Solving systems of polynomial equations over Galois-Eisenstein rings with the use of the canonical generating systems of polynomial ideals
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| 024 | 7 | 0 | |a 10.1515/156939204774148811 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/156939204774148811 | ||
| 245 | 0 | 0 | |a Solving systems of polynomial equations over Galois-Eisenstein rings with the use of the canonical generating systems of polynomial ideals |h [Elektronische Daten] |c [D.A. Mikhailov, A.A. Nechaev] |
| 520 | 3 | |a 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[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. | |
| 540 | |a Copyright 2004, Walter de Gruyter | ||
| 700 | 1 | |a Mikhailov |D D.A. |4 aut | |
| 700 | 1 | |a Nechaev |D A.A. |4 aut | |
| 773 | 0 | |t Discrete Mathematics and Applications |d Walter de Gruyter |g 14/1(2004-01-01), 41-73 |x 0924-9265 |q 14:1<41 |1 2004 |2 14 |o dma | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/156939204774148811 |q text/html |z Onlinezugriff via DOI |
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| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/156939204774148811 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mikhailov |D D.A. |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Nechaev |D A.A. |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Discrete Mathematics and Applications |d Walter de Gruyter |g 14/1(2004-01-01), 41-73 |x 0924-9265 |q 14:1<41 |1 2004 |2 14 |o dma | ||
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