An Efficient Implementation for Computing Gröbner Bases over Algebraic Number Fields

  • Masayuki Noro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4151)


In this paper we discuss Gröbner basis computation over algebraic number fields. Buchberger algorithm can be executed over any computable field, but the computation is often inefficient if the field operations for algebraic numbers are directly used. Instead we can execute the algorithm over the rationals by adding the defining polynomials to the input ideal and by setting an elimination order. In this paper we propose another method, which is a combination of the two methods above. We implement it in a computer algebra system Risa/Asir and examine its efficiency.


Algebraic Number Lexicographic Order Computer Algebra System Basis Computation Chinese Remainder Theorem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Masayuki Noro
    • 1
  1. 1.Kobe UniversityRokko, KobeJapan

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