Computing Homomorphisms Between HolonomicD-modules

✍ Scribed by Harrison Tsai; Uli Walther

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 390 KB
• Volume: 32
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.2001.0485

✦ Synopsis

Let K ⊆ C be a subfield of the complex numbers, and let D be the ring of K-linear differential operators on R = K[x 1 , . . . , xn]. If M and N are holonomic left D-modules we present an algorithm that computes explicit generators for the finite dimensional vector space Hom D (M, N ). This enables us to answer algorithmically whether two given holonomic modules are isomorphic. More generally, our algorithm can be used to get explicit generators for Ext i D (M, N ) for any i in the sense of Yoneda.