Elimination methods
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wien [u.a.]
Springer
2001
|
| Schriftenreihe: | Texts and monographs in symbolic computation
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Elimination methods |c D. Wang |
| 264 | 1 | |a Wien [u.a.] |b Springer |c 2001 | |
| 300 | |a XIII, 244 S. |b graph. Darst. | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008903681 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 DAT 540f 2001 A 35183 |
|---|---|
| DE-BY-TUM_katkey | 1171254 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010572044 |
| _version_ | 1820815237016715264 |
| adam_text | Contents
List of symbols xi
1 Polynomial arithmetic and zeros 1
1.1 Polynomials 1
1.2 Greatest common divisor, pseudo division, and polynomial
remainder sequences 4
1.3 Resultants and subresultants 9
1.4 Field extension and factorization 16
1.5 Zeros and ideals 18
1.6 Hilbert s Nullstellensatz 20
2 Zero decomposition of polynomial systems 21
2.1 Triangular systems 21
2.2 Characteristic set based algorithm 25
2.3 Seidenberg s algorithm refined 37
2.4 Subresultant based algorithm 45
3 Projection and simple systems 52
3.1 Projection 53
3.2 Zero decomposition with projection 61
3.3 Decomposition into simple systems 70
3.4 Properties of simple systems 79
4 Irreducible zero decomposition 84
4.1 Irreducibility of triangular sets 84
4.2 Decomposition into irreducible triangular systems 88
4.3 Properties of irreducible triangular systems 97
4.4 Irreducible simple systems 103
5 Various elimination algorithms 107
5.1 Regular systems 107
5.2 Canonical triangular sets 118
5.3 Grobner bases 127
5.4 Resultant elimination 134
6 Computational algebraic geometry and polynomial
ideal theory 151
6.1 Dimension 151
6.2 Decomposition of algebraic varieties 155
x Contents
6.3 Ideal and radical ideal membership 172
6.4 Primary decomposition of ideals 174
7 Applications 178
7.1 Solving polynomial systems 178
7.2 Automated geometry theorem proving 184
7.3 Automatic derivation of unknown relations 203
7.4 Other geometric applications 211
7.5 Algebraic factorization 220
7.6 Center conditions for certain differential systems 227
Bibliographic notes 232
References 235
Subject index 240
|
| any_adam_object | 1 |
| author | Wang, Dongming |
| author_facet | Wang, Dongming |
| author_role | aut |
| author_sort | Wang, Dongming |
| author_variant | d w dw |
| building | Verbundindex |
| bvnumber | BV013068947 |
| callnumber-first | Q - Science |
| callnumber-label | QA192 |
| callnumber-raw | QA192 |
| callnumber-search | QA192 |
| callnumber-sort | QA 3192 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| classification_tum | DAT 540f |
| ctrlnum | (OCoLC)43707204 (DE-599)BVBBV013068947 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV013068947 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:19:56Z |
| institution | BVB |
| isbn | 3211832416 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008903681 |
| oclc_num | 43707204 |
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| owner_facet | DE-739 DE-91G DE-BY-TUM DE-703 |
| physical | XIII, 244 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in symbolic computation |
| spellingShingle | Wang, Dongming Elimination methods Polynômes Élimination (Mathématiques) Elimination Eliminationsverfahren (DE-588)4413605-5 gnd |
| subject_GND | (DE-588)4413605-5 |
| title | Elimination methods |
| title_auth | Elimination methods |
| title_exact_search | Elimination methods |
| title_full | Elimination methods D. Wang |
| title_fullStr | Elimination methods D. Wang |
| title_full_unstemmed | Elimination methods D. Wang |
| title_short | Elimination methods |
| title_sort | elimination methods |
| topic | Polynômes Élimination (Mathématiques) Elimination Eliminationsverfahren (DE-588)4413605-5 gnd |
| topic_facet | Polynômes Élimination (Mathématiques) Elimination Eliminationsverfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008903681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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