In a preceding paper [9] we reported on some experience with a new version of the well known Gröbner algorithm with factorization and constraint inequalities. Here we discuss, how this approach may be refined to produce triangular systems in the sense of [12] and [13]. Such a refinement guarantees, different to the usual Gröbner factorizer, to produce a quasi prime decomposition, i.e. the resulting components are at least pure dimensional radical ideals. As in [9] our method weakens the usual restriction to lexicographic term orders.
Triangular systems are a very helpful tool between factorization at a heuristical level and full decomposition into prime components. Our approach grew up from a consequent interpretation of the algorithmic ideas in [5] as a delayed quotient computation in favour of early use of (multivariate) factorization. It is implemented in version 2.2 of the REDUCE package CALI [8].
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:32810 |
| Date | 25 January 2019 |
| Creators | Gräbe, Hans-Gert |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:conferenceObject, info:eu-repo/semantics/conferenceObject, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 978-3-540-60114-2 |
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