Symbolic asymptotics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Algorithms and computation in mathematics
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 235-240 |
| Beschreibung: | XI, 243 S. graph. Darst. 24 cm |
| ISBN: | 3540210970 |
Internformat
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
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| 490 | 1 | |a Algorithms and computation in mathematics |v 12 | |
| 500 | |a Literaturverz. S. 235-240 | ||
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| 650 | 4 | |a Asymptotic expansions | |
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Datensatz im Suchindex
| _version_ | 1804132977411620864 |
|---|---|
| adam_text | JOHN R. SHACKELL SYMBOLIC ASYMPTOTICS SPRINGER CONTENTS INTRODUCTION 1
ZERO EQUIVALENCE 7 2.1 ZERO-EQUIVALENCE OF CONSTANTS 8 2.1.1
RICHARDSON S UNIFORMITY CONJECTURE 11 2.2 ZERO-EQUIVALENCE OF FUNCTIONS
13 2.2.1 EXAMPLES 22 2.2.2 THE SETS SI 25 2.3 MODULAR METHODS IN ZERO
EQUIVALENCE 27 2.3.1 HENSEL LIFTING 28 2.3.2 EXAMPLES 30 2.4 GROWTH IN
DEGREES 31 2.4.1 CANONICAL FORMS 32 2.5 SYSTEMS OF PARTIAL DIFFERENTIAL
EQUATIONS 33 2.5.1 NOTATION 33 2.5.2 RADICAL DIFFERENTIAL IDEALS 35
2.5.3 COMPUTING CHARACTERISTIC SETS 36 2.5.4 THE ROSENFELD-GROBNER
ALGORITHM 36 2.5.5 CONSEQUENCES, APPLICATIONS 38 2.5.6 ZERO EQUIVALENCE
39 2.6 FINDING SYMMETRIES 39 HARDY FIELDS 43 3.1 DEFINITIONS AND
EXAMPLES . 43 3.2 BUILDING HARDY FIELDS 45 3.3 ROUGH COMPARISONS 50 3.4
THE MAP 72 54 OUTPUT DATA STRUCTURES 59 4.1 ASYMPTOTIC POWER SERIES 59
4.2 MULTISERIES 61 X CONTENTS 4.3 OPERATIONS ON MULTISERIES 63 4.3.1
SUBSTITUTING INTO A POWER SERIES 65 4.3.2 THE LOGARITHM OF A MULTISERIES
68 4.3.3 THE EXPONENTIAL OF A MULTISERIES 69 4.3.4 POWERS OF A
MULTISERIES 69 4.3.5 AMALGAMATING SCALES 70 4.3.6 SUBSTITUTING ONE
MULTISERIES INTO ANOTHER 70 4.4 NESTED EXPANSIONS 71 4.4.1 COMPARISON OF
NESTED FORMS 74 4.4.2 OPERATIONS ON NESTED FORMS AND EXPANSIONS 76 4.5
THE ALGEBRA OF STAR PRODUCTS 78 4.5.1 DEFINITIONS AND ELEMENTARY
PROPERTIES 78 4.5.2 DIFFERENTIATION AND STAR PRODUCTS 81 ALGORITHMS FOR
FUNCTION TOWERS 83 5.1 THE EXP-LOG ALGORITHM 84 5.1.1 CASE 1: /; = LOG
H, H E FI-I 85 5.1.2 CASE 2: F T = EXPH, H E TI- 86 5.1.3 HANDLING
DENOMINATORS AND OTHER POWERS 87 5.1.4 SUMMARY OF THE ALGORITHM 88 5.1.5
EXAMPLES 88 5.2 ASYMPTOTIC FIELDS 92 5.2.1 ADDING EXPONENTIALS 100 5.2.2
ADDING INTEGRALS 101 5.2.3 ALGEBRAIC EQUATIONS 110 5.3 COMPOSITIONS WITH
MEROMORPHIC FUNCTIONS 116 5.4 CARTESIAN REPRESENTATIONS 125 ALGEBRAIC
DIFFERENTIAL EQUATIONS 129 6.1 NESTED FORMS OF HARDY-FIELD SOLUTIONS 130
6.1.1 EXAMPLES 140 6.2 THE NUMBER OF CASES 144 6.3 REDUCING THE
COMPLEXITY 150 6.3.1 A THEOREM FOR SPARSE DIFFERENTIAL EQUATIONS 151
INVERSE FUNCTIONS 155 7.1 INVERTING A NESTED EXPANSION 156 7.1.1 SUMMARY
OF THE ALGORITHM FOR INVERSION 161 7.1.2 EXAMPLE 161 7.2 MULTISERIES OF
INVERSE FUNCTIONS 163 7.2.1 PROOF OF THE ITERATION FORMULA 169 7.2.2
ASYMPTOTIC FIELDS AND INVERSE FUNCTIONS 173 CONTENTS XI IMPLICIT
FUNCTIONS 175 8.1 A SPECIAL CASE 176 8.1.1 COMPUTATION AND CHECKING OF
CANDIDATES 177 8.1.2 EXAMPLES 178 8.2 SYSTEMS OF EXP-LOG EQUATIONS 179
8.2.1 ZERO EQUIVALENCE 180 8.2.2 SKETCH OF THE METHOD 180 8.2.3 BUILDING
