Cox D.A., Little J., O'Shea D. — Using Algebraic Geometry :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Cox D.A., Little J., O'Shea D. — Using Algebraic Geometry

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Using Algebraic Geometry

Авторы: Cox D.A., Little J., O'Shea D.

Аннотация:

This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grobner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 499

Добавлена в каталог: 20.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Perfect code      419 424
Permutation matrix      3799381 384 385
Pfister, A.      158 169 471
Pfister, g.      158 471
PID      5 39
Piecewise polynomial function      359 385-388 390 404
Pohl, W.      158 471
Poisson formula      92
Pole      451 452 454 463 466
Pole, order of      451 452 454 466
Poli, A.      414 473
Polyhedral complex      389-391 393 398 402 403 405
Polyhedral complex, cell of      see cell of
Polyhedral complex, dimension of      see dimension of
Polyhedral complex, edge of      see edge of a polyhedral complex
Polyhedral complex, hereditary      see hereditary complex
Polyhedral complex, pure      see pure complex
Polyhedral complex, pure, hereditary      see pure hereditary
Polyhedral complex, simplicial      see simplicial complex
Polyhedral complex, vertex of      see vertex of
Polyhedral region      359 361 373 374 376 389
Polyhedral region, unbounded      361 376
Polyhedral subdivision      344 (see also mixed subdivision and polyhedral complex)
Polyhedron      291
Polynomial      2
Polynomial ring ( $k[x_{1}, ..., x_{n}]$ )      2 165 222 227 231 233 234 359 364
Polynomial splines      see splines
Polynomial, relation to polytopes      290 294ff
Polytope      viii ix 290ff 316ff 327 336 340 345 346 389
Polytope, convex      see polytope
Polytope, dimension of      see dimension of
Polytope, edge of      see edge of
Polytope, face of      see face of
Polytope, facet of      see facet of
Polytope, fundamental lattice      see fundamental lattice polytope
Polytope, lattice      see lattice polytope
Polytope, lift of      see lift of a polytope
Polytope, Minokowski sum of      see Minkowski sum of polytopes
Polytope, Newton      see Newton polytope
Polytope, relation to homogenizing sparse equations      309 313
Polytope, relation to integer programming      359 361
Polytope, relation to sparse resultants      301ff 343 344
Polytope, supporting hyperplane of      see supporting hyperplane
Polytope, surface area of      see surface area of a polytope
Polytope, vertex of      see vertex of
Polytope, volume of      see volume of a polytope
Position-over-term      see POT order
POT order      201ff 219 223 441
Power method      see eigenvalues
Presentation matrix      189ff 197 222 223 226 237
Presentation matrix, of hom(, N)      192 (see also minimal presentation)
Presentation of a module      234 236-238 243 246
Primary decomposition      144 149
Primary ideal      149
Prime field      407
Prime ideal      5 23 136
Primitive element (of a field extension)      412 414 426 431 434 436 445 450 459 460 465
Primitive inward pointing normal      see inward pointing normal primitive
Primitive vector in $\mathbb{Z}^{n}$       333 340 341
Principal axis theorem      65
Principal ideal      5 247 425
Principal ideal domain (PID)      see FID
prism      326
Product of ideals      22
Product of rings      44 141 149
Product order      15 174 372
Projection map      86 88 119
Projective closure      451 454
Projective curve      451 453 454 457 463
Projective dimension of a module      249
Projective embedding      452
Projective Extension Theorem      86 119
Projective module      194 230-233 245
Projective n-dimensional space ( $\mathbb{P}^{n}$ )      85 89 108 119 252 266 270 307ff 402 466
Projective variety      18 85 90 252
Projective variety, affine part ( $\mathbb{C}\cap V$ )      90
Projective variety, part at infinity ( $\mathbb{P}^{n-one}\cap V$ )      90
Projective, Projective Images principle      308 312
Projective, Projective Varieties in Affine Space principle      90
Puiseux expansion      331
Punctured codes      450 451
Pure complex      389 391 398
Pure, hereditary complex      391 392 394 396 397 402 405
Qhull      348 350
Qi, D.      274 474
QR algorithm      56
Quadratic formula      109
Quadratic splines      387 388 400
Quillen - Suslin Theorem      187 194 231 232
Quillen, D.      187 194 231 473
Quintic del Pezzo surface      288
Quotient ideal (I: )      6 23 221
Quotient module (M/N)      183 190 206 210 225ff 235 244 440 443
Quotient of modules (M: N)      193
Quotient ring ( $k[x_{1}, ..., x_{n}]/I$ )      35 36 130 182 264 268 269 272 273 276 278 279 285 289 354 356 375 381 383 384 4066408 414 425 427-434 440 436 453 457 465 467
R-module      see module
Radical ideal      4 5 22 23 39 43 44 58 59 62 121 465
Radical Ideal Property      4
Radical membership test      171
Radical of an ideal $I(\sqrt{I})$       4 5 20 39 40 171
Raimondo      169 173 175 468
Rank of a matrix      65 69 232 233
Rank of a module      232
Rational function      2 131 252 437 451 452 454 458 463 466
Rational function, field ( $k(x_{1}, ..., x_{n})$ )      252 264 327 328
Rational function, field of a curve      see rational function field
Rational function, field of transcendence degree one      449 452 454
Rational mapping      288 466
Rational normal curve      266 287
Rational normal scroll      287
Rational point over $\mathbb{F}_{q}(X(\mathbb{F}_{q}))$       451 452 454 455 457 462-464
Rational quartic curve      240 286
Received word      436 438 445-447
Recurrence relation      437 447
Reduce      39 167 206 240
REDUCE, CALI package      167 206 219 224 240 241
Reduced Gr $\ddot{o}$ bner basis      see Gr $\ddot{o}$ bner basis reduced
Reduced monomial      101 102
Reduced monomial, in toric context      315
Reducible variety      171
Reduction of by (Red())      156 157 160 161 163 164
Reed - Muller code      407 449ff
Reed - Muller code, binary      450
Reed - Muller code, once-punctured      458
Reed - Muller code, punctured      458 459 461
Reed - Muller code, unpunctured      461 462 464
Reed - Solomon code      426-428 431-436 444 447 449 450 452 460
Reed - Solomon decoding      435ff 449
Reed - Solomon, extended      449
Rege, A.      122 470
Regular sequence      467
Reif, J.      67 468
Reisner, G.      406
Relations among generators      188 189 193
Remainder      9 10 12 35 365-367 373 382 408 425 429-432 436 443 447 448 458 461
Remainder, in local case      159ff 165 166 168 172 173
Remainder, in module case      202-204 206 212 214
Remainder, remainder arithmetic      35
Remainder, Uniqueness of Remainders      12
Removable singularity      33
Residue classes      226 (see also coset)
Residue field ()      226
Resolution, finite free      see finite free resolution
Resolution, free      see free resolution
Resolution, graded      see graded resolution
Resolution, graded free      see graded free
Resolution, homogenization of      see homogenize a
Resolution, isomorphsim of      see isomorphic resolutions
Resolution, length of      see length of a finite free resolution
Resolution, minimal      see minimal resolution

