001438190 000__ 06781cam\a2200673\i\4500
001438190 001__ 1438190
001438190 003__ OCoLC
001438190 005__ 20230309004252.0
001438190 006__ m\\\\\o\\d\\\\\\\\
001438190 007__ cr\cn\nnnunnun
001438190 008__ 210717s2021\\\\sz\\\\\\ob\\\\001\0\eng\d
001438190 019__ $$a1266810052
001438190 020__ $$a9783030780173$$q(electronic bk.)
001438190 020__ $$a3030780171$$q(electronic bk.)
001438190 020__ $$z9783030780166
001438190 0247_ $$a10.1007/978-3-030-78017-3$$2doi
001438190 035__ $$aSP(OCoLC)1260343578
001438190 040__ $$aEBLCP$$beng$$erda$$epn$$cEBLCP$$dGW5XE$$dOCLCO$$dOCLCF$$dYDX$$dDCT$$dUKAHL$$dOCLCQ$$dOCLCO$$dOCL$$dOCLCQ
001438190 0411_ $$aeng$$hger
001438190 049__ $$aISEA
001438190 050_4 $$aQA155.7.E4$$bK64 2021
001438190 08204 $$a512.00285$$223
001438190 1001_ $$aKoepf, Wolfram.
001438190 24010 $$aComputeralgebra.$$lEnglish
001438190 24510 $$aComputer algebra :$$ban algorithm-oriented introduction /$$cWolfram Koepf.
001438190 264_1 $$aCham, Switzerland :$$bSpringer,$$c2021.
001438190 300__ $$a1 online resource (394 pages)
001438190 336__ $$atext$$btxt$$2rdacontent
001438190 337__ $$acomputer$$bc$$2rdamedia
001438190 338__ $$aonline resource$$bcr$$2rdacarrier
001438190 347__ $$atext file
001438190 347__ $$bPDF
001438190 4901_ $$aSpringer undergraduate texts in mathematics and technology
001438190 500__ $$a10.7 Exercises.
001438190 504__ $$aIncludes bibliographical references and index.
001438190 5050_ $$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
001438190 5058_ $$a3.2 Integer Arithmetic: Addition and Multiplication -- 3.3 Integer Arithmetic: Division with Remainder -- 3.4 The Extended Euclidean Algorithm -- 3.5 Unique Factorization -- 3.6 Rational Arithmetic -- 3.7 Additional Remarks -- 3.8 Exercises -- Chapter 4 Modular Arithmetic -- 4.1 Residue Class Rings -- 4.2 Modulare Square Roots -- 4.3 Chinese Remainder Theorem -- 4.4 Fermat's Little Theorem -- 4.5 Modular Logarithms -- 4.6 Pseudoprimes -- 4.7 Additional Remarks -- 4.8 Exercises -- Chapter 5 Coding Theory and Cryptography -- 5.1 Basic Concepts of Coding Theory -- 5.2 Prefix Codes
001438190 5058_ $$a5.3 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
001438190 5058_ $$a7.3 Algebraic Numbers -- 7.4 Finite Fields -- 7.5 Resultants -- 7.6 Polynomial Systems of Equations -- 7.7 Additional Remarks -- 7.8 Exercises -- Chapter 8 Factorization in Polynomial Rings -- 8.1 Preliminary Considerations -- 8.2 Efficient Factorization in Zp[x] -- 8.3 Squarefree Factorization of Polynomials over Finite Fields -- 8.4 Efficient Factorization in Q[x] -- 8.5 Hensel Lifting -- 8.6 Multivariate Factorization -- 8.7 Additional Remarks -- 8.8 Exercises -- Chapter 9 Simplification and Normal Forms -- 9.1 Normal Forms and Canonical Forms
001438190 5058_ $$a9.2 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
001438190 506__ $$aAccess limited to authorized users.
001438190 520__ $$aThis textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using Mathematica code, the book is fully supported by downloadable sessions in Mathematica, Maple, and Maxima. Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration. Computer Algebra is an indispensable resource for mathematics and computer science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.
001438190 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 22, 2021).
001438190 650_0 $$aAlgebra$$xData processing.
001438190 650_0 $$aComputer science$$xMathematics.
001438190 650_0 $$aComputer algorithms.
001438190 650_0 $$aAlgorithms.
001438190 650_6 $$aAlgèbre$$xInformatique.
001438190 650_6 $$aInformatique$$xMathématiques.
001438190 650_6 $$aAlgorithmes.
001438190 655_0 $$aElectronic books.
001438190 77608 $$iPrint version:$$aKoepf, Wolfram.$$tComputer Algebra.$$dCham : Springer International Publishing AG, ©2021$$z9783030780166
001438190 830_0 $$aSpringer undergraduate texts in mathematics and technology.
001438190 852__ $$bebk
001438190 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-78017-3$$zOnline Access$$91397441.1
001438190 909CO $$ooai:library.usi.edu:1438190$$pGLOBAL_SET
001438190 980__ $$aBIB
001438190 980__ $$aEBOOK
001438190 982__ $$aEbook
001438190 983__ $$aOnline
001438190 994__ $$a92$$bISE