Involution: the formal theory of differential equations and its applications in computer algebra
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Algorithms and computation in mathematics
24 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXII, 650 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642012860 |
Internformat
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| 245 | 1 | 0 | |a Involution |b the formal theory of differential equations and its applications in computer algebra |c Werner M. Seiler |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XXII, 650 S. |b Ill., graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and computation in mathematics |v 24 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Involution |0 (DE-588)4162262-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017601503 | ||
Datensatz im Suchindex
| _version_ | 1804139187546357760 |
|---|---|
| adam_text | CONTENTS 1 INTRODUCTION 1 2 FORMAL GEOMETRY OF DIFFERENTIAL EQUATIONS 9
2.1 A PEDESTRIAN APPROACH TO JET BUNDLES 10 2.2 AN INTRINSIC APPROACH TO
JET BUNDLES 18 ADDENDUM: THE CONTACT STRUCTURE A LA GARDNER-SHADWICK 27
2.3 DIFFERENTIAL EQUATIONS 29 2.4 SOME EXAMPLES 48 2.5 NOTES 58 3
INVOLUTION I: ALGEBRAIC THEORY 63 3. 1 INVOLUTIVE DIVISIONS 64 ADDENDUM:
SOME ALGORITHMIC CONSIDERATIONS 72 3.2 POLYNOMIAL ALGEBRAS OF SOLVABLE
TYPE 76 3.3 HUBERT S BASIS THEOREM AND GROEBNER BASES 86 3.4 INVOLUTIVE
BASES 94 3.5 NOTES 100 4 COMPLETION TO INVOLUTION 105 4.1 CONSTRUCTIVE
DIVISIONS 106 4.2 COMPUTATION OF INVOLUTIVE BASES 110 ADDENDUM: RIGHT
AND TWO-SIDED IDEALS 118 4.3 POMMARET BASES AND 5-REGULARITY 122 4.4
CONSTRUCTION OF MINIMAL BASES AND OPTIMISATIONS 132 4.5 SEMIGROUP ORDERS
141 4.6 INVOLUTIVE BASES OVER RINGS 156 4.7 NOTES 161 5 STRUCTURE
ANALYSIS OF POLYNOMIAL MODULES 167 5. 1 COMBINATORIAL DECOMPOSITIONS 168
5.2 DIMENSION AND DEPTH 175 XVII BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/994282214 DIGITALISIERT DURCH XVIII CONTENTS 5.3
NOETHER NORMALISATION AND PRIMARY DECOMPOSITION 182 ADDENDUM: STANDARD
PAIRS 190 5.4 SYZYGIES AND FREE RESOLUTIONS 193 ADDENDUM: ITERATED
POLYNOMIAL ALGEBRAS OF SOLVABLE TYPE 207 5.5 MINIMAL RESOLUTIONS AND
CASTELNUOVO-MUMFORD REGULARITY 210 5.6 NOTES 228 6 INVOLUTION II:
HOMOLOGICAL THEORY 235 6. 1 SPENCER COHOMOLOGY AND KOSZUL HOMOLOGY 236
6.2 CARTAN S TEST 246 6.3 POMMARET BASES AND HOMOLOGY 254 6.4 NOTES 260
7 INVOLUTION III: DIFFERENTIAL THEORY 263 7.1 (GEOMETRIC) SYMBOL AND
PRINCIPAL SYMBOL 264 7.2 INVOLUTIVE DIFFERENTIAL EQUATIONS 281 7.3
COMPLETION OF ORDINARY DIFFERENTIAL EQUATIONS 296 ADDENDUM: CONSTRAINED
HAMILTONIAN SYSTEMS 302 7.4 CARTAN-KURANISHI COMPLETION 305 7.5 THE
PRINCIPAL SYMBOL REVISITED 310 7.6 -REGULARITY AND EXTENDED PRINCIPAL
SYMBOLS 317 7.7 NOTES 322 8 THE SIZE OF THE FORMAL SOLUTION SPACE 329
8.1 GENERAL SOLUTIONS 330 8.2 CARTAN CHARACTERS AND HUBERT FUNCTION 334
8.3 DIFFERENTIAL RELATIONS AND GAUGE SYMMETRIES 343 ADDENDUM: EINSTEIN S
STRENGTH 352 8.4 NOTES 353 9 EXISTENCE AND UNIQUENESS OF SOLUTIONS 357
9.1 ORDINARY DIFFERENTIAL EQUATIONS 358 9.2 THE CAUCHY-KOVALEVSKAYA
THEOREM 370 9.3 FORMALLY WELL-POSED INITIAL VALUE PROBLEMS 374 9.
