Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases
The authors present a new fraction-free algorithm for the computation of a diagonal form of a matrix over a certain non-commutative Euclidean domain over a computable field with the help of Gröbner bases. They investigate Ore localizations of common operator algebras over \(K[x]\) and use them in the unimodularity analysis of transformation matrices \(U\) and \(V\). Their algorithm, which is implemented in the computer algebra system \texttt{SINGULAR:PLURAL} following the fraction-free strategy, shows impressive performance compared with methods which directly use fractions.
decoupling of systems of functional equations
scientific article; zbMATH DE number 6053102
scientific article