
Linear Algebra over Polynomial Rings 263
see the following references: [45], [47], [58], [64, §6.4], [93], [144], [164], [213],
[214], [258], [259].
8.4 Algorithms for linear algebra over polynomial rings
8.4.1 Introduction: elementary row and column operations
Our naive goal is to construct an algorithm as simple and efficient as Gaus-
sian elimination which would compute an (as yet unspecified) canonical form
for matrices over a polynomial ring. This goal is almost certainly not practical,
but nonetheless in this section we describe some useful algorithms that can
be used in many cases to simplify polynomial matrices very substantially.
To begin, let