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Dongming Wang — Elimination Practice: Software Tools and Applications
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Название: Elimination Practice: Software Tools and ApplicationsАвтор: Dongming Wang Аннотация: With a software library included, this book provides an elementary introduction to polynomial elimination in practice. The library Epsilon, implemented in Maple and Java, contains more than 70 well-documented functions for symbolic elimination and decomposition with polynomial systems and geometric reasoning. The book presents the functionality, implementation, and performance of Epsilon and demonstrates the usefulness of the elimination tool by a number of selected applications, together with many examples and illustrations. The reader will find Epsilon an efficient tool, applicable to a wide range of problems in science, engineering, and industry, and this book an accessible exposition and a valuable reference for elimination theory, methods, and practice.
Язык: Рубрика: Руководства по программному обеспечению /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 232Добавлена в каталог: 31.10.2010Операции: Положить на полку |
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20 30 37 20 Algebraic routine 45 Algebraic variety 23 173 Algebraic variety, irreducible 33 59 Algorithm, 87 Algorithm, BasSet 31 Algorithm, CharSetN 31 42 117 135 Algorithm, Discover 136 Algorithm, ExtendedCharacteristicSeries 32 Algorithm, FactorA 34 181 184 Algorithm, FactorB 34 18If Algorithm, FGLM 86 Algorithm, GenCharSet 30 f Algorithm, IrrCharSer 32 124 Algorithm, IrrCharSerE 32 124 Algorithm, IrrTriSer 53 124 Algorithm, IrrVarDec 34 53 60 Algorithm, LexTriangular 86 Algorithm, MacRes 90 Algorithm, ModCharSet 30 f Algorithm, PrildeDec 34 Algorithm, PriTriSys 117 135 Algorithm, ProjA 114 Algorithm, ProverB 125 Algorithm, ProverC 125 Algorithm, ProverD 125 Algorithm, QualrrTriSer 32 53 Algorithm, RegSer 58 Algorithm, SimSer 58 Algorithm, SubresChain 91 Algorithm, TriangularForm 31 42 Algorithm, TriangularFormC 31 42 Algorithm, TriSer 32 52 123 Algorithm, TriSerP 52 113 Algorithm, TriSerS 57 123 Ascending set 29 Ascending set, differential 36 Associated prime 24 33 Aubry, P. 84 Barth sextic 9 Barth, W. 12 Basic set 42 Bertrand curve 194 Bertrand theorem 194 Bezout matrix 89 Bezout resultant 89 Bezout, E. 89 Blaschke, W. 132 Bradford, R. 83 Brahmagupta formula 138 Brillhart, J. 141 Bronstein, M. 110 Buchberger, B. 85 f Buse, L. 90 Butterfly Theorem 4 81 Cayley cubic 13 Center 185 Ceva theorem 81 Characteristic series 31 57 Characteristic series, differential 37 f Characteristic series, extended 31 Characteristic series, irreducible 22 32 59 Characteristic series, quasi-irreducible 32 Characteristic set 28 30 37 66 115 Characteristic set, differential 36 f Characteristic set, modified 30 42 CharSer 31 f 123 Cherkas condition 191 Cherkas, L.A. 191 Cheung, C.W.S. 91 Chinese matrix method 96 Chou, S.-C. 83 Chtcherba, A. 89 class 19 35 Clifford algebra 115 Codazzi — Mainardi equation 197 Conclusion 115 Constant 19 Contradictory 29 Curvature 167 194 198 Cyclic system 99 Czapor, S.R. 109 Derivative 35 Desargues theorem 81 Differential 24 37 Differential ascending set 36 Differential characteristic series 37 f Differential characteristic series, irreducible 39 57 Differential characteristic series, quasi-irreducible 38 Differential characteristic set 36 f Differential characteristic set, modified 37 Differential polynomial 35 Differential polynomial set 36 Differential polynomial system 36 Differential pseudo-remainder 36 f Differential quasi-ascending set 36 Differential quasi-characteristic set 36 f Differential quasi-characteristic set, modified 37 Differential routine 45 Differential triangular series 24 55 Differential triangular series, fine 24 55 Differential triangular series, quasi-irreducible 56 Differential triangular set 36 Differential triangular set, fine 37 Differential triangular set, irreducible 38 Differential triangular system 24 55 Differential triangular system, fine 24 55 Differential weak-ascending set 36 Differential weak-characteristic series 37 f Differential weak-characteristic series, irreducible 57 Differential weak-characteristic series, quasi-irreducible 38 Differential weak-characteristic set 36 f Differential weak-characteristic set, modified 37 Discriminant surface 180 Dixon matrix 89 Dixon, A.L. 89 Dubuque, B. 84 Emiris, I.Z. 91 Equality type 116 Equidimensional 173 Eulerline 81 Extended characteristic series 31 Extended weak-characteristic series 31 Extraneous circle 161 Faugere, J.