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

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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.

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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

Stirling s formula      464
Strang, G.      401 404
Strong Nullstellensatz      21 41 43 54 62 83 99 141 148 149 171 465
Sturm s Theorem      69 70
Sturm sequence      70
Sturmfels, B.      ix x 82 92 93 119 122 187 284 304 306-308 324 336 337 340 343 346 347 353 354 356 359 375 377 378 383 384 386 401 469474
Subdivision, algebraic (non-polyhedral)      404 405
Subdivision, coherent      see mixed subdivision coherent
Subdivision, mixed      see mixed subdivision
Subdivision, polyhedral      see polyhedral complex and polyhedral subdivison
Subfield      408 409 413
SubMatrix      426
Submodule      180ff 197ff 217 224 228 239 244246 250 254 262 399 4409442
Submodule membership problem      197
Submodule, generated by elements of       182 217
Submodule, graded      see graded submodule
Submodule, membership test      365 371 372
Submonoid      377
Subpolytope      326
Subring, generated by $f_{1}, ..., f_{n}$ $(k[f_{1}, ..., f_[n}])$       365
Sum of ideals (I )      6 22
Sum of submodules ( M)      191 242 243
Supporting hyperplane of a polytope      293 294 309 319 320 325
Supporting line      362
Surface area of a polytope      326
Surjective      235 245 265 281 312 313 365 382 414
Suslin, A.      187 194 231 474
Sweedler, M.      x
Sylvester determinant      see resultant Sylvester
Symbolic computation      56 104 113 352
Symbolic parameter      327
Symmetric bilinear form      64 65
Symmetric magic square      see magic square symmetric
Syndrome      421 424 436
Syndrome decoding      421 435
Syndrome polynomial      437 438 440 445 446
Systematic encoder      419 430 431 466
Systematic generator matrix      419 422 423
Syzygy      175 189 199 200 21
Syzygy module (Syz $(f_{1}, ..., f_{t}$ ))      189 190 194 197 199 208 211ff 231-233 234 236ff 245ff 257 263 264 271 275-277 279 280 286 395 397 398 403
Syzygy Problem      197 210
Syzygy theorem      see Hilbert Syzygy Theorem
Syzygy, homogeneous      see homogeneous syzygy
Syzygy, over a local ring      223 224 228 230
Szpirglas, A.      63 64 66 67 473
Tangent cone      170 177 178
Taylor series      138
Term      2 74
Term orders (in local case)      151ff (see also ordering monomials)
Term orders (in local case), term-over-position      see TOP order
Ternary quadric      82 83
Tessier $\mu^{*}$ -invariant      178
tetrahedron      403
Third isomorphism theorem      193
Third syzygy      234 238-240
Thomas, R.      359 474
Tjurina number      138 148 168 170 177
Tjurina number, top down ordering      201 209
TOP order      201ff 223 441
Toric GCP      see generalized characteristic polynomial toric
Toric ideal      383
Toric variety      viii 305 306 307ff 331 336 359 375 383 384
Total degree of a polynomial (deg())      2 74 163 455 456 460
Total ordering      7 152 153 201 369
Trace of a matrix (Tr())      64 66
Translate of a subset in $\mathbb{R}^{n}$       297 298 320 321 326
Transpose of a matrix ( $M^{T}$ )      125 126 182 356 423
Traverso, C.      158 169 359 363 372 373 470 472
TREE      400
Trivial resolution      263
Trivial splines      395 397 398 400
Trucking firm      359 360
Tsfasman      448 463 464 474
Twist of a graded module ()      255 267
Twisted Chow form      see Chow form twisted

Twisted cubic      247 269 289
Twisted free module      see graded free module
U-resultant      110ff 118 122 128 144 353 354 356
Unbounded polyhedral region      see polyhedral region unbounded
Unimodular row      187 194 233
Union of varieties ( $U\cup V$ )      19 22
Uniqueness of Monic Gr $\ddot{o}$ bner Bases      15
Uniqueness of Remainders      see remainder
Unit cube in $\mathbb{R}^{n}$       292
Unit of a ring      131 132 137 159 162 163 225
Univariate splines      385 386 388 390
Universal categorical quotient      312
Universal polynomials      85 95 101 102
University of Kaiserslautern      167
University of Minnesota      348
Unpunctured code      see Reed - Muller code unpunctured
Unshortenable      224 225
Valuation ring      135 136
van der Geer, G.      449 475
Van der Waerden, B.      73 80 110 474
Van Lint, J.      415 420 427 449 475
Vandermonde determinant      426 434
Varchenko, V.      178 468
Variety      18 130 177 274 451 462
Variety, affine      see affine variety
Variety, degree      see degree of
Variety, dimension of      see dimension of
Variety, ideal of      see ideal of
Variety, irreducible      see irreducible variety
Variety, irreducible component of      see irreducible component
Variety, Jacobian      see Jacobian variety
Variety, of an ideal (V(1))      20
Variety, projective      see projective variety
Variety, reducible      see reducible variety
Variety, toric      see toric variety
Vector f (in a free module)      180ff 236
Verlinden, P.      338 340 475
Veronese map      308 313
Veronese surface      287
Verschelde, J.      338 340 471 475
Vertex monomial      311 312 316
Vertex of a graph      398
Vertex of a polyhedral complex      389 390 4033405
Vertex of a polytope      292-294 311 326 349 352 362 374
Vision      305
Vladut, S.      448 463 464 474
Volume of a polytope Q (Vol ${}_{n}$ ())      292 319-324 326 327
Volume of a polytope Q (Vol ${}_{n}$ ()), normalized      319-322 326 352
Volume of a polytope Q (Vol ${}_{n}$ ()), relation to mixed volume      3222324 326 327 345 346
Volume of a polytope Q (Vol ${}_{n}$ ()), relation to sparse resultants      3022304
Wang, X.      337 342 472 473
Warren, J.      102 468
Web site      x 167
Weierstrass gap theorem      452 454
Weierstrass point      454
Weierstrass weight      454
Weight (of a variable)      100 107 108 282
Weight order      15 368 372 440
Weighted degree of a monomial      289
Weighted homogeneous polynomial      178 282 289
Weispfenning, V.      vii 4 9 12-15 25 37 51 63 69 174 468
Well-ordering      7 152 155 201 369
Weyman, J.      343 475
White, J.      x
Wilkinson, J.      30 31 475
Woodburn, C.      x 187 472
Words      see codewords
Yoke      189
Zalgaller, V.      316 320 323 469
Zariski closure      23 301 302 308 313 342 383
Zdimradical (Maple procedure)      45
Zelevinski, A.      76 80 87 89 93 94 103 119 301 302 304 307 308 316 336 342 343 353 471 474
Zero function      17
Zero-dimensional ideal      37ff 41 44-46 48 51 53 55 59 61 62 64 65 130 138 149-151 176
Ziegler, G.      291 475
Zink      448 463 464 474

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