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TitleSolving systems of polynomial equations over Galois-Eisenstein rings with the use of the canonical generating systems of polynomial ideals.
Author(s) D.A. Mikhailov, A.A. Nechaev
TypeArticle in Journal
AbstractA Galois–Eisenstein ring or a GE-ring is a finite commutative chain ring. We consider two methods of enumeration of all solutions of some system of polynomial equations over a GE-ring R. The first method is the general method of coordinate-wise linearisation. This method reduces to solving the initial polynomial system over the quotient field = R/ Rad R and then to solving a series of linear equations systems over the same field. For an arbitrary ideal of the ring R[x 1, . . . , x k ] a standard base called the canonical generating system (CGS) is constructed. The second method consists of finding a CGS of the ideal generated by the polynomials forming the left-hand side of the initial system of equations and solving instead of the initial system the system with polynomials of the CGS in the left-hand side. For systems of such type a modification of the coordinate-wise linearisation method is presented.
ISSN0924-9265; 1569-3929/e
URL http://www.degruyter.com/view/j/dma.2004.14.issue-1/156939204774148811/156939204774148811.xml
JournalDiscrete Math. Appl.
PublisherDe Gruyter, Berlin
Translation No
Refereed No