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Mignotte M., Stefanescu D. — Polynomials: An Algorithmic Approach
Mignotte M., Stefanescu D. — Polynomials: An Algorithmic Approach

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Название: Polynomials: An Algorithmic Approach

Авторы: Mignotte M., Stefanescu D.

Аннотация:

This textbook gives a well-balanced presentation of the classic procedures of polynomial algebra which are computationally relevant and some algorithms developed during the last decade. The first chapter discusses the construction and the representation of polynomials. The second chapter focuses on the computational aspects of the analytical theory of polynomials. Polynomials with coefficients in a finite field are then described in chapter three, and the final chapetr is devoted to factorization of polynomials with integral coefficients. The book is primarily aimed at graduate students taking courses in Polynomial Algebra, with a prerequisite knowledge of set theory, usual fields and basic algebra. Fully worked out examples, hints and references complement the main text, and details concerning the implementation of algorithms as well as indicators of their efficiency are provided. The book is also useful as a supplementary text for courses in scientific computing, analysis of algorithms, computational polynomial factorization, and computational geometry of polynomials.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 315

Добавлена в каталог: 15.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abnormal prs      22
Algorithm, A1      277
Algorithm, A2      278
Algorithm, basis reduction      271
Algorithm, Berlekamp over large fields      215
Algorithm, Berlekamp over small fields      211
Algorithm, Euclidean division      17
Algorithm, Euclidean pseudo-division      20
Algorithm, fast polynomial multiplication      170
Algorithm, generalized Euclidean division      23
Algorithm, Hasse — Teichmueller      234
Algorithm, Horner      11
Algorithm, Kronecker factorization      242 243
Algorithm, Kronecker — Haussmann      245
Algorithm, linear lift      253
Algorithm, LLL      279
Algorithm, Niederreiter      237
Algorithm, Niederreiter — Goettfert      232
Algorithm, polynomial GCD      18
Algorithm, sparse polynomial multiplication      10
Algorithm, squarefree polynomial decomposition      201
Algorithm, Zassenhaus — Berlekamp      256
Angermueller, G.      76
Apolar polynomials      95
Apostol, T.M.      161 162
Artin, E.      193
Associated elements      14
Base points      48
Basis, reduced      262
Berlekamp, algebra      208 223
Berlekamp, algorithm      204
Berlekamp, E.R.      204 241 249
Berlekamp, matrix      208
Bezout, M.      33
Binary length      268
binomial      192
Birkhoff, G.D.      117
Blaschke multiplicator      79
Blaschke, W.      79
Boyd, D.W.      84 90
Brillhart, J.      135
Cantor, D.G.      180 249
Cantor, G.      169
Cauchy, A.L.      33 114
Characteristic polynomial      39
Characteristic, zero      31
Chinese remainder theorem      54
Chipart, M.H.      107
Circular region      93
Coefficient      2
Coefficient, ring      3 5
Coefficients of similarity      21
Cohn, A.      110 112
Companion matrix      39
Complexity, space      6
Complexity, time      6
Content      22
Convolution      165
Cooley, J.W.      162 166
Cost      6
Cost, exponential      6
Cost, polynomial      6
Degree of a polynomial      2
Degree of a rational function      3
Degree of an algebraic number      81
Degree, index      66
Derivative of a polynomial with respect to a point      93
Derivative, formal      31
Derivative, kth polar      96
Derivative, polar      93 96
DFT      163
Dickson, L.E.      182 191 196
Difference of ith order      53
Difference order      54
Difference polynomial      66
Difference table      53
Discriminant      39
Divide and conquer      9
Divisor      13
Divisor, improper      13
Domain, GCD      14
Domain, integral      14
Domain, unique factorization      14
Dumas, G.      70
Durand, A.      88
Eisenstein, G.      58 59
Element, irreducible      14
Element, primitive      145 198
Elements, associated      14
Euclidean prs      22
Euclidean remainder sequence      18
Euler, L.      33
Exponent of a polynomial      186
Exponential cost      6
FFT      168
Field characteristic      142
Field, algebraically closed      66
Field, finite      142
Field, Galois      144
Field, perfect      201 230
Field, prime      142
Field, splitting      143
Filaseta, M.      135
Flammang, V.      91
Fleishmann, P.      222
Form, Hermitean      108
Formal derivative      31
Formal power series      69
Fourier transform, discrete      163
Fourier transform, fast      168
Fourier transform, finite      163
Fujiwara, M.      108 115
Function, elementary symmetric      42
Function, Euler      155
Function, Moebius      156
Function, polynomial      3
Function, rational      3
Function, Von Mangoldt      172
Galois field      144
Galois, E.      144
Gao, S.      222