Resolution, minimal graded      see minimal graded
Resolution, partial graded      see partial graded resolution
Resolution, trivial      see trivial resolution
Resultant      vii-ix 71 290
Resultant, (unmixed) sparse resultant      342
Resultant, and multiplicities      144 145
Resultant, computing      96ff 342ff
Resultant, d-resultant      see resultant sparse
Resultant, dense      302
Resultant, geometric meaning      85ff
Resultant, mixed      see resultant mixed
Resultant, mixed sparse      342 343 347 348 351 353 354 357
Resultant, multipolynomial      viii 71 78ff 298-302 304 307 308 330 343 347 348 353
Resultant, of two polynomials      71ff
Resultant, properties of      80 89ff
Resultant, solving equations via      see solving polynomial equations
Resultant, sparse      viii 82 106 129 298ff 306ff 330 342ff
Resultant, Sylvester determinant for      71 278
Resultant, u-resultant      see u-resultant
Revenue function      360 362 367 368
Richter, P.      32 34 473
Riemann - Roth Theorem      449 458 463 466
Riemann hypothesis      452
Ring, Cohen-Macaulay      see Cohen-Macaulay ring
Ring, commutative      see commutative ring
Ring, convergent power series      see convergent power series ring
Ring, formal power series      see formal power series ring
Ring, homomorphism of      44 52 117 120 141 149 275 281 364 367 371 377 378 406 414
Ring, integral domain      see integral domain
Ring, isomorphism of      44 137 149 150 406 430 433
Ring, localization of      see localization
Ring, Noetherian      see Noetherian ring
Ring, of invariants ( $S^{G}$ )      281 283 284
Ring, polynomial      see polynomial ring
Ring, product of      see product of rings
Ring, quotient      see quotient ring
Ring, valuation      see valuation ring
Robbiano, L.      153 473
Rojas, J.M.      x 308 336 342 337 356 473
Rose, L.      385 386 395 398-401 469 473
Row operation      195 196 230
Row operation, integer      see integer row operation
Row reduction      422
Roy, M. - F.      63 64 66 67 473
Ruffini, P.      27
S-polynomial      13 14 165 166 207 211 366
S-vector ((f, g))      2044206 212-214
Saints, K      436 449 458 471
Saito      274 474
Sakata, S.      436 473
Salmon, G.      83 103 473
Sch $\ddot{o}$ nemann, H.      158 471
Schenk, H.      386 401 473
Schmale, W.      x
Schreyer s Theorem      212 224 238 240 245 257 395
Schreyer, F. - O.      211 212 273 284 473 474
Schrijver, A.      359 474
Second fundamental theorem of invariant theory      93
Second isomorphism theorem      193
Second syzygies      234 238ff 284
Sederberg      274 278-280 470 474
Segre map      309
Semigroup of pole orders      451 452 454
Semigroup order      152ff 164-166 173
Serre problem      187 194 231
Serre's Conjecture      see Serre problem
Serre, J. - P.      187 474
Shafarevich, I.      86 88 90 91 94 474
Shannon s Theorem      420
Shape lemma      62
Shifted module      see twist of a graded module $M$

