Non-commutative Computer Algebra and its Applications with the Computer Algebra System Singular:Plural
Sprache des Vortragstitels:
Englisch
Original Kurzfassung:
We describe the origins, the domain of applicability and the functionality of a subsystem PLURAL of the computer algebra system SINGULAR, devoted to the non-commutative computations (in particular, Groebner bases). We show, how main computational objects (GR-algebras) arise and which properties (e.g. ring-theoretic) they possess. We discuss the impact of some nice properties in applications. Among others, we explain the notion of non-commutative Cohen-Macaulay algebras and show its connection with the fast computation of e.g. controllability degree for modules, arising from the System and Control theory. Several illustrative examples will be computed live.
Forschungs-