LEADER 04863nam 2200469 450 001 9910492138303321 005 20220327064714.0 010 $a3-030-78017-1 035 $a(CKB)4100000011979377 035 $a(MiAaPQ)EBC6676453 035 $a(Au-PeEL)EBL6676453 035 $a(OCoLC)1260343578 035 $a(PPN)258304308 035 $a(EXLCZ)994100000011979377 100 $a20220327d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputer algebra $ean algorithm-oriented introduction /$fWolfram Koepf 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (394 pages) 225 1 $aSpringer Undergraduate Texts in Mathematics and Technology 311 $a3-030-78016-3 327 $aIntro -- Preface -- Contents -- Chapter 1 Introduction to Computer Algebra -- 1.1 Capabilities of Computer Algebra Systems -- 1.2 Additional Remarks -- 1.3 Exercises -- Chapter 2 Programming in Computer Algebra Systems -- 2.1 Internal Representation of Expressions -- 2.2 Pattern Matching -- 2.3 Control Structures -- 2.4 Recursion and Iteration -- 2.5 Remember Programming -- 2.6 Divide-and-Conquer Programming -- 2.7 Programming through Pattern Matching -- 2.8 Additional Remarks -- 2.9 Exercises -- Chapter 3 Number Systems and Integer Arithmetic -- 3.1 Number Systems -- 3.2 Integer Arithmetic: Addition and Multiplication -- 3.3 Integer Arithmetic: Division with Remainder -- 3.4 The Extended Euclidean Algorithm -- 3.5 Unique Factorization -- 3.6 Rational Arithmetic -- 3.7 Additional Remarks -- 3.8 Exercises -- Chapter 4 Modular Arithmetic -- 4.1 Residue Class Rings -- 4.2 Modulare Square Roots -- 4.3 Chinese Remainder Theorem -- 4.4 Fermat's Little Theorem -- 4.5 Modular Logarithms -- 4.6 Pseudoprimes -- 4.7 Additional Remarks -- 4.8 Exercises -- Chapter 5 Coding Theory and Cryptography -- 5.1 Basic Concepts of Coding Theory -- 5.2 Prefix Codes -- 5.3 Check Digit Systems -- 5.4 Error Correcting Codes -- 5.5 Asymmetric Ciphers -- 5.6 Additional Remarks -- 5.7 Exercises -- Chapter 6 Polynomial Arithmetic -- 6.1 Polynomial Rings -- 6.2 Multiplication: The Karatsuba Algorithm -- 6.3 Fast Multiplication with FFT -- 6.4 Division with Remainder -- 6.5 Polynomial Interpolation -- 6.6 The Extended Euclidean Algorithm -- 6.7 Unique Factorization -- 6.8 Squarefree Factorization -- 6.9 Rational Functions -- 6.10 Additional Remarks -- 6.11 Exercises -- Chapter 7 Algebraic Numbers -- 7.1 Polynomial Quotient Rings -- 7.2 Chinese Remainder Theorem -- 7.3 Algebraic Numbers -- 7.4 Finite Fields -- 7.5 Resultants -- 7.6 Polynomial Systems of Equations. 327 $a7.7 Additional Remarks -- 7.8 Exercises -- Chapter 8 Factorization in Polynomial Rings -- 8.1 Preliminary Considerations -- 8.2 Efficient Factorization in Zp[x] -- 8.3 Squarefree Factorization of Polynomials over Finite Fields -- 8.4 Efficient Factorization in Q[x] -- 8.5 Hensel Lifting -- 8.6 Multivariate Factorization -- 8.7 Additional Remarks -- 8.8 Exercises -- Chapter 9 Simplification and Normal Forms -- 9.1 Normal Forms and Canonical Forms -- 9.2 Normal Forms and Canonical Forms for Polynomials -- 9.3 Normal Forms for Rational Functions -- 9.4 Normal Forms for Trigonometric Polynomials -- 9.5 Additional Remarks -- 9.6 Exercises -- Chapter 10 Power Series -- 10.1 Formal Power Series -- 10.2 Taylor Polynomials -- 10.3 Computation of Formal Power Series -- 10.3.1 Holonomic Differential Equations -- 10.3.2 Holonomic Recurrence Equations -- 10.3.3 Hypergeometric Functions -- 10.3.4 Efficient Computation of Taylor Polynomials of Holonomic Functions -- 10.4 Algebraic Functions -- 10.5 Implicit Functions -- 10.6 Additional Remarks -- 10.7 Exercises -- Chapter 11 Algorithmic