Comprehensive Gröbner Bases in a Java Computer Algebra System
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| Titel: | Comprehensive Gröbner Bases in a Java Computer Algebra System |
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| Autoren: | Heinz Kredel |
| Weitere Verfasser: | The Pennsylvania State University CiteSeerX Archives |
| Quelle: | http://krum.rz.uni-mannheim.de/kredel/jas-ascm2009.pdf. |
| Publikationsjahr: | 2009 |
| Bestand: | CiteSeerX |
| Beschreibung: | We present an implementation of the algorithms for computing comprehensive Gröbner bases in a Java computer algebra system (JAS). Contrary to approaches to implement comprehensive Gröbner bases with minimal requirements to the computer algebra system, we aim to provide and utilize all necessary algebraic structures occurring in the algorithm. In the implementation of a condition we aim at the maximal semantic exploitation of the occurring algebraic structures: the set of equations equal zero are implemented as an ideal (with Gröbner base computation) and the set of inequalities are implemented as a multiplicative set which is simplified to polynomials of minimal degrees using, for example, square-free decomposition. With our approach we can also make the transition of a comprehensive Gröbner system to a polynomial ring over a (commutative, finite, von Neuman) regular coefficient ring and test or compute Gröbner bases in such polynomial rings. |
| Publikationsart: | text |
| Dateibeschreibung: | application/pdf |
| Sprache: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.341 |
| Verfügbarkeit: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.341 http://krum.rz.uni-mannheim.de/kredel/jas-ascm2009.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Dokumentencode: | edsbas.538EADB3 |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | We present an implementation of the algorithms for computing comprehensive Gröbner bases in a Java computer algebra system (JAS). Contrary to approaches to implement comprehensive Gröbner bases with minimal requirements to the computer algebra system, we aim to provide and utilize all necessary algebraic structures occurring in the algorithm. In the implementation of a condition we aim at the maximal semantic exploitation of the occurring algebraic structures: the set of equations equal zero are implemented as an ideal (with Gröbner base computation) and the set of inequalities are implemented as a multiplicative set which is simplified to polynomials of minimal degrees using, for example, square-free decomposition. With our approach we can also make the transition of a comprehensive Gröbner system to a polynomial ring over a (commutative, finite, von Neuman) regular coefficient ring and test or compute Gröbner bases in such polynomial rings. |
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