-C. 85 87 158 165 Fee, G. 109 Feuerbach theorem 81 Fine 20 55 Fine differential triangular series 24 55 Fine differential triangular set 37 Fine differential triangular system 24 55 Fine triangular series 20 Fine triangular set 20 Fine triangular system 20 First fundamental form 196 Focal value 185 Frenet formula 194 Full projection 52 Function, advance 87 Function, algebraic 69 77 116 Function, bezout 89 Function, BezoutMatrix 89 Function, bezres 89 f 157 Function, cfactor 34 47 181 184 Function, char set 30 43 46 182 Function, charser 31f 46f Function, CharSet 19 31 Function, charsets [ivd] 65 187 192 Function, char_series 83 Function, Chinese 69 Function, Click 75 Function, convert 87 Function, coordinate 67 77 81 116 Function, csolve 34 f 47 48 Function, dcharset 36 f 48 Function, dcs 37 48 Function, decompose 83f Function, degree 29 Function, Demo 75 Function, depend 40 Function, df 40 Function, dies 38 f 48 Function, diff 2 10 Function, discrim 2 Function, diss 37 f 40 Function, dits 55 f 195 Function, dmcharset 36 f 48 Function, dmes 37 48 Function, Dprover 71 79 194 Function, dqics 38 48 Function, dqits 53 55 Function, drim 53 55 57 Function, drs 37f Function, dtriser 55 Function, ecs 31 f 46 Function, eics 32 42 47 Function, English 69 Function, factor 2 Function, fglm 87 Function, format 40 Function, gbasis 86f Function, GCprover 71 80 118 Function, Generic 70 73 78 81 Function, Geometric 7 72 154 Function, Gprover 71 80 Function, Groebner[normalf] 120 126 Function, ics 25 32 34 42 47 65 174 Function, implicit 91 158 161 Function, indext 92 f Function, iniset 22 29 34 93 Function, irreducibleCharacteristic Series 83 Function, its 25 51 53 58 65 99 102 108 110 112 125 146 160 169 171 174 179 188 Function, ivd 33 f 42 47 51 53 59 65 174 178 188 192 Function, lcoeff 41 Function, Let 67 f 77 Function, lextriangular 87 Function, licon 93 185 187 191 Function, Load 74 f 154 Function, Logic 69 f Function, macres 90 f 157 Function, mcharset 30 f 34 42 46 49 102 107 Function, mecs 31 f 42 46 Function, mes 31 f 42 46 63 98 Function, minibasis 86f Function, multires 90 Function, mvresultant 91 Function, normalf 118 120 126 Function, normat 61 92 108 112 175 183 Function, pid 33 f 64 178 Function, pquo 183 Function, prem 6 20 41 117 123 126 Function, Print 72 f Function, Prove 24 70 Function, qics 32 42 47 63 152 184 Function, qits 53 58 63 Function, regser 51 57 62 64 98 111 113 157 163 Function, remset 20 29 Function, resultant 2 89 Function, rim 53 178 Function, Rosenfeld — Groebner 198 Function, Search 74 f Function, simser 57 62 64 98 113 Function, sisys [its] 25 60 64 Function, sisys [qits] 53 63 Function, sisys [triser] 59 63 98 Function, sisys[ivd] 65 Function, solve 35 Function, solvet 3 Function, ssolve 57 Function, subres 91 Function, subresultantChain 91 Function, Subresultants 91 Function, Sylvester 89 Function, SylvesterMatrix 89 Function, system 26 72 Function, Tprover 71 78f 125 Function, triang 83 Function, TRIANGSYS 84 Function, triser 52 57 62 98 113 125 178 Function, trisys [its] 25 51 53 65 99 102 108 110 112 125 146 160 169 171 174 179 188 Function, trisys [ivd] 51 65 192 Function, trisys [qits] 53 63 Function, trisys [triser] 62f 98 113 125 178 Function, tsolve 53 84 Function, uvd 22 59 64 Function, Wprover 70 80 118 134 Gao, X.-S. 83 Gauss equation 197 Gauss formula 197 Gauss line 81 Gauss point 81 Gaussian curvature 167 Gaussian elimination 96 Geddes, K. O. 109 Gelernter, H. 115 GENERIC 116 125 Geometric dependent 118 Global variable, _contracted_ 43 Global variable, _factorized_ 54f 61 111 Global variable, _reduced_ 54 f 62 98 Gontard, M.C. 82 Grobner basis 3 28 66 82 85 96 115 Hemmecke, R. 100 Hilbert driven algorithm 86 Hilbert, D. 186 Hillebrand, D. 83 Hu, S. 34 Hypothesis 115 Index triple 92 Inequation 145 Initial 6 19 35 Irreducible 12 16 22 32 38 Irreducible characteristic series 22 32 59 Irreducible differential characteristic series 39 57 Irreducible differential triangular set 38 Irreducible differential weak-characteristic series 57 Irreducible triangular series 22 59 Irreducible triangular set 22 Irreducible variety 33 59 Irreducible weak-characteristic series 59 Jin, X. 81 191 Jouanolou, J.-P. 90 Kalkbrener, M. 84 f Kapur method 71 Kepler law 199 Kukles system 190 Kukles, I. S. 190 Kutzler — Stifter method 71 Lazard, D. 84 86 Lead 35 Leading coefficient 41 Leading term 97 Leading variable 3 6 29 Leisenring line 142 Leisenring theorem 81 142 Li, Z. 156 Liapunov constant 93 185 Lloyd, N.G. 192 Locus equation 145
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