Exponential space computation of Gröbner bases:
Abstract: "Given a polynomial ideal and a term order, there is a unique reduced Gröbner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of finding this normal form for any given polynomial, w...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
München
1996
|
| Series: | Technische Universität <München>: TUM-I
9606 |
| Subjects: | |
| Summary: | Abstract: "Given a polynomial ideal and a term order, there is a unique reduced Gröbner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of finding this normal form for any given polynomial, without prior computation of the Gröbner basis. This is done by transforming a representation of the normal form into a system of linear equations and solving this system. Using the ability to find normal forms, we show how to obtain the Gröbner basis in exponential space." |
| Physical Description: | 14 S. |
Staff View
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| 245 | 1 | 0 | |a Exponential space computation of Gröbner bases |c Klaus Kühnle ; Ernst W. Mayr |
| 264 | 1 | |a München |c 1996 | |
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| 490 | 1 | |a Technische Universität <München>: TUM-I |v 9606 | |
| 520 | 3 | |a Abstract: "Given a polynomial ideal and a term order, there is a unique reduced Gröbner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of finding this normal form for any given polynomial, without prior computation of the Gröbner basis. This is done by transforming a representation of the normal form into a system of linear equations and solving this system. Using the ability to find normal forms, we show how to obtain the Gröbner basis in exponential space." | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a Gröbner bases | |
| 650 | 4 | |a Ideals (Algebra) | |
| 650 | 4 | |a Polynomial rings | |
| 700 | 1 | |a Mayr, Ernst W. |d 1950- |e Verfasser |0 (DE-588)109817923 |4 aut | |
| 830 | 0 | |a Technische Universität <München>: TUM-I |v 9606 |w (DE-604)BV006185376 |9 9606 | |
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Record in the Search Index
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| author | Kühnle, Klaus Mayr, Ernst W. 1950- |
| author_GND | (DE-588)109817923 |
| author_facet | Kühnle, Klaus Mayr, Ernst W. 1950- |
| author_role | aut aut |
| author_sort | Kühnle, Klaus |
| author_variant | k k kk e w m ew ewm |
| building | Verbundindex |
| bvnumber | BV011109102 |
| ctrlnum | (OCoLC)36404470 (DE-599)BVBBV011109102 |
| format | Book |
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| id | DE-604.BV011109102 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:04:08Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007443162 |
| oclc_num | 36404470 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-91G DE-BY-TUM |
| physical | 14 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series | Technische Universität <München>: TUM-I |
| series2 | Technische Universität <München>: TUM-I |
| spelling | Kühnle, Klaus Verfasser aut Exponential space computation of Gröbner bases Klaus Kühnle ; Ernst W. Mayr München 1996 14 S. txt rdacontent n rdamedia nc rdacarrier Technische Universität <München>: TUM-I 9606 Abstract: "Given a polynomial ideal and a term order, there is a unique reduced Gröbner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of finding this normal form for any given polynomial, without prior computation of the Gröbner basis. This is done by transforming a representation of the normal form into a system of linear equations and solving this system. Using the ability to find normal forms, we show how to obtain the Gröbner basis in exponential space." Algebras, Linear Gröbner bases Ideals (Algebra) Polynomial rings Mayr, Ernst W. 1950- Verfasser (DE-588)109817923 aut Technische Universität <München>: TUM-I 9606 (DE-604)BV006185376 9606 |
| spellingShingle | Kühnle, Klaus Mayr, Ernst W. 1950- Exponential space computation of Gröbner bases Technische Universität <München>: TUM-I Algebras, Linear Gröbner bases Ideals (Algebra) Polynomial rings |
| title | Exponential space computation of Gröbner bases |
| title_auth | Exponential space computation of Gröbner bases |
| title_exact_search | Exponential space computation of Gröbner bases |
| title_full | Exponential space computation of Gröbner bases Klaus Kühnle ; Ernst W. Mayr |
| title_fullStr | Exponential space computation of Gröbner bases Klaus Kühnle ; Ernst W. Mayr |
| title_full_unstemmed | Exponential space computation of Gröbner bases Klaus Kühnle ; Ernst W. Mayr |
| title_short | Exponential space computation of Gröbner bases |
| title_sort | exponential space computation of grobner bases |
| topic | Algebras, Linear Gröbner bases Ideals (Algebra) Polynomial rings |
| topic_facet | Algebras, Linear Gröbner bases Ideals (Algebra) Polynomial rings |
| volume_link | (DE-604)BV006185376 |
| work_keys_str_mv | AT kuhnleklaus exponentialspacecomputationofgrobnerbases AT mayrernstw exponentialspacecomputationofgrobnerbases |