Algebraic extensions for symbolic summation

Abstract......Page 5
Zusammenfassung......Page 7
Introduction......Page 11
A brief overview......Page 13
Notation and conventions......Page 15
Summation in finite terms......Page 17
Difference fields and summation......Page 21
Towers of difference fields......Page 22
First order linear extensions......Page 23
Homogeneous and inhomogeneous extensions......Page 24
-factorization......Page 29
Tests for -radicals......Page 31
Algebraic extensions for summation in finite terms......Page 33
Commutative algebra......Page 35
D-rings......Page 36
Difference/differential equations over algebraic extensions......Page 38
Structure of algebraic extensions......Page 42
Extensions of algebraic extensions......Page 50
Creative telescoping over algebraic extensions......Page 54
Nullspace computation over rational function fields......Page 57
Outline of approach......Page 59
BLAS optimized output sensitive x-adic lifting......Page 61
Nullspace via outer product adjoint formula......Page 63
Performance comparison......Page 64
Implementation......Page 67
Notation and Symbols......Page 73
Bibliography......Page 75