=ADD=
=reftype=
14
=number=
97-18
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1997/97-18.ps.gz
=year=
1997
=author=
Moritsugu; Shiuchi + Kuriyama; Kazuko
=title=
Fraction-free Method for Computing Rational Normal Forms of Polynomial Matrices
=month=
06
=abstract=
In this paper, we present a fraction-free algorithm for computing rational
normal forms of matrices with univariate polynomial entries.
In the traditional algorithm based on Danilevskii's method,
its principal transformations are similar to Gaussian elimination.
When they are carried out exactly by computer 
algebra system, the elements of intermediate matrices
extremely swell and it requires much CPU-time
to compute g.c.d.s of polynomials for reducing rational expressions.
\par
In order to avoid such difficulty, 
we give a fraction-free algorithm analogous to
Bareiss' single-step fraction-free elimination.
We have implemented it on the computer algebra system Reduce3.5.
The experimental result shows the efficiency of our algorithm.
=location=
2
=owner=
2
=source=
3