viii Table of Contents
3.3.1 Computing the Most Rapidly Varying Sub expressions
:
39
3.3.2 Rewriting Functions in the Same Comparability Class
:
43
3.3.3 Series Expansion
:::::: ::::::::::: :::::
48
3.3.4 Moving up in the Asymptotic Scale
::::::: :::::
50
3.4 Pro of of Termination
::::: :::::::::: :::::::::
52
3.4.1 Global Iteration
:::::: ::::::::::: :::::
52
3.4.1.1 Rewriting Process
::::::: :::::::::
53
3.4.1.2 Series Expansion
::::: :::::::::: ::
54
3.4.1.3 Moving Up in the Scale
:::: :::::::::
57
3.4.2 Recursive Calls
::::::: ::::::::::: :::::
58
3.5 A Complete Example
::::: :::::::::: :::::::::
60
4 Related Work
::::::: ::::::::::: :::::::::: ::
63
4.1 Nested Forms
::::: ::::::::::: :::::::::: ::
63
4.1.1 Algorithm for Computing Nested Forms
::::::: ::
67
4.1.2 Comparison
:::::: :::::::::: :::::::::
68
4.2 Ghost and Shadow Approach
::::::: :::::::::: ::
73
5 Extensions
:::::: :::::::::: ::::::::::: :::::
75
5.1 Tractable Functions
::::: :::::::::: :::::::::
75
5.2 Essential Singularities
::::::: ::::::::::: :::::
79
5.3
Mrv
H
elds
:::::: ::::::::::: :::::::::: ::
85
6 Asymptotic Series
::::: ::::::::::: :::::::::: ::
89
6.1 The
MrvAsympt
Algorithm
:::: ::::::::::: :::::
90
6.2 Hierarchical Series
:::::: :::::::::: :::::::::
95
7 Implementation
:::::: ::::::::::: :::::::::: ::
97
7.1 Series Computation
:::::: :::::::::: :::::::::
97
7.1.1 Models to Represent General Power Series
:::::: ::
98
7.1.1.1 Truncated Power Series
:::: :::::::::
98
7.1.1.2 Innite Power Series
:::::: :::::::::
99
7.1.2 Lazy Evaluated General Sparse Power Series in Maple
:
100
7.1.3 Fixed Point Denitions
:::::: :::::::::: ::
103
7.2 Zero Recognition
::::::: :::::::::: :::::::::
106
7.3 The Properties of
! : ::::::::::: :::::::::: ::
111
7.4 Branch Cuts
:::::: ::::::::::: :::::::::: ::
112
7.5 Computing with Parameters
:::: ::::::::::: :::::
115
7.6 The
limit
Routine in the Maple Library
:::: :::::::::
116
8 Comparison
::::: :::::::::: ::::::::::: :::::
121
9 Conclusions
::::: :::::::::: ::::::::::: :::::
129
A Maple Code for Computing Limits of exp-log Functions
::::: ::
131
Curriculum Vitae
::::::: ::::::::::: :::::::::: ::
145
评论0
最新资源