CONTENTS XIX 10.5 BASIC ALGEBRAIC ANALYSIS 458 10.6 THE INVERSE SYZYGY
PROBLEM 466 ADDENDUM: COMPUTING EXTENSION GROUPS 473 ADDENDUM: ALGEBRAIC
SYSTEMS THEORY 475 10.7 COMPLETION TO INVOLUTION 480 10.8 LINEAR SYSTEMS
OF FINITE TYPE WITH CONSTANT COEFFICIENTS 494 10.9 NOTES 504 A
MISCELLANEOUS 509 A. 1 MULTI INDICES AND ORDERS 509 ADDENDUM: COMPUTING
DERIVATIVE TREES 515 A.2 REAL-ANALYTIC FUNCTIONS 517 A.3 ELEMENTARY
TRANSFORMATIONS OF DIFFERENTIAL EQUATIONS 519 A.4 MODIFIED STIRLING
NUMBERS 525 B ALGEBRA 529 B. 1 SOME BASIC ALGEBRAIC STRUCTURES 530 B.2
HOMOLOGICAL ALGEBRA 544 B.3 COALGEBRAS AND COMODULES 559 B.4 GROEBNER
BASES FOR POLYNOMIAL IDEALS AND MODULES 567 C DIFFERENTIAL GEOMETRY 585
C.I MANIFOLDS 585 C.2 VECTOR FIELDS AND DIFFERENTIAL FORMS 592 C.3
DISTRIBUTIONS AND THE FROBENIUS THEOREM 600 C.4 CONNECTIONS 604 C.5 LIE
GROUPS AND ALGEBRAS 608 C.6 SYMPLECTIC GEOMETRY AND GENERALISATIONS 610
REFERENCES 617 GLOSSARY 637 INDEX 639
|
| any_adam_object | 1 |
| author | Seiler, Werner M. |
| author_GND | (DE-588)114897395 |
| author_facet | Seiler, Werner M. |
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| author_sort | Seiler, Werner M. |
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| building | Verbundindex |
| bvnumber | BV035545517 |
| callnumber-first | Q - Science |
| callnumber-label | QA371 |
| callnumber-raw | QA371 |
| callnumber-search | QA371 |
| callnumber-sort | QA 3371 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 SK 500 SK 540 SK 920 ST 134 |
| ctrlnum | (OCoLC)382399577 (DE-599)DNB994282214 |
| 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 | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9783642012860 |
| language | English |
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| physical | XXII, 650 S. Ill., graph. Darst. 235 mm x 155 mm |
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| series2 | Algorithms and computation in mathematics |
| spelling | Seiler, Werner M. Verfasser (DE-588)114897395 aut Involution the formal theory of differential equations and its applications in computer algebra Werner M. Seiler Berlin [u.a.] Springer 2010 XXII, 650 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 24 Hier auch später erschienene, unveränderte Nachdrucke Differential equations Involution (DE-588)4162262-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Involution (DE-588)4162262-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-01287-7 Algorithms and computation in mathematics 24 (DE-604)BV011131286 24 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017601503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seiler, Werner M. Involution the formal theory of differential equations and its applications in computer algebra Algorithms and computation in mathematics Differential equations Involution (DE-588)4162262-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4162262-5 (DE-588)4012249-9 |
| title | Involution the formal theory of differential equations and its applications in computer algebra |
| title_auth | Involution the formal theory of differential equations and its applications in computer algebra |
| title_exact_search | Involution the formal theory of differential equations and its applications in computer algebra |
| title_full | Involution the formal theory of differential equations and its applications in computer algebra Werner M. Seiler |
| title_fullStr | Involution the formal theory of differential equations and its applications in computer algebra Werner M. Seiler |
| title_full_unstemmed | Involution the formal theory of differential equations and its applications in computer algebra Werner M. Seiler |
| title_short | Involution |
| title_sort | involution the formal theory of differential equations and its applications in computer algebra |
| title_sub | the formal theory of differential equations and its applications in computer algebra |
| topic | Differential equations Involution (DE-588)4162262-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differential equations Involution Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017601503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
| work_keys_str_mv | AT seilerwernerm involutiontheformaltheoryofdifferentialequationsanditsapplicationsincomputeralgebra |