A modular algorithm to compute the generalized Hermite normal form for -lattices

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• 作者：Rui-Juan Jing ^{rjing@amss.ac.cn} ; Chun-Ming Yuan ^{cmyuan@mmrc.iss.ac.cn}
• 关键词：Generalized Hermite normal form ; Reduced Grö ; bner bases ; Modular algorithm ; Hensel Lifting
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：July-August 2017
• 年：2017
• 卷：81
• 期：Complete
• 页码：97-118
• 全文大小：554 K
• 卷排序：81

文摘

In this paper, a modular algorithm is given to compute the generalized Hermite normal form of matrices over Z[x]Z[x], or equivalently, the reduced Gröbner basis of Z[x]Z[x]-modules in Z[x]nZ[x]n. The main advantage of the algorithm is that the special structure of the Gröbner basis of ideals in Z[x]Z[x] is taken into consideration. The algorithm is deterministic and seems to be the most efficient available algorithm for inputs with relatively low degrees.