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Séminaire Calcul Formel

Some 'What', 'Why' and 'How' on Row Reducing Matrices over Ore Polynomial Rings

by Dr. Johan Rosenkilde (TU Denmark)

jeudi 8 mars 2018 de au (Europe/Paris)
at Bâtiment XLIM ( Salle XR203 )
Description
Ore polynomials, also known as skew polynomials, are non-commutative
polynomials which can algebraically model differential equations,
time-dependent systems, linear maps over finite fields, and more.
Matrices over Ore polynomial rings can model systems of these objects
and have found applications in diverse areas. Computing normal forms of
such matrices can be useful for checking system equivalence or finding
special elements in the space, e.g. shortest vectors.

In this talk I will introduce Ore polynomial rings, some important
examples hereof, and describe some recent work on computing certain
reduced normal forms of matrices of Ore polynomials.