Computation of replicable functions on Risa/Asir
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
The geobucket data structure for polynomials
Journal of Symbolic Computation
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
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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.