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Dongming Wang — Elimination Practice: Software Tools and Applications
Dongming Wang — Elimination Practice: Software Tools and Applications

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Название: Elimination Practice: Software Tools and Applications

Автор: 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: en

Рубрика: Руководства по программному обеспечению/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 232

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathbb F$-modified      20 30 37
$\mathbb F$-modified quasi-characteristic set      20
Algebraic routine      45
Algebraic variety      23 173
Algebraic variety, irreducible      33 59
Algorithm, ${F}_{4}$      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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