olivier, M.: User’s Guide to PARI-GP (2005), http://pari.math.u-bordeaux.fr
  3. [BH96]
    Bilu, Y., Hanrot, G.: Solving Thue equations of high degree. J. Number Th. 60, 373–392 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [BCP97]
    Bosma, W., Canon, J.J., Playoust, K.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24(3-4), 235–265 (1997), http://magma.maths.usyd.edu.au zbMATHCrossRefMathSciNetGoogle Scholar
  5. [CN04]
    Celler, F., Neunhöffer, M.: GAP package XGAP: a graphical user interface for GAP (2004), http://www-gap.mcs.st-and.ac.uk/Packages/xgap.html
  6. [DF+97]
    Daberkow, M., Fieker, C., Klüners, J., Pohst, M., Roegner, K., Schörnig, M., Wildanger, K.: KANT V4. J. Symb. Comp. 11, 267–283 (1997) CrossRefGoogle Scholar
  7. [DW96]
    Daberkow, M., Weber, A.: A Database for Number Fields. In: Limongelli, C., Calmet, J. (eds.) DISCO 1996. LNCS, vol. 1128, pp. 320–330. Springer, Heidelberg (1996)Google Scholar
  8. [Fi97]
    Fieker, C.: Über relative Normgleichungen in algebraischen Zahlkörpern, Dissertation, TU Berlin (1997)Google Scholar
  9. [Fi02]
    Fieker, C.: Computing class fields via the Artin map. Math. Comp. 70(235), 1293–1303 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [GAP]
    GAP: Groups, Algorithms, Programming, http://www.gap-system.org
  11. [GMP]
    GMP: GNU Multiple Precision Arithmetic Library, http://www.swox.com/gmp
  12. [Ge05]
    Geissler, K.: Berechnung von Galoisgruppen über Zahl- und Funktionenkörpern, Dissertation, TU Berlin (2003)Google Scholar
  13. [He02]
    Hess, F.: Computing Riemann-Roch spaces in algebraic function fields and related topics. J. Symbolic Comput. 33(4), 425–445 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  14. [HPP03]
    Hess, F., Pauli, S., Pohst, M.E.: Computing the Multiplicative Group of Residue Class Rings. Mathematics of Computation 72 (2003)Google Scholar
  15. [Hul05]
    Hulpke, A.: Constructing Transitive Permutation Groups. J. Symb. Comp. 39, 1–30 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  16. [KP06]
    Karve, A., Pauli, S.: GiANT: Graphical Algebraic Number Theory (preprint, 2006), http://giantsystem.sourceforge.net
  17. [Ma05]
    Maplesoft, Maple (2005), http://www.maplesoft.com
  18. [Mu05]
    MuPad: Multi Processing Algebra Data Tool, http://www.mupad.de/
  19. [MPFR]
    MPFR library for multiple precision floating point computation, http://www.mpfr.org/
  20. [OM]
    OpenMath: an extensible standard for representing the semantics of mathematical objects, http://www.openmath.org/
  21. [Pa01]
    Pauli, S.: Factoring polynomials over local fields. J. Symb. Comp. 32 (2001)Google Scholar
  22. [PSQL]
  23. [Sc+93]
    Schönert, M., et al.: GAP: Groups, Algorithms, Programming – version 3.27, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1993), http://www-gap.mcs.st-and.ac.uk/Gap3/gap3.html
  24. [St06]
    Stein, W., et al.: SAGE: Software for Algebra and Geometry Experimentation (2006), http://sage.scipy.org/sage
  25. [Wi00]
    Wildanger, K.: Über das Lösen von Einheiten- und Indexformgleichungen in algebraischen Zahlkörpern. J. Number Theory 82(2), 188–224 (2000)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sebastian Freundt
    • 1
  • Aneesh Karve
    • 2
  • Anita Krahmann
    • 1
  • Sebastian Pauli
    • 1
  1. 1.Institut für Mathematik, MA 8–1Technische Universität BerlinBerlinGermany
  2. 2.Computer Sciences DepartmentUniversity of Wisconsin – MadisonMadisonUSA

Personalised recommendations