A modular algorithm to compute the generalized Hermite normal form for Z[x]-lattices

In this paper, a modular algorithm is given to compute the generalized Hermite normal form of matrices over Z[x], or equivalently, the reduced Gröbner basis of Z[x]-modules in Z[x]n. The main advantage of the algorithm is that the special structure of the Gröbner basis of ideals in Z[x] is taken int...

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Bibliographic Details
Published in:Journal of symbolic computation Vol. 81; pp. 97 - 118
Main Authors: Jing, Rui-Juan, Yuan, Chun-Ming
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.07.2017
Subjects:
Generalized Hermite normal form
Hensel Lifting
Modular algorithm
Reduced Gröbner bases
Reduced Gröbner bases
Hensel Lifting
Generalized Hermite normal form
Modular algorithm
ISSN:0747-7171, 1095-855X
Online Access:Get full text
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Summary:In this paper, a modular algorithm is given to compute the generalized Hermite normal form of matrices over Z[x], or equivalently, the reduced Gröbner basis of Z[x]-modules in Z[x]n. The main advantage of the algorithm is that the special structure of the Gröbner basis of ideals in 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.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2016.12.005