Series and Series expansion. #41
Conversation
Formal Power Series and fourier series
|
@leosartaj I have added you as a collaborator. |
|
You also could have created a branch on this repo. |
| @@ -17,6 +17,10 @@ \subsection{Matrices} | |||
| % Physics module (some sampling, to show that it is there) | |||
| \subsection{Physics} | |||
|
|
|||
| % Series module (Formal Power Series, Fourier Series) | |||
| \subsection{Series} | |||
| \input{series.tex} | |||
There was a problem hiding this comment.
This imports content of another .tex file. This way fewer merge conflicts for everyone.
| observation that a truncated Taylor series, is in fact a polynomial. | ||
| Ring-series uses the efficient representation and operations of sparse | ||
| polynomials. The choice of sparse polynomials is deliberate as it performs | ||
| well in a wider range of cases than a dense representation. It gives the user |
|
Please review. Ping @isuruf @scopatz @shivamvats |
|
This needs to be updated wrt to master and still needs a review. |
TODO- Add reference to benchmark.
| The function \texttt{rs\_series} makes use of these elementary functions to | ||
| intelligently expand an arbitrary SymPy expression. Currently it only supports | ||
| expansion about 0 and is under active development. Ring Series is several times | ||
| faster than the default implementation with the speed difference increasing |
There was a problem hiding this comment.
You could add a comment here. When you have the benchmarks you can add them here. @shivamvats
|
@scopatz Could you please review this? |
| >>> x, y = symbols('x, y') | ||
| >>> series(sin(x+y) + cos(x*y), x, 0, 2) | ||
| 1 + sin(y) + x*cos(y) + O(x**2) | ||
| \end{verbatim} |
There was a problem hiding this comment.
I don't think this code block is tied well to the text around it.
| 1 + sin(y) + x*cos(y) + O(x**2) | ||
| \end{verbatim} | ||
|
|
||
| The newer and much faster approach called Ring Series makes use of the |
There was a problem hiding this comment.
also, I am not sure that the adjective newer is useful here. Maybe alternative.
There was a problem hiding this comment.
Similarly with faster, do we have a citation for this or is this something that we can easily prove? If not, we may want to leave it out.
There was a problem hiding this comment.
There are a few speed comparisons here. What sort of citation would do?
Every series that ring series expands, it does so a couple of times faster than the default series method. We were planning to benchmark the two methods. What would be a good way to go about that?
There was a problem hiding this comment.
Maybe you could consolidate the information in that link into a table?
| 1 + sin(y) + x*cos(y) + O(x**2) | ||
| \end{verbatim} | ||
|
|
||
| The newer and much faster\cite{sympyRingSeries} approach called Ring Series makes use of the |
There was a problem hiding this comment.
@scopatz I have cited the SymPy doc here. Will update the doc with more speed comparisons.
|
Thanks @leosartaj! Just the one small issue that I am sure to notice in the full read through. |
|
Thanks to @asmeurer for merging. |
@leosartaj I have reopened our PR here. Were you able to compile the code you added?