Elimination of variables in linear solvable polynomial algebras and partial derivative-holonomicity

[摘要] Let k be a field of characteristic 0. Based on the Gelfand-Kirillov dimension computation of modules over solvable polynomial k-algebras, where solvable polynomial algebras are in the sense of A. Kandri-Rody and V. Weispfenning (1990, J. Symbolic Comput. 9, 1-26), we prove that the elimination lemma, obtained from D. Zeilberger (1990, J. Comput. Appl. Math. 32, 321-368) by using holonomic modules over the Weyl algebra A,(k) and used in the automatic proving of special function identities, holds for a class of solvable polynomial k-algebras without any holonomicity restriction. This opens a way to the solution of the extension/contraction problem stemming from the automatic proving of multivariate identities with respect to the partial derivative -finiteness in the sense of F. Chyzak and B. Salvy (1998, J. Symbolic Comput. 26, 187-227). It also yields a partial derivative -holonomicity so that automatic proving of multivariate identities may be dealt with by manipulating polynomial function coefficients instead of rational functions. (C) 2000 Academic Press.

[发布日期] 2000-12-01