Summation -- 11.1 Definite Summation -- 11.2 Difference Calculus -- 11.3 Indefinite Summation -- 11.4 Indefinite Summation of Hypergeometric Terms -- 11.5 Definite Summation of Hypergeometric Terms -- 11.6 Additional Remarks -- 11.7 Exercises -- Chapter 12 Algorithmic Integration -- 12.1 The Bernoulli Algorithm for Rational Functions -- 12.2 Algebraic Prerequisites -- 12.3 Rational Part -- 12.4 Logarithmic Case -- 12.5 Additional Remarks -- 12.6 Exercises -- References -- List of Symbols -- Mathematica List of Keywords -- Index. 410 0$aSpringer undergraduate texts in mathematics and technology. 606 $aAlgebra$xData processing 606 $aComputer science$xMathematics 615 0$aAlgebra$xData processing. 615 0$aComputer science$xMathematics. 676 $a512.0285 700 $aKoepf$b Wolfram$0481654 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910492138303321 996 $aComputer Algebra$92280300 997 $aUNINA LEADER 03243nam 2200757 a 450 001 9910782845603321 005 20230721005335.0 010 $a661207048X 010 $a1-282-07048-7 010 $a9786612070488 010 $a1-4416-0539-8 010 $a600-00-1240-3 010 $a1-60750-362-X 035 $a(CKB)1000000000723312 035 $a(EBL)433443 035 $a(OCoLC)646807186 035 $a(SSID)ssj0000340435 035 $a(PQKBManifestationID)11293921 035 $a(PQKBTitleCode)TC0000340435 035 $a(PQKBWorkID)10387278 035 $a(PQKB)10931512 035 $a(MiAaPQ)EBC433443 035 $a(Au-PeEL)EBL433443 035 $a(CaPaEBR)ebr10285488 035 $a(CaONFJC)MIL207048 035 $a(EXLCZ)991000000000723312 100 $a20090514d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMining massive data sets for security$b[electronic resource] $eadvances in data mining, search, social networks and text mining, and their applications to security /$fedited by Franc?oise Fogelman-Soulie? ... [et al.] 210 $aAmsterdam $cIOS Press$d2008 215 $a1 online resource (388 p.) 225 1 $aNATO science for peace and security series. Sub-series D, Information and communication security,$x1874-6268 ;$vv. 19 300 $a"Proceedings of the NATO Advanced Study Institute on Mining Massive Data Sets for Security, Gazzada (Varese), Italy, 10-21 September, 2007."--T.p. verso. 300 $aPublished in cooperation with NATO Public Diplomacy Division. 311 $a1-58603-898-2 320 $aIncludes bibliographical references and indexes. 327 $aTitle page; Mining Massive Data Sets for Security; Contents; Data Mining; Search; Social Networks; Text Mining; Security Applications; Subject Index; Author Index 330 $aThe real power for security applications will come from the synergy of academic and commercial research focusing on the specific issue of security. This book is suitable for those interested in understanding the techniques for handling very large data sets and how to apply them in conjunction for solving security issues. 410 0$aNATO science for peace and security series.$nSub-series D,$pInformation and communication security ;$vv. 19. 606 $aData mining$vCongresses 606 $aComputer algorithms$vCongresses 606 $aTerrorism$xPrevention$vCongresses 606 $aTerrorism risk assessment$vCongresses 610 1 $aData sets 610 1 $aSecurity informatics 610 2 $aNATO 615 0$aData mining 615 0$aComputer algorithms 615 0$aTerrorism$xPrevention 615 0$aTerrorism risk assessment 676 $a006.3 676 $a006.32 701 $aFogelman-Soulie?$b Franc?oise$f1948-$0347669 712 02$aNorth Atlantic Treaty Organization.$bPublic Diplomacy Division. 712 12$aNATO Advanced Study Institute on Mining Massive Data Sets for Security 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782845603321 996 $aMining massive data sets for security$93792318 997 $aUNINA