Titlebook: Mathematical Software - ICMS 2006; Second International Andrés Iglesias,Nobuki Takayama Conference proceedings 2006 Springer-Verlag Berlin

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Making Change and Finding Repfigits: Balancing a Knapsack real relaxation is large; in a sense this translates to a poor choice of variables. Lattice reduction methods have been developed in the past few years to improve handling of such problems. We show explicitly how they may be applied to computation of Frobenius instances, Keith numbers (also called

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Robust HGCD with No Backup Stepseen notoriously difficult, with the need for “backup steps” in various forms. This paper explains why backup steps are necessary for algorithms based directly on the quotient sequence, and proposes a robustness criterion that can be used to construct a “half-gcd” algorithm without any backup steps.

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The Design of CoCoALibffort has been invested in making the code clean and portable while not neglecting run-time performance; one of the primary goals is to offer freely available reference implementations of the most important algorithms in the field.

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An Efficient Implementation for Computing Gröbner Bases over Algebraic Number Fieldsionals 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.

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