Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10325746 | Journal of Symbolic Computation | 2005 | 11 Pages |
Abstract
A well-known lemma of Suslin says that for a commutative ring A if (v1(X),â¦,vn(X))â(A[X])n is unimodular where v1 is monic and nâ¥3, then there exist γ1,â¦,γââEnâ1(A[X]) such that the ideal generated by Res(v1,e1.γ1t(v2,â¦,vn)),â¦,Res(v1,e1.γât(v2,â¦,vn)) equals A. This lemma played a central role in the resolution of Serre's Conjecture. In the case where A contains a set E of cardinality greater than degv1+1 such that yâyâ² is invertible for each yâ yâ² in E, we prove that the γi can simply correspond to the elementary operations L1âL1+yiâj=2nâ1uj+1Lj, 1â¤iâ¤â=degv1+1, where u1v1+â¯+unvn=1. These efficient elementary operations enable us to give new and simple algorithms for reducing unimodular rows with entries in K[X1,â¦,Xk] to t(1,0,â¦,0) using elementary operations in the case where K is an infinite field. Another feature of this paper is that it shows that the concrete local-global principles can produce competitive complexity bounds.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Henri Lombardi, Ihsen Yengui,