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© in This Web Service Cambridge University Press Cambridge University Press 978-1-107-03903-2 - Modern Computer Algebra: Third Edition Joachim Von Zur Gathen and Jürgen Gerhard Index More information Index A page number is underlined (for example: 667) when it represents the definition or the main source of information about the index entry. For several key words that appear frequently only ranges of pages or the most important occurrences are indexed. AAECC ......................................... 21 analytic number theory . 508, 523, 532, 533, 652 Abbott,John .............................. 465, 734 AnalyticalEngine ............................... 312 Abel,NielsHenrik .............................. 373 Andrews, George Eyre . 644, 697, 729, 735 Abeliangroup ................................... 704 QueenAnne .................................... 219 Abramov, Serge˘ı Aleksandrovich (Abramov annihilating polynomial ......................... 341 SergeiAleksandroviq) 7, 641, 671, 675, annihilator, Ann( ) .............................. 343 734, 735 annusconfusionis· ................................ 83 Abramson, Michael . 738 Antoniou,Andreas ........................ 353, 735 Achilles ......................................... 162 Antoniszoon, Adrian (Metius) .................... 82 ACM . see Association for Computing Machinery Aoki,Kazumaro .......................... 542, 751 active attack . 580 Apéry, Roger . 671, 684, 697, 761 Adam,Charles .................................. 729 number ....................................... 684 Adams,DouglasNoël ..................... 729, 796 Apollonius of Perga (᾿Απολλώνιος ὁ Περγα˜ιος) additionchain .................................... 88 .............................................. 198 additive group . 250, 578, 703, 713 Apostol,TomMike ......................... 62, 735 Adleman, Leonard Max 16, 421, 509, 531, 576, 735, Archimedean valuation . 274 762 Archimedes of Syracuse (᾿Αρχιμήδης ὁ affinepart ....................................... 568 Συρακούσιος) 24, 82, 218, 294, 358, 372, 374, Agrawal, Manindra . 517, 543, 735 622, 669, 735 Aho, Alfred Vaino . 286, 292, 332, 735 Aristotle (᾿Αριστοτέλης)......................... 24 Ajtai,Miklos .............................. 496, 735 arithmetic Albanese, Andres . 215, 735 circuit . 36, 39, 43, 88, 101, 199, 223, 224, 234, Albert, Abraham Adrian . 572, 728 235, 248, 252, 495, 619 D’Alembert, Jean le Rond . 676, 729 representation . 495, 497, 498, 501 Alford, William Robert (Red) . 529, 532, 735 hardware ............................. 279,283 ∼ algebra operation ....................... 31, 32, 34, 35, 40 fundamental theorem of .............. 372,711 ∼ Artin,Emil ............................... 568,748 homomorphism ............................... 231 Arwin,Axel .............................. 418,735 algebraic ........................................ 710 Aryabhat¯ .a ................................... 61,90 closure ................................. 711, 716 Aryabhat¯ .¯ıya ................................. 61,286 complexity theory . 243, 338, 721 ascending chain condition . 604, 610 computation problem .......................... 97 Asmuth,CharlesA. ....................... 131, 735 curve . 11, 172, 174, 175, 696 associate . 46, 147, 518, 707, 708 degree of an element . 710 ∼ associated sequence . 669 equation ...................................... 696 Association for Computing Machinery (ACM) . 533 field extension . see field extension Journal of the ................................ 21 ∼ geometry .......................... 558, 568, 595 SIGSAM ...................................... 21 computational . 4, 591, 595, 619 ∼ asymmetric cryptosystem . 17, 575 integers ................................ 707, 708 asymptotic complexity ....................... 6, 338 number ............................ 203, 640, 663 Atkin, Arthur Oliver Lonsdale . 532, 735 field ....................... 279,378, 473, 533 authentication . 576, 578 variety . 172, 198, 586, 591, 613, 614 automorphism . 441, 713, 714, 715 algebraically closed . 172, 595, 617, 621, 711 Frobenius ................... 398, 420, 465, 713 ALGOLIB ....................................... 697 ∼ average ......................................... 718 al-Hajjaj¯ ................................. see Hajjaj¯ . case analysis . 61, 62, 162, 419, 523 Alice . 16–18, 503, 504, 573, 574, 577–580 depth al-Kash¯ ¯ı.................................. see Kash¯ ¯ı al-Khwarizm¯ ¯ı ...................... see Khwarizm¯ ¯ı ofaHuffmantree .......................... 308 Almkvist,Gert ....................... 641, 671, 735 ofastochasticmobile ........... 306, 307, 308 and Zeilberger integration . 632, 637, 643 Avicenna (Abu¯ ֒Al¯ı al-H. usayn bin ֒Abd Allah¯ bin Alon,Noga ............................... 215,735 S¯ına,¯ úæJ áK . é<Ë@ YJ.