Gröbner deformations of hypergeometric differential equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2000
|
| Schriftenreihe: | Algorithms and computation in mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | VIII, 254 S. graph. Darst. |
| ISBN: | 3540660658 9783642085345 |
Internformat
MARC
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| 100 | 1 | |a Saito, Mutsumi |d 1960- |e Verfasser |0 (DE-588)121330451 |4 aut | |
| 245 | 1 | 0 | |a Gröbner deformations of hypergeometric differential equations |c Mutsumi Saito ; Bernd Sturmfels ; Nobuki Takayama |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a VIII, 254 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and computation in mathematics |v 6 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 0 | 7 | |a Hypergeometrische Differentialgleichung |0 (DE-588)4261657-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gröbner-Basis |0 (DE-588)4276378-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hypergeometrische Differentialgleichung |0 (DE-588)4261657-8 |D s |
| 689 | 0 | 1 | |a Gröbner-Basis |0 (DE-588)4276378-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sturmfels, Bernd |d 1962- |e Verfasser |0 (DE-588)121330435 |4 aut | |
| 700 | 1 | |a Takayama, Nobuki |d 1959- |e Verfasser |0 (DE-588)121330486 |4 aut | |
| 830 | 0 | |a Algorithms and computation in mathematics |v 6 |w (DE-604)BV011131286 |9 6 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008661268 | ||
Datensatz im Suchindex
| _version_ | 1804127404846743552 |
|---|---|
| adam_text | Contents
1. Basic Notions 1
1.1 Grobner Bases in the Weyl Algebra 2
1.2 Weight Vectors and Non-term Orders 11
1.3 The Gauss Hypergeometric Equation 16
1.4 Holonomic Systems 28
1.5 Integrals of Products of Linear Forms 40
2. Solving Regular Holonomic Systems 51
2.1 The Grobner Fan 51
2.2 Semi-Continuity of the Holonomic Rank 62
2.3 Torus Action and Frobenius Ideals 66
2.4 Regular Holonomic Systems 77
2.5 Canonical Series Solutions 88
2.6 Construction of Series Solutions 96
3. Hypergeometric Series 103
3.1 GKZ-Hypergeometric Ideal for Generic Parameters 104
3.2 Standard Pairs and Triangulations 109
3.3 The Hypergeometric Fan 120
3.4 Logarithm-free Hypergeometric Series 127
3.5 Lower Bound for the Holonomic Rank 134
3.6 Unimodular Triangulations 138
4. Rank versus Volume 151
4.1 The Fake Indicial Ideal and an Upper Bound 154
4.2 Hypergeometric Functions from Toric Curves 161
4.3 Koszul Complexes and Cohen-Macaulay Property 167
4.4 Integer Programming and Parametric 6-functions 174
4.5 The Exceptional Hyperplane Arrangement 181
4.6 w-fiatness 186
5. Integration of Z?-modules 193
5.1 6-functions for Holonomic D-ideals 193
5.2 Computing Restrictions 199
VIII Contents
5.3 Powers of Polynomials 211
5.4 Hypergeometric Integrals 219
5.5 Computing Integrals 227
5.6 Asymptotic Expansions of Hypergeometric Integrals 235
Appendix 241
References 245
Index 251
|
| any_adam_object | 1 |
| author | Saito, Mutsumi 1960- Sturmfels, Bernd 1962- Takayama, Nobuki 1959- |
| author_GND | (DE-588)121330451 (DE-588)121330435 (DE-588)121330486 |
| author_facet | Saito, Mutsumi 1960- Sturmfels, Bernd 1962- Takayama, Nobuki 1959- |
| author_role | aut aut aut |
| author_sort | Saito, Mutsumi 1960- |
| author_variant | m s ms b s bs n t nt |
| building | Verbundindex |
| bvnumber | BV012737153 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)845317527 (DE-599)BVBBV012737153 |
| dewey-full | 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012737153 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:49Z |
| institution | BVB |
| isbn | 3540660658 9783642085345 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008661268 |
| oclc_num | 845317527 |
| open_access_boolean | |
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| physical | VIII, 254 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spelling | Saito, Mutsumi 1960- Verfasser (DE-588)121330451 aut Gröbner deformations of hypergeometric differential equations Mutsumi Saito ; Bernd Sturmfels ; Nobuki Takayama Berlin [u.a.] Springer 2000 VIII, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 6 Hier auch später erschienene, unveränderte Nachdrucke Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd rswk-swf Gröbner-Basis (DE-588)4276378-2 gnd rswk-swf Hypergeometrische Differentialgleichung (DE-588)4261657-8 s Gröbner-Basis (DE-588)4276378-2 s DE-604 Sturmfels, Bernd 1962- Verfasser (DE-588)121330435 aut Takayama, Nobuki 1959- Verfasser (DE-588)121330486 aut Algorithms and computation in mathematics 6 (DE-604)BV011131286 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008661268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saito, Mutsumi 1960- Sturmfels, Bernd 1962- Takayama, Nobuki 1959- Gröbner deformations of hypergeometric differential equations Algorithms and computation in mathematics Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd Gröbner-Basis (DE-588)4276378-2 gnd |
| subject_GND | (DE-588)4261657-8 (DE-588)4276378-2 |
| title | Gröbner deformations of hypergeometric differential equations |
| title_auth | Gröbner deformations of hypergeometric differential equations |
| title_exact_search | Gröbner deformations of hypergeometric differential equations |
| title_full | Gröbner deformations of hypergeometric differential equations Mutsumi Saito ; Bernd Sturmfels ; Nobuki Takayama |
| title_fullStr | Gröbner deformations of hypergeometric differential equations Mutsumi Saito ; Bernd Sturmfels ; Nobuki Takayama |
| title_full_unstemmed | Gröbner deformations of hypergeometric differential equations Mutsumi Saito ; Bernd Sturmfels ; Nobuki Takayama |
| title_short | Gröbner deformations of hypergeometric differential equations |
| title_sort | grobner deformations of hypergeometric differential equations |
| topic | Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd Gröbner-Basis (DE-588)4276378-2 gnd |
| topic_facet | Hypergeometrische Differentialgleichung Gröbner-Basis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008661268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
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