Shipping problem      359 360 363 365 367 368 370
Shurman, J.      x
Siebert      158 471
Signature of a symmetric bilinear form over $\mathbb{R}$       65 66 69
Simple root      33
simplex      292 294 324 330 347
Simplicial complex      401 404
Singer, M.      x
Singleton bound      420 427 462
singular      39 158 167 168 172 178 206 209 210 219 224 240 241 249 366 370 373 432
Singular curve      454
Singular homepage      167
Singular ideal      167 168 172 242 250 370
Singular milnor package      178
Singular module      210
Singular point      see singularity
Singular poly      172 370
Singular reduce      172 370
Singular res      242
Singular ring      167 172 209 219 242 250 370
Singular sres      249 250
Singular std      370
Singular syz      219
Singular vdim      168
Singular vector      209 210
Singularity      130 147 148 451
Singularity, isolated      147 148 177 178
Singularity, ordinary double point      150
Skew-symmetric matrix      288
Slack variable      363-367
Sloane, N.      415 427 472
Smooth curve      451 453 454 455 457
Solutions at $\infty$       108 112 115 144 329 330 part
Solving polynomial equations      viii-ix 46 60 327
Solving polynomial equations via eigenvalues      viii 51 54ff 122ff 354
Solving polynomial equations via eigenvectors      59ff 127 354
Solving polynomial equations via elimination      24ff 56
Solving polynomial equations via homotopy continuation      see homotopy continuation method
Solving polynomial equations via resultants      viii ix 71 108ff 114ff 305 329 338 342 353
Solving polynomial equations via toric varieties      313 (see also numerical methods)
Solving polynomial equations, determinant formulas      71 83 103 119
Solving polynomial equations, real solutions      63ff 67
Sparse B $\acute{e}$ zout's Theorem      see Bernstein's Theorem
Sparse Polynomial      298 329 330
Sparse resultant      see resultant sparse
Sparse system of equations      339 340
Special position      451 452 454 467
Spectral theorem      65
Speder, J. - P.      178
Spence, L.      149 471
Splines      viii ix 385ff
Splines, $C^{r}$       see $C^{r}$ splines
Splines, bivariate      see bivariate splines
Splines, cubic      see cubic spline
Splines, multivariate      see multivariate splines
Splines, nontrivial      see nontrivial splines
Splines, one variable      see univariate splines
Splines, quadratic      see quadratic splines
Splines, trivial      see trivial splines
Splines, univariate      see univariate splines (see also piecewise polynomial functions)
Split exact sequence      see exact sequence split
Square-free part of p ( $p_{red}$ )      39 40 149
Stable quotient of with respect to (I: $f^{\infty}$ )      175
Standard basis of $R^{m}$       186 198 199 207-209 219 220 236 242 246 250 255 258 259 261 294
Standard basis of a module over a local ring      223 224 441
Standard basis of an ideal      viii 164ff 175-177
Standard form of a polynomial      382 425
Standard form of an integer programming problem      364
Standard monomial      36 382-384 430 431
Standard monomial basis      see basis monomials (see also basis monomials)
Standard representative      see standard form of
Stanfield, M.      x
Stanley, R.      283 284 375 384 405 406 474
Start system      338 339
Start system, dense      339 340
Statistics      375 384
Stetter, H.      55 129 468 474
Stichtenoth, H.      449 452 453 458 463 464 471 474
Stillman      386 401 473

1 2 3 4 5

О проекте