GSoC 2014: Mathematics Projects - Ordinary Differential Equations, Series expansions, Group theory, Polynomials module

[Saket Dewangan]

Hi,

I am a pre-final year student at IIT Delhi, majoring in Electrical Engineering with a minor in Mathematics and Computing Applications. I have a huge motivation in computer algebra. I have a vast experience with Python and I have also used SymPy before for applications in Neural Networks. I am interested in Google SoC and would be really happy to code under SymPy's banner.

I wanted to implement different transforms techniques (FFT, Circular DFT, IDFT, Discrete Cosine Transform etc)  for my project. I know laplace is there in SymPy already, and I sure hope so for Fourier and even z-transform, but I am not so sure about others. Do tell me if this idea sounds any good.

http://en.wikipedia.org/wiki/Fast_Fourier_transform

http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Circular_convolution_theorem_and_cross-correlation_theorem

http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Expressing_the_inverse_DFT_in_terms_of_the_DFT

http://en.wikipedia.org/wiki/Discrete_cosine_transform

In the listed projects ( at https://github.com/sympy/sympy/wiki/GSoC-2014-Ideas), following projects  (in the order of preference) struck me out the most:

1. Series expansions

2. ODEs

3. Group Theory

4. Polynomials module (Univariate)

Expecting a positive response.

Thank you.

PS- I tried posting once before, I do't know if that got posted. Pardon for a re-post.

[Saket Dewangan]

I was wondering if anyone liked the idea or not. I would be really glad if Aaron or anyone else would have a say in this.

Thank you.

--
You received this message because you are subscribed to the Google Groups "sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email to sympy+un...@googlegroups.com.
To post to this group, send email to sy...@googlegroups.com.
Visit this group at http://groups.google.com/group/sympy.
For more options, visit https://groups.google.com/groups/opt_out.

--

------------------------------------------------------

Saket Dewangan,

Third Year Undergraduate Student,

Electrical Engineering Department,
IIT Delhi.
Ph- 8860715533
e-mail: sake...@gmail.com

-------------------------------------------------------

[Matthew Rocklin]

Hi Saket, 

Thanks for reaching out.  Sorry for not getting back to you the first time; we're all a little busy.  

I personally find signals processing transforms to be very interesting.  I usually think about these from a numerical perspective though, not a symbolic one.  Maybe you can describe how signals processing would fit into the rest of SymPy and the symbolic computing world.

-Matt

[Saket Dewangan]

Hey Matt,

Thanks for a reply. I guess I was getting a little too excited.

I admit signal transforms are typically numerical in nature, but there are many problems in digital signal processing (DSP) that can be converted into algebraic problems over Laurent and polynomial rings and are generally easy to solve with current methods of symbolic computation. Most Real and complex-valued data satisfy the mathematical properties of a field. I am mostly concentrated on using the method of Gröbner bases as the computational tool.

Besides this, there is also a whole different category of symbolic signals, which do not rely on any mathematical structure.  Symbolic signals differ from numeric signals in that symbolic sets have no additional mathematical structure. A set of symbols is not a field because algebraic operations on symbols are usually not meaningful. For example, addition, multiplication, and numeric ordering cannot be performed on symbols.Although this is a second part is optional for my project. I am mostly focused on symbolic computation and signal processing.  

Please let me know what you think about it.

References:
1. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=809533
2. http://en.wikipedia.org/wiki/Gr%C3%B6bner_basis
3. http://en.wikipedia.org/wiki/Polynomial_ring

[Saket Dewangan]

Also, I will be able to complete fourier and laplace transforms during the project (as suggested in the ideas list) , most probably in the first two-three weeks.

               "generalized functions -- Dirac delta, P(1/x), etc... Convolution, Fourier and Laplace transforms
                             Fourier and Laplace transforms are implemented but we can not do many cases involving distributions is                              this enough alone for a project though? -Aaron "

Expecting a positive response.

[Harsh Gupta]

> Also, I will be able to complete fourier and laplace transforms during the project (as suggested in the ideas list) , most probably in the first two-three weeks.

Currently sympy evaluates the transforms by simply computing their
respective integrals. But this way we are not able to solve transforms
for many cases. So, the current transforms module is also not "aware"
of the convolution theorem or the derivatives of the integrals or
differentials. It will helpful if you provide more concrete ideas
about how you are going to improve the calculation of transforms.

You might want to look at the small discussion I had with Aaron on
handling derivatives in calculating inverse laplace transform at
https://groups.google.com/forum/#!searchin/sympy/Laplace$20Transform/sympy/YX7dQE8m1ew/XAohT3xPZmMJ.
Also searching the mailing list for Transforms might give you some
pointers to start.

--
Harsh