# Discrete Mathematics & Theoretical Computer Science

## Volume 1 n° 1 (1997), pp. 139-147

author: | S. Cojocaru and V. Ufnarovski |
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title: | BERGMAN under MS-DOS and Anick’s resolution |

keywords: | Gröbner basis, Hilbert series, resolution |

abstract: | Noncommutative algebras, defined by the generators and relations, are considered. The definition and main results connected with the Gröbner basis, Hilbert series and Anick’s resolution are formulated. Most attention is paid to universal enveloping algebras. Four main examples illustrate the main concepts and ideas. Algorithmic problems arising in the calculation of the Hilbert series are investigated. The existence of finite state automata, defining thebehaviour of the Hilbert series, is discussed. The extensions of the BERGMAN package for IBM PC compatible computers are described. A table is provided permitting a comparison of the effectiveness of the calculations in BERGMAN with the other systems. |

reference: | S. Cojocaru and V. Ufnarovski (1997),
BERGMAN under MS-DOS and Anick’s resolution,
Discrete Mathematics and Theoretical Computer Science 1, pp. 139-147 |

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