| Abstract:
Ore matrices are matrices over Ore algebras (including differential
operators and difference operators), which have a long research history, at
least dated back to Jacobson's seminal work in 1940s. In past two decades,
Ore matrices have attracted more and more people in computer algebra area,
and many important properties of Ore matrices have been discussed by using
symbolic computation methods, for example, various fast algorithms for
computing Hermite forms and Smith forms; fraction-free algorithms for
computing Popov forms. In this talk, we will outline some fast algorithms
for computing normal forms of Ore matrices.
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