| 1.Introduction 2.Overview 2.1 Outline 2.2 Statement of Main Results 2.3 References and Related Works 2.4 Open Problems 3.Technical Prerequisites 3.1 Subresultants and the Euclidean Algorithm 3.2 The Cost of Arithmetic 4.Change of Basis 4.1 Computing Taylor Shifts 4.2 Conversion to Falling Factorials 4.3 Fast Multiplication in the Falling Factorial Basis 5.Modular Squarefree and Greatest Factorial Factorization 5.1 Squarefree Factorization 5.2 Greatest Factorial Factorization 6.Modular Hermite Integration 6.1 Small Primes Modular Algorithm 6.2 Prime Power Modular Algorithm 6.3 Implementation 7.Computing All Integral Roots of the Resultant 7.1 Application to Hypergeometric Summation 7.2 Computing All Integral Roots Via Factoring 7.3 Application to Hyperexponential Integration 7.4 Modular LRT Algorithm 8.Modular Algorithms for the Gosper-Petkov~ek Form 8.1 Modular GP~-Form Computation 9.Polynomial Solutions of Linear First Order Equations 9.1 The Method of Undetermined Coefficients 9.2 Brent and Kung's Algorithm for Linear Differential Equations.. 9.3 Rothstein's SPDE Algorithm 9.4 The ABP Algorithm 9.5 A Divide-and-Conquer Algorithm: Generic Case 9.6 A Divide-and-Conquer Algorithm: General Case 9.7 Barkatou's Algorithm for Linear Difference Equations 9.8 Modular Algorithms 10. Modular Gosper and Almkvist & Zeilberger Algorithms 10.1 High Degree Examples References Index |
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