Gröbner bases for binomials with parametric exponents:
Abstract: "We study the uniformity of Buchberger algorithms for computing Gröbner bases with respect to a natural number parameter k in the exponents of the input polynomials. The problem is motivated by positive results of T. Takahashi on special exponential parameter series of polynomial sets...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Passau
Fak. für Math. und Informatik, Univ. Passau
2004
|
| Schriftenreihe: | MIP
2004,02 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We study the uniformity of Buchberger algorithms for computing Gröbner bases with respect to a natural number parameter k in the exponents of the input polynomials. The problem is motivated by positive results of T. Takahashi on special exponential parameter series of polynomial sets in singularity theory. For arbitrary input sets uniformity is in general impossible. By way of contrast we show that the Buchberger algorithm is indeed uniform up to a finite case distinction on the exponential parameter k for inputs consisting of monomials and binomials only. Under this hypothesis the case distinction is algorithmic and partitions the parameter range into Presburger sets. In each case the Buchberger algorithm is uniform and can be described explicitly and algorithmically. In the course of the algorithm the exponential parameter k enters also the coefficients as exponent. Thus the uniformity in k is established with respect to parametric exponents in both terms and coefficients. These results are obtained as a consequence of a much more general theorem concerning Buchberger algorithms for sets of monomials and binomials with arbitrary parametric coefficients and exponents, generalizing the construction of Gröbner systems." |
| Beschreibung: | 14, 3 S. |
Internformat
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| 490 | 1 | |a MIP |v 2004,02 | |
| 520 | 3 | |a Abstract: "We study the uniformity of Buchberger algorithms for computing Gröbner bases with respect to a natural number parameter k in the exponents of the input polynomials. The problem is motivated by positive results of T. Takahashi on special exponential parameter series of polynomial sets in singularity theory. For arbitrary input sets uniformity is in general impossible. By way of contrast we show that the Buchberger algorithm is indeed uniform up to a finite case distinction on the exponential parameter k for inputs consisting of monomials and binomials only. Under this hypothesis the case distinction is algorithmic and partitions the parameter range into Presburger sets. In each case the Buchberger algorithm is uniform and can be described explicitly and algorithmically. In the course of the algorithm the exponential parameter k enters also the coefficients as exponent. Thus the uniformity in k is established with respect to parametric exponents in both terms and coefficients. These results are obtained as a consequence of a much more general theorem concerning Buchberger algorithms for sets of monomials and binomials with arbitrary parametric coefficients and exponents, generalizing the construction of Gröbner systems." | |
| 650 | 4 | |a Gröbner bases | |
| 650 | 4 | |a Polynomials | |
| 830 | 0 | |a MIP |v 2004,02 |w (DE-604)BV000905393 |9 2004,02 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010699162 | |
Datensatz im Suchindex
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|---|---|
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| author | Weispfenning, Volker 1944- |
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| author_sort | Weispfenning, Volker 1944- |
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| building | Verbundindex |
| bvnumber | BV017822297 |
| classification_rvk | SS 5600 |
| ctrlnum | (OCoLC)57192929 (DE-599)BVBBV017822297 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV017822297 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:05:00Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010699162 |
| oclc_num | 57192929 |
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| physical | 14, 3 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Fak. für Math. und Informatik, Univ. Passau |
| record_format | marc |
| series | MIP |
| series2 | MIP |
| spelling | Weispfenning, Volker 1944- Verfasser (DE-588)108063550 aut Gröbner bases for binomials with parametric exponents V. Weispfenning Passau Fak. für Math. und Informatik, Univ. Passau 2004 14, 3 S. txt rdacontent n rdamedia nc rdacarrier MIP 2004,02 Abstract: "We study the uniformity of Buchberger algorithms for computing Gröbner bases with respect to a natural number parameter k in the exponents of the input polynomials. The problem is motivated by positive results of T. Takahashi on special exponential parameter series of polynomial sets in singularity theory. For arbitrary input sets uniformity is in general impossible. By way of contrast we show that the Buchberger algorithm is indeed uniform up to a finite case distinction on the exponential parameter k for inputs consisting of monomials and binomials only. Under this hypothesis the case distinction is algorithmic and partitions the parameter range into Presburger sets. In each case the Buchberger algorithm is uniform and can be described explicitly and algorithmically. In the course of the algorithm the exponential parameter k enters also the coefficients as exponent. Thus the uniformity in k is established with respect to parametric exponents in both terms and coefficients. These results are obtained as a consequence of a much more general theorem concerning Buchberger algorithms for sets of monomials and binomials with arbitrary parametric coefficients and exponents, generalizing the construction of Gröbner systems." Gröbner bases Polynomials MIP 2004,02 (DE-604)BV000905393 2004,02 |
| spellingShingle | Weispfenning, Volker 1944- Gröbner bases for binomials with parametric exponents MIP Gröbner bases Polynomials |
| title | Gröbner bases for binomials with parametric exponents |
| title_auth | Gröbner bases for binomials with parametric exponents |
| title_exact_search | Gröbner bases for binomials with parametric exponents |
| title_full | Gröbner bases for binomials with parametric exponents V. Weispfenning |
| title_fullStr | Gröbner bases for binomials with parametric exponents V. Weispfenning |
| title_full_unstemmed | Gröbner bases for binomials with parametric exponents V. Weispfenning |
| title_short | Gröbner bases for binomials with parametric exponents |
| title_sort | grobner bases for binomials with parametric exponents |
| topic | Gröbner bases Polynomials |
| topic_facet | Gröbner bases Polynomials |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT weispfenningvolker grobnerbasesforbinomialswithparametricexponents |