ESTIMATES FROM THE TOWER OF FIELDS 182 8.2.4 EXTENSION BY A LOGARITHM
182 8.2.5 EXTENSION BY AN EXPONENTIAL 183 8.2.6 OBTAINING THE NESTED
FORMS 184 8.2.7 EXAMPLE 1 185 8.2.8 EXAMPLE 2 187 8.2.9 EXAMPLE 3 189
STAR*PRODUCT EXPANSIONS 191 9.1 EXP-LOG EXPANSIONS 191 9.1.1 REWRITING
EXP-LOG EXPRESSIONS INTO STANDARD STAR EXPANSION FORM 193 9.1.2 ORDER
COMPARISONS 196 9.2 GROWTH CLASSES IN HARDY FIELDS 201 9.2.1
GENERALIZING THE 7 N S 201 9.3 GENERALIZED STAR PRODUCTS 204 9.3.1
EXPANSIONS 207 9.3.2 NON-INTEGRAL ITERATES AND MULTIPLE SCALES 208 9.4
REAL ITERATES OF INCREASING FUNCTIONS 209 OSCILLATING FUNCTIONS 215 10.1
AN INTERVAL CALCULUS ALGORITHM 216 10.1.1 OUR CALCULUS OF INTERVALS 217
10.2 LIM-SUPS AND LIM-INFS 220 10.3 WANDERING FUNCTIONS 224 10.4
WANDERING EXPANSIONS 231 REFERENCES 235 INDEX 241
|
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| author | Shackell, John R. 1943- |
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| author_facet | Shackell, John R. 1943- |
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| dewey-full | 511/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.4 |
| dewey-search | 511/.4 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| indexdate | 2024-07-09T20:01:23Z |
| institution | BVB |
| isbn | 3540210970 |
| language | English |
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| physical | XI, 243 S. graph. Darst. 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
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| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spelling | Shackell, John R. 1943- Verfasser (DE-588)129213977 aut Symbolic asymptotics John R. Shackell Berlin [u.a.] Springer 2004 XI, 243 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 12 Literaturverz. S. 235-240 Algorithms Asymptotic expansions Computeralgebra (DE-588)4010449-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 s Asymptotik (DE-588)4126634-1 s Computeralgebra (DE-588)4010449-7 s DE-604 Algorithms and computation in mathematics 12 (DE-604)BV011131286 12 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012945274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shackell, John R. 1943- Symbolic asymptotics Algorithms and computation in mathematics Algorithms Asymptotic expansions Computeralgebra (DE-588)4010449-7 gnd Asymptotik (DE-588)4126634-1 gnd Reelle Funktion (DE-588)4048918-8 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)4126634-1 (DE-588)4048918-8 |
| title | Symbolic asymptotics |
| title_auth | Symbolic asymptotics |
| title_exact_search | Symbolic asymptotics |
| title_full | Symbolic asymptotics John R. Shackell |
| title_fullStr | Symbolic asymptotics John R. Shackell |
| title_full_unstemmed | Symbolic asymptotics John R. Shackell |
| title_short | Symbolic asymptotics |
| title_sort | symbolic asymptotics |
| topic | Algorithms Asymptotic expansions Computeralgebra (DE-588)4010449-7 gnd Asymptotik (DE-588)4126634-1 gnd Reelle Funktion (DE-588)4048918-8 gnd |
| topic_facet | Algorithms Asymptotic expansions Computeralgebra Asymptotik Reelle Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012945274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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