02.03.2011 22:31, Alexey U. Gudchenko пишет:
23.02.2011 06:12, Ronan Lamy пишет:
I think that a significant part of the difficulties in the discussions
about Taylor series and the like has been the lack of a common and
unambiguous vocabulary. So, I've started a wiki page defining some
concepts in order to clarify things:
https://github.com/sympy/sympy/wiki/Function-expansions
Feel free to expand or amend it, add links to and from it, etc.
NB: I had to use Markdown syntax because I couldn't figure out how to
get LaTeX to work in rST.
Also while writing it, I've noticed 2 additional problems with
Expr.series:
* The order is off by one.
* Its name is misleading since it doesn't return a series.
I am going to insert some little updates to this page.
But after thinkings, my opinion shaped that the title must be extended
On the one hand the series and expansion have self-dependent meanings
but they are intersected with each other on the other hand, that is why
they can be considered altogether. So for the present I create separated
page [2] temporary.
Changes:
- added classical **Laurent series**
- separated Series and expansions sections.
- for **Taylor series** added X = x - x0
- "generating function" sections added
- At Current situation "Sum" (summation) class mentioned.
If you have not objections I will insert changes to original [1] (for
changes history tracking) then (if I will be able to) rename it to the
"Series and function expansions" title.
[1] https://github.com/sympy/sympy/wiki/Function-expansions
[2] https://github.com/sympy/sympy/wiki/Function-expansions-and-series
Then I plan to add a few lines about mathematical reasons for series and
asymptotic expansions, and about purpose-oriented mathematical operation
with them. After that I will be able to formulate what I want from sympy
technically.
Alexey U.
Added:
In [2] added:
* remarks what is *formal* means
* In "current situation" section added:
- "But the present method "series" which returns various kinds of
series is convenient and used for the task of *limits* processing..."
- mention that "Also the implementation of some series methods for
solving IDEs is processing now in Saptarshi's branch"
- "problems and remarks which we encounter" subsection
* "Usage and application" section
[2] https://github.com/sympy/sympy/wiki/Function-expansions-and-series
Alexey U.
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