Modular Algorithms in Symbolic Summation and Symbolic Integration

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Modular Algorithms in Symbolic Summation and Symbolic Integration / J?rgen Gerhard, Takeo Kanade

資料種別:

電子ブック

出版情報:

Springer eBooks Computer Science
Springer Berlin / Heidelberg, 2005

著者名:

ISBN:

9783540240617 [3540240616]
9783540301370 [3540301372]

書誌ID:

OB00352758

子書誌情報

フルテキスト

所蔵情報

書誌詳細

言語:

英語

目次情報:

Introduction / 1：

Overview / 2：

Outline / 2.1：

Statement of Main Results / 2.2：

References and Related Works / 2.3：

Open Problems / 2.4：

Technical Prerequisites / 3：

Subresultants and the Euclidean Algorithm / 3.1：

The Cost of Arithmetic / 3.2：

Change of Basis / 4：

Computing Taylor Shifts / 4.1：

Conversion to Falling Factorials / 4.2：

Fast Multiplication in the Falling Factorial Basis / 4.3：

Modular Squarefree and Greatest Factorial Factorization / 5：

Squarefree Factorization / 5.1：

Greatest Factorial Factorization / 5.2：

Modular Hermite Integration / 6：

Small Primes Modular Algorithm / 6.1：

Prime Power Modular Algorithm / 6.2：

Implementation / 6.3：

Computing All Integral Roots of the Resultant / 7：

Application to Hypergeometric Summation / 7.1：

Computing All Integral Roots Via Factoring / 7.2：

Application to Hyperexponential Integration / 7.3：

Modular LRT Algorithm / 7.4：

Modular Algorithms for the Gosper-PetkovÜek Form / 8：

Modular GP′-Form Computation / 8.1：

Polynomial Solutions of Linear First Order Equations / 9：

The Method of Undetermined Coefficients / 9.1：

Brent and Kung's Algorithm for Linear Differential Equations / 9.2：

Rothstein's SPDE Algorithm / 9.3：

The ABP Algorithm / 9.4：

A Divide-and-Conquer Algorithm: Generic Case / 9.5：

A Divide-and-Conquer Algorithm: General Case / 9.6：

Barkatou's Algorithm for Linear Difference Equations / 9.7：

Modular Algorithms / 9.8：

Modular Gosper and Almkvist & Zeilberger Algorithms / 10：

High Degree Examples / 10.1：

References

Index

Introduction / 1：

Overview / 2：

Outline / 2.1：

Statement of Main Results / 2.2：

References and Related Works / 2.3：

Open Problems / 2.4：

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