Abstract
Recently, several authors studied methods based on endomorphisms for localizing and computing the common zeros of systems of polynomial equations f i (x 1,..., x n )=0, i=1,..., s, in case the ideal I generated by f 1,..., f s has dimension zero. The main idea is to consider the trace and the eigenvalues of the endomorphisms Ф f: [g] ↦ [g · f], where [·] denotes equivalence classes modulo I in the polynomial ring. In this paper we give discuss some of these methods and combine them with the concept of dual bases for describing zero dimensional ideals.
This work is supported in part by the CEC, ESPRIT Basic Research Action 6846 (PoSSo)
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Möller, H.M. (1993). Systems of algebraic equations solved by means of endomorphisms. In: Cohen, G., Mora, T., Moreno, O. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993. Lecture Notes in Computer Science, vol 673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56686-4_32
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DOI: https://doi.org/10.1007/3-540-56686-4_32
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