D.A. Mikhailov, A.A. Nechaev
Solving systems of polynomial equations over Galois–Eisenstein rings with the use of the canonical generating systems of polynomial ideals
A 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[x1, . . . , xk ] 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.
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 14, 01/2004
Pages: 41 - 73
Show full article (external site)
Show all available items of this journal
Search
