On computing the coefficients of bivariate holonomic formal series

Autor:	Paolo Massazza, R. Radicioni
Jazyk:	angličtina
Předmět:	Work (thermodynamics) Pure mathematics General Computer Science Series (mathematics) Holonomic Holonomic systems Holonomic constraints Bivariate analysis Coefficient problem Theoretical Computer Science Formal series Cost criterion Calculus Finite set Computer Science(all) Mathematics
Zdroj:	Theoretical Computer Science. (2-3):418-438
ISSN:	0304-3975
DOI:	10.1016/j.tcs.2005.08.011
Popis:	In this work, we study the problem of computing the coefficients of holonomic formal series in two commuting variables. Given a formal series φ(x, y) = Σn,k ≥ 0 cnkxnyk specified by a holonomic system Σj=0d1 pj(x, y)∂xjφ = 0 and Σj=0d2qj(x, y)∂yjφ = 0 with a suitable finite set of intial conditions {[xayb]φ(x, y)}, we show that the coefficient [xiyj]φ(x, y) can be computed in time O(i + j) under the uniform cost criterion.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21ce3a0e9c6a74fae22e5ef7432ae716 Zobrazit plný text záznamu