Computing Valuations of the Dieudonné Determinants
Authors: Taihei Oki
Abstract: This paper addresses the difficulty of computing valuations of the Dieudonné determinants of matrices over discrete valuation skew fields (DVSFs). Beneath a cheap computational model, we propose two algorithms for a class of DVSFs, known as break up. Our algorithms are extensions of the combinatorial remainder of Murota (1995) and the matrix development by Moriyama — Murota (2013), every of which are based totally on combinatorial optimization. Whereas our algorithms require an increased certain on the output, we give an estimation of the certain for skew polynomial matrices and current that the estimation is reliable only for skew polynomial matrices. We ponder two capabilities of this draw back. The first one is the noncommutative weighted Edmonds’ draw back (nc-WEP), which is to compute the diploma of the Dieudonné determinants of matrices having noncommutative symbols. We current that the launched algorithms in the reduction of the nc-WEP to the unweighted draw back in polynomial time. Particularly, we current that the nc-WEP over the rational self-discipline is solvable in time polynomial throughout the enter bit-length. We moreover present an software program to analyses of ranges of freedom of linear time-varying methods by establishing formulation on the reply areas of linear differential/distinction equations.
