Details:
Title  Solving systems of polynomial equations over GaloisEisenstein rings with the use of the canonical generating systems of polynomial ideals.  Author(s)  D.A. Mikhailov, A.A. Nechaev  Type  Article in Journal  Abstract  A Galois–Eisenstein ring or a GEring is a finite commutative chain ring. We consider two methods of enumeration of all solutions of some system of polynomial equations over a GEring R. The first method is the general method of coordinatewise 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 lefthand side of the initial system of equations and solving instead of the initial system the system with polynomials of the CGS in the lefthand side. For systems of such type a modification of the coordinatewise linearisation method is presented.  ISSN  09249265; 15693929/e 
URL 
http://www.degruyter.com/view/j/dma.2004.14.issue1/156939204774148811/156939204774148811.xml 
Language  English  Journal  Discrete Math. Appl.  Volume  14  Number  1  Pages  2151  Publisher  De Gruyter, Berlin  Year  2004  Edition  0  Translation 
No  Refereed 
No 
