کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10325746 | 676795 | 2005 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Suslin's algorithms for reduction of unimodular rows
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 39, Issue 6, June 2005, Pages 707-717
Journal: Journal of Symbolic Computation - Volume 39, Issue 6, June 2005, Pages 707-717
نویسندگان
Henri Lombardi, Ihsen Yengui,