An algorithm for unimodular completion over Laurent polynomial rings

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• 作者：Morou Amidou ; Ihsen Yengui
• 关键词：Quillen– ; Suslin theorem ; Multivariate Laurent polynomial matrices ; Computer algebra
• 刊名：Linear Algebra and its Applications
• 出版年：2008
• 出版时间：1 October 2008
• 年：2008
• 卷：429
• 期：7
• 页码：1687-1698
• 全文大小：150 K

文摘

We present a new and simple algorithm for completion of unimodular vectors with entries in a multivariate Laurent polynomial ring over an infinite field K. More precisely, given n3 and a unimodular vector (that is, such that v₁,…,v_n=R), the algorithm computes a matrix M in M_n(R) whose determinant is a monomial such that , and thus M^-1 is a completion of to an invertible matrix.