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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| Veröffentlicht in: | Journal of symbolic computation Jg. 81; S. 97 - 118 |
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01.07.2017
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Yuan, Chun-Ming Jing, Rui-Juan |
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| SubjectTerms | Generalized Hermite normal form Hensel Lifting Modular algorithm Reduced Gröbner bases |
| Title | A modular algorithm to compute the generalized Hermite normal form for Z[x]-lattices |
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