2009/01/01 by Mark Giesbrecht, Myung Sub Kim · 6 citations
Computer Science · Mathematics · #Algebra over a field #Computer science #Differential (mechanical device) #Hermite polynomials #Mathematics #Mathematics and Applications #Matrix (chemical analysis) #Matrix Theory and Algorithms #Physics #Polynomial and algebraic computation #Pure mathematics #cs.MS #cs.SC
paper · pdf · doi:10.1007/978-3-642-04103-7_12
published in Lecture notes in computer science, 118-129 (Springer Science+Business Media)
openalex publication_date 2009/01/01 · arxiv created 2009/06/22 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given an n x n matrix over the ring of differential polynomials F(t)[\D;δ], we show how to compute the Hermite form H of A, and a unimodular matrix U such that UA=H. The algorithm requires a polynomial number of operations in terms of n, degD(A), and degt(A). When F is the field of rational numbers, it also requires time polynomial in the bit-length of the coefficients.