=ADD=
=reftype=
14
=number=
97-35
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1997/97-35.ps.gz
=year=
1997
=author=
Moritsugu; Shuichi + Kuriyama; Kazuko
=title=
A Linear Algebra Method for Solving Systems of Algebraic Equations
=month=
11
=keywords=
Stetter's method, U-resultant
=abstract=
We consider a linear algebra method in residue class rings
for solving systems of algebraic equations.
We construct multiplication tables using a Gr\"{o}bner basis
of a zero-dimensional ideal. Then, we analyze the tables 
by exactly computing their Frobenius normal forms.
The derogatoriness and the diagonalizability are determined 
by the normal forms, and the problem is divided into four cases:\par
(1) nonderogatory and diagonalizable case,                      \par
(2) nonderogatory and nondiagonalizable case,                   \par
(3) derogatory and diagonalizable case,                         \par
(4) derogatory and nondiagonalizable case.                      \\
Subsequently, we construct common eigenvectors symbolically,
and compute all the exact zeros with their multiplicities.
In the appendix, we show the minute description of multiple zeros
using only the normal set basis, where we do not need 
explicit computation of differential conditions.
=location=
2
=owner=
2
=source=
3