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Computer algebra : an algorithm-oriented introduction / / Wolfram Koepf
| Computer algebra : an algorithm-oriented introduction / / Wolfram Koepf |
| Autore | Koepf Wolfram |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (394 pages) |
| Disciplina | 512.0285 |
| Collana | Springer Undergraduate Texts in Mathematics and Technology |
| Soggetto topico |
Algebra - Data processing
Computer science - Mathematics |
| ISBN | 3-030-78017-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- 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.
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 -- 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. |
| Record Nr. | UNINA-9910492138303321 |
Koepf Wolfram
|
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Computer algebra : an algorithm-oriented introduction / / Wolfram Koepf
| Computer algebra : an algorithm-oriented introduction / / Wolfram Koepf |
| Autore | Koepf Wolfram |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (394 pages) |
| Disciplina | 512.0285 |
| Collana | Springer Undergraduate Texts in Mathematics and Technology |
| Soggetto topico |
Algebra - Data processing
Computer science - Mathematics Àlgebra Processament de dades Algorismes computacionals |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-78017-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- 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.
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 -- 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. |
| Record Nr. | UNISA-996466389303316 |
|
Koepf Wolfram
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||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Hypergeometric Summation : An Algorithmic Approach to Summation and Special Function Identities / / by Wolfram Koepf
| Hypergeometric Summation : An Algorithmic Approach to Summation and Special Function Identities / / by Wolfram Koepf |
| Autore | Koepf Wolfram |
| Edizione | [2nd ed. 2014.] |
| Pubbl/distr/stampa | London : , : Springer London : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (290 p.) |
| Disciplina | 515.55 |
| Collana | Universitext |
| Soggetto topico |
Algorithms
Computer software Special functions Differential equations Combinatorics Mathematical Software Special Functions Ordinary Differential Equations |
| ISBN | 1-4471-6464-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- The Gamma Function -- Hypergeometric Identities -- Hypergeometric Database -- Holonomic Recurrence Equations -- Gosper’s Algorithm -- The Wilf-Zeilberger Method -- Zeilberger’s Algorithm -- Extensions of the Algorithms -- Petkovˇsek’s and Van Hoeij’s Algorithm -- Differential Equations for Sums -- Hyperexponential Antiderivatives -- Holonomic Equations for Integrals -- Rodrigues Formulas and Generating Functions. |
| Record Nr. | UNINA-9910299989803321 |
|
Koepf Wolfram
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||
| London : , : Springer London : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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ISSAC 2010 : proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, 25-28 July 2010, Munich Germany
| ISSAC 2010 : proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, 25-28 July 2010, Munich Germany |
| Autore | Koepf Wolfram |
| Pubbl/distr/stampa | [Place of publication not identified], : ACM, 2010 |
| Descrizione fisica | 1 online resource (366 pages) |
| Collana | ACM Other conferences |
| Soggetto topico |
Engineering & Applied Sciences
Computer Science |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
International Symposium on Symbolic and Algebraic Computation 2010
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation ISSAC '10 International Symposium on Symbolic and Algebraic Computation, Munich, Germany - July 25 - 28, 2010 |
| Record Nr. | UNINA-9910376242503321 |
|
Koepf Wolfram
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| [Place of publication not identified], : ACM, 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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