Elimination in non--commutative $G$--algebras and Applications to $D$--modules
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
Tenth Meeting on Computer Algebra and Applications (EACA) 2006
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
The notion of elimination is one of the most important constructions in Computer Algebra and is a building block for many algorithms. We are going to discuss the correctness of this notion and give the criteria for existence of elimination ideals for the wide class of non--commutative G-algebras. We show how the elimination is implemented in Computer Algebra System Singular. We present a new \textsc{Singular:Plural} library dmod.lib, which provides implementations of two algorithms for computing the $D$--module structure of localizations $\K[x_1,\dots,x_n, F^{-1}]$. With this implementation we are able to tackle some challenging examples, e.g. posed by Ucha and Castro
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