Abstract
In this paper we prove some properties of Gröbner bases under specialization maps. In particular we state sufficient conditions for the image of a Gröbner basis to be a Gröbner basis. We apply these results to the resolution of systems of polynomial equations. In particular we show that, if the system has a finite number of solutions, (in an algebraic closure of the base field K), the problem is totally reduced to a single Gröbner basis computation (w.r.t. purely lexicographical ordering), followed by a search for the roots of univariate polynomials and a “few” evaluations in suitable algebraic extensions of K.
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© 1989 Springer-Verlag Berlin Heidelberg
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Gianni, P. (1989). Properties of Gröbner bases under specializations. 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_128
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DOI: https://doi.org/10.1007/3-540-51517-8_128
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Online ISBN: 978-3-540-48207-9
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