Complexity of Janet basis of a D-module (2007)
Chistov, Alexander, Grigoriev, Dima
We prove a double-exponential upper bound on the degree and on the complexity of constructing a Janet basis of a $D$-module. This generalizes a well known bound on the complexity of a Gr\"obner basis...
On the construction of a family of transversal subspaces over finite fields (2007)
Chistov, Alexander, Fournier, Hervé, Koiran, Pascal, Perifel, Sylvain
Let k be a field. We are interested in the families of r-dimensional subspaces of kn with the following transversality property: any linear subspace of kn of dimension n-r is transversal to at least...
On the construction of a family of transversal subspaces over finite fields (2007)
Chistov, Alexander, Fournier, Hervé, Koiran, Pascal, Perifel, Sylvain
Let k be a field. We are interested in the families of r-dimensional subspaces of kn with the following transversality property: any linear subspace of kn of dimension n-r is transversal to at least...
Vandermonde Matrices, NP-Completeness, and Transversal Subspaces. (2002)
Chistov, Alexander, Fournier, Hervé, Gurvits, Leonid, Koiran, Pascal
(eng) Let E be a vector space of dimension n over an infinite field K. We give polynomial time constructions of families of r-dimensional subspaces of E with the following transversality property:...
Polynomial Time Algorithms for Modules Over Finite Dimensional Algebras (1997)
Alexander Chistov, Gábor Ivanyos, Marek Karpinski
We present polynomial time algorithms for some fundamental tasks from representation theory of finite dimensional algebras. These involve testing (and constructing) isomorphisms of modules as well as...