« áK . á mÌ'@ úΫ ñK.@) . 88 Amerbach, Bonifatius . 25 AXIOM ...................................... 20,24 Amoroso, Francesco . 618, 735 axiom amplitude ................................. 360, 362 inaproofsystem .................. 677, 678, 679 analogsignal .................................... 360 ofchoice ...................................... 63 analysis of algorithms . 29, 278, 697 Azra, Jean-Pierre . 745 769 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-03903-2 - Modern Computer Algebra: Third Edition Joachim Von Zur Gathen and Jürgen Gerhard Index More information 770 Index B-number . 550, 551, 553, 556, 557, 568 Berman, Benjamin P. 640, 737 Babai, László . 198, 724, 736 Bernardin, Laurent . 469 Babbage, Charles . 312, 676, 725, 727, 729 Bernoulli, Jakob (1654–1705) baby step/giant step strategy . 544 number ............................ 650, 669, 672 Babylonians .............................. 286, 291 randomvariable .............................. 719 Bach, Carl Eric 6, 61, 287, 421, 529, 531–535, 568, Bernoulli, Johann (1667–1748) . 640, 737 736 Bernstein, Daniel Julius . 247, 287, 353, 737 Bach, Johann Sebastian . 86, 736 Bernstein, Jeremy . 725 Bachet, Claude Gaspard, sieur de Méziriac . 61, 513, Bert ............................................. 135 736 Bertossi,Leopoldo ................................ 6 Bachmann, Paul Gustav Heinrich . 531, 724 Bertrand, Joseph Louis François, postulate . 525 back-tracking ................................... 678 Beschorner, Andreas . 7 Bacon, Lord Francis . 0, 725 Beth,Thomas ............................. 747, 760 Bailey, David Harold . 2, 83, 337, 736, 737 Bézier, Pierre Étienne . 138, 737 Baker, George Allen, Jr. 132, 736 curve ......................................... 138 Ball, Walter William Rouse . 531, 534, 736 spline ........................................ 138 Barbour, James Murray . 91, 736 Bézout, Étienne . 172, 197, 590, 724, 728, 737 Bareiss,ErwinHans ...................... 132, 736 -coprime ............................... 450, 471 Barnett, Michael . 7 coefficients . 58, 62, 141, 153, 155, 161, 197, 325, Barrau,Théophile ............................... 725 326 Barrow,Isaac ................................... 218 matrix .................................. 197,201 basis theorem . 157, 172, 173, 175, 198, 560, 692 Gröbner ..................... see Gröbner basis Bible .................................. 24,219,711 ∼ Hilbert theorem . 586, 601, 604, 605, 606, 618 Biermann,Gottlieb .............................. 725 ∼ normal ................................. 76,580 big Oh, O( ) 2, 30, 32, 703, 715, 720, 721, 723, 724 ∼ ofalattice .............................. 473, 477 big prime modular· algorithm . see modular algorithm of a vector space . 209, 212, 475, 714, 715, 717 bijective .................................. 704, 705 of an ideal . 593, 601, 608, 706 bilinear orthogonal ............................ 475,717 complexity ............................. 337, 338 ∼ reduced ....................... see reduced basis map .......................................... 355 ∼ reduction 475, 478, 479, 480, 484, 488, 492, 493, Bimberg,Guido ................................. 766 496, 497, 499, 500, 503, 505–509, 576, 580 binary standard .................................... 591 calendar . 84 ∼ Bauer,Andrej ............................. 671, 736 EuclideanAlgorithm ................. 61, 65, 738 Baur,Walter .............................. 352,736 rational ....................................... 200 Bayer,David ......................... 618, 619, 736 representation . 75, 88, 100, 262, 283, 408, 504 BCH code . 3, 209, 210, 211, 212–215, 325, 332, tree . 296, 303, 305–307, 309 377, 412, 416, 417, 756 Binet, Jacques Philippe Marie . 61, 737 designed distance of a ................ 212, 213 Bini,DarioAndrea .............................. 352 ∼ generator polynomial of a . 211, 212, 214, 215, binomial . 230, 463, 616, 681 ∼ 416 coefficient . 76, 166, 658–660, 669, 670, 684, 713, Beame, Paul William . 6, 697, 736 768 Becker, Thomas . 618, 736 ideal ............................... 616,681, 697 Beiler,AlbertH. .......................... 534, 736 theorem ........................ 76, 667, 669, 673 Bell, Eric Temple (John Taine) . 10, 96, 219, 644, BIPOLAR ............... 3,279, 281–283, 461, 462 725, 726, 729, 736 Birch,Thomas .................................. 726 Beltrami,Eugenio ......................... 729, 734 birthdayproblem .......................... 546, 548 Benecke, Christof . 698, 736 bitoperation ..................................... 32 Ben-Or, Michael . 410, 411, 421, 498, 619, 736, 737, bivariate 759 factorization . 433, 457, 459, 493, 496, 497, 586 Berenstein, Carlos Alberto . 618, 737 interpolation .................................. 134 Berggren, Lennart . 90, 729, 735,
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