Elimination methods in polynomial computer algebra:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1998
|
| Series: | Mathematics and its applications
448 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 237 S. Ill., graph. Darst. |
| ISBN: | 0792352408 |
Staff View
MARC
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| 245 | 1 | 0 | |a Elimination methods in polynomial computer algebra |c by Valery Bykov ; Alexander Kytmanov and Mark Lazman |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1998 | |
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Record in the Search Index
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| adam_text | Table of Contents
INTRODUCTION vii
PREFACE TO THE ENGLISH EDITION ix
PREFACE BY THE ENGLISH EDITOR x
LIST OF SYMBOLS xi
Chapter 1. BASIC MATHEMATICAL FACTS 1
1. The logarithmic residue 1
2. The Newton recursion formulas 6
3. Localization theorems for the real zeros of a polynomial 11
4. The local residue (of Grothendieck) 16
5. The multidimensional logarithmic residue 21
6. The classical scheme for elimination of unknowns 24
Chapter 2. A MODIFIED ELIMINATION METHOD 31
7. A generalized transformation formula for local residues 31
8. A modified elimination method 35
9. A formula for the logarithmic derivative of the resultant 63
10. Multidimensional analogues of the Newton formulas 78
11. Elimination of unknowns in different variables. Real roots 88
Chapter 3. APPLICATIONS IN MATHEMATICAL KINETICS 99
12. Short schemes 101
12.1. The parallel scheme 101
12.2. The sequential scheme 116
13. The search for all stationary solutions 127
14. The kinetic polynomial. Single route mechanisms 137
15. Construction of the kinetic polynomial in the general case 162
Chapter 4. COMPUTER REALIZATIONS 173
16. Analytic manipulations on the computer 173
16.1. Special features, field of applications 173
16.2. The system Maple 175
17. Basic problems in computer algebra of polynomials 180
17.1. Applied problems and polynomial algebra 180
17.2. Methods and algorithms 184
17.2.1. The resultant of two polynomials 184
17.2.2. Algorithms for elimination of unknowns 185
V
vi TABLE OF CONTENTS
17.2.3. The algorithms of solvability theory 191
18. Realization of the elimination method 193
18.1. Calculation of the resultant of two polynomials 193
18.2. Conditions for non uniqueness of steady states 195
18.3. Realization of the method of Grobner bases 199
19. The construction of the resultant 207
19.1. Systems of type (8.2) 207
19.2. Kinetic polynomials, resultants and Grobner bases 215
19.3. A program for calculating the kinetic polynomial 218
List of applications 225
Bibliography 227
Index 235
|
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| indexdate | 2024-07-09T18:31:48Z |
| institution | BVB |
| isbn | 0792352408 |
| language | English Russian |
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| physical | XI, 237 S. Ill., graph. Darst. |
| publishDate | 1998 |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bykov, Valerij I. Verfasser aut Elimination methods in polynomial computer algebra by Valery Bykov ; Alexander Kytmanov and Mark Lazman Dordrecht [u.a.] Kluwer 1998 XI, 237 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 448 Algorithmes ram Algèbre - Informatique ram Calcul polynôme Informatique ram Polynômes ram Table numérique Tables ram Équations différentielles non linéaires ram Datenverarbeitung Algebra Data processing Computer algorithms Differential equations, Nonlinear Elimination Polynomials Eliminationsverfahren (DE-588)4413605-5 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Computeralgebra (DE-588)4010449-7 s Eliminationsverfahren (DE-588)4413605-5 s DE-604 Kytmanov, Aleksandr M. 1949- Verfasser (DE-588)121733785 aut Lazman, Mark Verfasser aut Mathematics and its applications 448 (DE-604)BV008163334 448 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008617887&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bykov, Valerij I. Kytmanov, Aleksandr M. 1949- Lazman, Mark Elimination methods in polynomial computer algebra Mathematics and its applications Algorithmes ram Algèbre - Informatique ram Calcul polynôme Informatique ram Polynômes ram Table numérique Tables ram Équations différentielles non linéaires ram Datenverarbeitung Algebra Data processing Computer algorithms Differential equations, Nonlinear Elimination Polynomials Eliminationsverfahren (DE-588)4413605-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4413605-5 (DE-588)4010449-7 |
| title | Elimination methods in polynomial computer algebra |
| title_auth | Elimination methods in polynomial computer algebra |
| title_exact_search | Elimination methods in polynomial computer algebra |
| title_full | Elimination methods in polynomial computer algebra by Valery Bykov ; Alexander Kytmanov and Mark Lazman |
| title_fullStr | Elimination methods in polynomial computer algebra by Valery Bykov ; Alexander Kytmanov and Mark Lazman |
| title_full_unstemmed | Elimination methods in polynomial computer algebra by Valery Bykov ; Alexander Kytmanov and Mark Lazman |
| title_short | Elimination methods in polynomial computer algebra |
| title_sort | elimination methods in polynomial computer algebra |
| topic | Algorithmes ram Algèbre - Informatique ram Calcul polynôme Informatique ram Polynômes ram Table numérique Tables ram Équations différentielles non linéaires ram Datenverarbeitung Algebra Data processing Computer algorithms Differential equations, Nonlinear Elimination Polynomials Eliminationsverfahren (DE-588)4413605-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Algorithmes Algèbre - Informatique Calcul polynôme Informatique Polynômes Table numérique Tables Équations différentielles non linéaires Datenverarbeitung Algebra Data processing Computer algorithms Differential equations, Nonlinear Elimination Polynomials Eliminationsverfahren Computeralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008617887&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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