Gauss' integers      24
Gauss, C.F.      24 26 58 93 178
GCD      14
Generating function      202
Glesser, Ph.      73
Goettfert, R.      222 230
Goncalves, G.      80
Grace, J.H.      97
Group generator      144
Group, cyclic      144
Gueting, R.      89
Hardy, G.H.      184
Hasse — Teichmueller derivative      234
Hasse — Teichmueller space      234
Hausmann, B.A.      245
Height of a polynomial      83
Henrici, P.      120
Hensel, K.      249
Hermite, C.      108 112
Horner's method      11
Horner, W.G.      11
Hurwitz polynomial      101
Hurwitz, A.      102 105
Hyperderivative of order k      31
Inclusion radius      113
Indeterminate      2
Index degree      66
Integer cyclotomic      175
Integers of Gauss      24
Integral, domain      14
Interpolation, Lagrange      49
Interpolation, Lagrange — Hermite      49 50
Interpolation, linear      48
Interpolation, Newton      50 51
Interpolation, Newton — Hermite      52
Interpolation, polynomial      48
Interpolation, problem      48
Interpolation, Taylor      51
Irreducible element      14
Irreducible polynomial      26 58
Jacobi, C.G.      33
Kaltofen, E.      169 180
Knuth, D.E.      260
Kronecker, L.      58 241 242
Kuniyeda, M.      118
Lagrange — Hermite interpolation      50
Lagrange, interpolation formula      49
Lagrange, J.L.      49 50
Laguerre, E.      94 96
Landau, E.      79 80
Lattice      261
Lattice, basis      261
Lattice, determinant      261
Lattice, rank      261
LCM      14
Leading coefficient      2
Leading term      2
Legendre, A.M.      178
Lehmer, D.H.      90
Length of a multivariate polynomial      85
Length of a polynomial      83
Length, binary      268
Lenstra, A.K.      241 261
Lenstra, H.W.      241 261
Lienard, A.      107
Lift, linear      253
Lift, quadratic      255
Linear interpolation      48
List representation      4
Lovasz, L.      241 261
Lucas, F.      93
MacEleice, R.J.      220
Mahler, K.      79
Matrix of the DFT      164
Matrix representation      152
Matrix, Berlekamp      208
Matrix, companion      39
Measure of a multivariate polynomial      82
Measure of a polynomial      79
Measure of an algebraic number      81
Mignotte, M.      87 89 139 182 282
Minimal distance between two roots      137
Moebius inversion formula      157
Moebius, A.F.      156
Montel, P.      125 131
Multiplicative order of an integer      187
Multiplicity of a root      30
Newton — Hermite interpolation      52
Newton's formulas      45
Newton, diagram      69
Newton, I.      45
Newton, interpolation      50
Newton, polygon      69
Nicolas, J.L.      182
Niederreiter space      223
Niederreiter, H.      221
Norm of a polynomial      78
Normal prs      22
Number, algebraic      81
Odlyzko, A.      135
Order of a group      143
Order of a polynomial      186
Order of an element      143
Order, multiplicative      187
Ostrowski, A.M.      128
Panaitopol, L.      60 69 133 135
Peano, G.      36
Pellet, A.      114
Perfect field      201
Period of a polynomial      186
Polynomial      2
Polynomial in n variables      3
Polynomial, Artin — Schreier      193
Polynomial, bivariate      3
Polynomial, c-primitive      148
Polynomial, characteristic      39
Polynomial, coefficient      2
Polynomial, cost      6
Polynomial, CRT      55
Polynomial, cyclotomic      154
Polynomial, difference      66
Polynomial, exponent      186
Polynomial, height      83
Polynomial, Hurwitz      101
Polynomial, irreducible      26 58
Polynomial, lacunary      132
Polynomial, length      83
Polynomial, measure      79
Polynomial, minimal      81
Polynomial, monic      2
Polynomial, multivariate      3
Polynomial, null      2
Polynomial, order      186
Polynomial, primitive      22
Polynomial, reciprocal      108
Polynomial, reducible      58
Polynomial, reducing      209
Polynomial, representation      149
Polynomial, squarefree      200
Polynomial, stable      101
Polynomial, symmetric      42
Polynomials, apolar      95
Polynomials, similar      21
Power representation      148
Primitive element      145 198
Primitive polynomial      22
Primitive prs      22
Primitive root of unity      154
Procedure, reduced1      270
Procedure, reduced2      270
PRS      21
Prs, abnormal      22
Prs, Euclidean      22
Prs, normal      22
Prs, primitive      22
Prs, reduced      22
Pseudo-division      20
Pseudo-quotient      20
Pseudo-remainder      20
Pseudo-remainder sequence      21
Quadratic norm of a multivariate polynomial      82
Quadratic norm of a polynomial      77
Quadratic reciprocity law      178
Quotient      16
Reciprocal polynomial      108
Reduced basis      262
Reduced prs      22
Reducible polynomial      58
Reducing polynomial      209
Relatively prime      14
Remainder      16
Representation, dense      4
Representation, g-adic      9
Representation, list      4
Representation, matrix      152
Representation, polygonal      4
Representation, polynomial      149
Representation, power      148
Representation, sparse      4
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