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Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases. (English) Zbl 1245.65051
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 SINGULAR:PLURAL following the fraction-free strategy, shows impressive performance compared with methods which directly use fractions.
MSC:
65F30 Other matrix algorithms (MSC2010)
68W30 Symbolic computation and algebraic computation
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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