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TitleAn efficient implementation for computing Gr\"obner bases over algebraic number fields.
Author(s) Masayuki Noro
TypeBook, Chapter in Book, Conference Proceeding
AbstractIn 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.
URL http://link.springer.com/chapter/10.1007%2F11832225_9
PublisherBerlin: Springer
Translation No
Refereed No