Abstract
Most ideal theoretic problems in a polynomial ring are extremely hard to solve, if the ideal is given by an arbitrary basis. B. Buchberger, 1965, was the first to show that for polynomials over a field it is possible to construct a "detaching" basis from a given arbitrary one, such that the problems mentioned above become easily soluble. Other authors (e.g. M. Lauer, 1976, and S.C. Schaller, 1979) have considered different coefficient domains. In this paper we investigate a method, developed by C.Sims and C.Ayoub, for constructing "detaching" bases in the ring of polynomials over Z, where the power products are ordered lexicographically. We show that the method also works for polynomials over a field, with only weak conditions on the ordering of the power products. New proofs of correctness and termination are presented. Furthermore we are able to improve the complexity behaviour of Ayoub's algorithm for the case of polynomials over a field.
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References
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© 1983 Springer-Verlag
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Winkler, F. (1983). An algorithm for constructing detaching bases in the ring of polynomials over a field. In: van Hulzen, J.A. (eds) Computer Algebra. EUROCAL 1983. Lecture Notes in Computer Science, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12868-9_101
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DOI: https://doi.org/10.1007/3-540-12868-9_101
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