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| Burgisser P., Clausen M., Shokrollahi M.A. — Algebraic complexity theory |
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| Предметный указатель |
Restriction and scalar extension 383
Restriction of bilinear maps 361
Restriction of tensors 362
Resultant 63 254 263 275
Resultant, lower bound for 174 204
Resultant, upper bound for 93 174
Reverse of a power series 57
Riemann — Roch theorem 497 502
Right-kernel of a bilinear map 363
Right-kernel of a quadratic map 457
Ring  372
RNF problem sequence 435
Rolle’s Theorem 288 290
Root of unity, primitive 32
Root of unity, principal 32
Roots approximating 286
Ryser’s formula 569
Satisfiability problem 544
Scalar extension 382
Scalar extension and rank 414
Scalar restriction 382
Scaling a bilinear computation 477
Schoenhage’s example 387
Scholz — Brauer conjecture 23
Schur Relations 330
Schwarz genus 286
Search problem 574
Secant variety 516 522
Segre embedding 521
Segre variety 522
Semi-algebraic decision complexity 205
Semi-algebraic map 266
Semi-algebraic Morse — Sard theorem 267
Semi-algebraic set 18 121
Semiring  369 372
Separable by a computation 464
Separable degree 216
Separation lemma 457
Separation of points 456
Sequence, generating polynomial of 92 450
Sequence, linearly generated 92 450
Sequence, minimum polynomial of 92 450
Set disjointness 274
Set equality 278
Set inclusion 278
Shattered 84
Sign determination 452
Simple algebra 458
Simple algebra, lower bound for the rank of 459
Simple module 329
simplex 80
Slices (of a tensor) 365
SLS problem sequence 451
Smallest enclosing circle 276
Smooth curve 290
Solving a linear system 451
Sorting 273
Sparse polynomials 371
Splitting lemma I 527
Splitting lemma II 532
Spr problem sequence 449
Squarefree factorization 62 90
Squaring,  -matrices 371
Squaring, power series 31
Standard K-DAG 315
Star chain 23
Stirling’s approximation 321
Straight-line program 15 124
Straight-line program, (in)consistent 106
Straight-line program, concatenation of 106
Straight-line program, depth of 562
Straight-line program, executable 105
Straight-line program, homogeneous 551
Straight-line program, length of 105
Straight-line program, linear 306
Straight-line program, universal input for 106
Strassen’s algorithm 11—13 377
Strassen’s algorithm, optimality of 459 462
Strassen’s degree bound 185
Strongly convex function 54
Structural maps of algebras 356
Structural tensor of a bilinear map 358
Sturm’s algorithm 93
Sturm’s Theorem 63 93
Submodule 329
Subresultant 98 254
Subresultant coefficient 254
Subresultant theorem 255 261
Substitution 144 145
Substitution method 143—160 285
Substitution, family of 146
Sum of reciprocals, complexity of 158
Sum of squares, complexity of 144 149
Summation map 522
| Superconcentrator 9 322
Superregular matrix 318
Support 391 392
Support simplex 423
Supporting an FFT 33
Supporting hyperplane 80
Symbolic computation 27
Symbolic integration 62
Symmetric polynomials, elementary 39 54
Symmetric polynomials, power sums 46
Taylor approximations of exp 243
Taylor approximations of log 222 243
Taylor expansion 48
Taylor series (truncated) 162
Tensor product of bilinear maps 359
Tensor product of k-spaces 357
Tensor product of tensors 359
Tensor, as a quadruple 358 381
Tensor, class 369
Tensor, concise 363
Tensor, concise version of 363
Tensor, coordinate 365
Tensor, indecomposable 372
Tensor, null 368
Tensor, of minimal border rank 419
Tensor, permutation of 358
Tensor, rank of 358
Tensor, restriction of 362
Tensor, slices of 365
Tensor, trilinear form associated to 366
Tensor, with 0, 1-entries 239
Tensors, direct sum of 359
Tensors, equivalence of 368
Tensors, isomorphic 358
Tensors, tensor product of 359
Term 289
Test for regularity 452
Theorem on fibers 186
Threshold function 277
Tight set 396 398 402 417
TInv problem sequence 427
Toeplitz matrix 311 481
Topological complexity 286
Topological degeneration 536
Total arithmetic cost 28
Total complexity 28
Totally regular matrix 318
Transcendence degree bound 131 285 309
Transitive closure 445
Traveling salesman problem 83
Triad 357
Triangulation 80
Trilinear aggregating 420
Trilinear form 366
Truncated Taylor series 162
Turing machine 124 544
Type of a degree pattern 63
Typical degree pattern 90 139
Typical rank 522
Uniformity 83 124
Universal differential 345
Universal input 106 124
Universality of DET (PER) 554 570
Valiant matrix 557
Valiant’s analogue of Nick’s class 568
Valiant’s class of p-computable families 19 545
Valiant’s class of p-definable families 20 546
Valiant’s class of p-expressible families 550
Valiant’s class of qp-computable families 562
Valiant’s hypothesis 549
Vandermonde matrix 77
Vandermonde matrix generic 318
Vandermonde matrix superregular 345
Vapnik — Chervonenkis-dimension see "VC-dimension"
Variation 93 298
Variety affine 178
Variety projective 178
VC-dimension 84 95 96
Veronese mapping 192 239
Vertex 80
Vieta’s theorem 39
Walsh — Hadamard transform 309
Wedderbum’s structure theorem 329 372 463 482
Weight 212
Weighted external path length 40 41
Width (generic) 281
Wiedemann’s algorithm 453
Witt-index 353
Witt’s Theorem 353
Young lattice 342
Young’s branching theorem 343
Zariski closed subset 123
Zariski closed subset, defined over k 216
Zariski topology 123
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