Abstract
It is demonstrated that, when using Buchberger's Algorithm with the purely lexicographic ordering of terms, it is not generally feasible to interreduce basis polynomials during the progress of the algorithm. A heuristic is obtained (for polynomials over the rationals) which improves the efficiency of the reduction sub-algorithm, when the basis is not inter-reduced. Some improvements are made to a recent scheme for combining Buchberger's Algorithm with multivariate factorization. We present a hybrid variant of this scheme, in which extraneous sub-problems are detected outside of the lexicographic/elimination algorithm. Through this approach, the reduced solution bases for dense systems (previously impossible in the lexicographic ordering) may be found.
This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A8967.
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References
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© 1989 Springer-Verlag Berlin Heidelberg
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Czapor, S.R. (1989). Solving algebraic equations via Buchberger's algorithm. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_125
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DOI: https://doi.org/10.1007/3-540-51517-8_125
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