Jason Suagee wrote:
>
> I am interested in working on the project about implementing Mark van
> Hoeij's algorithm to factor linear ODE's. Currently, I am a fourth year PhD
> student in the Math Department at George Washington University (Washington
> DC, USA). My research area is in low dimensional topology, which has not
> much to do with Differential Galois theory. I am very interested, however,
> in learning more about it, and even possibly doing future work related to
> differential Galois theory for PDE's.
>
> I looked at the SPAD language (in particular the Pascal's Triangle example
> on http://axiom-wiki.newsynthesis.org/PascalTriangle) and am confident that
> I could get up to speed using it pretty fast. Reading and understanding the
> necessary parts of Hoeij's thesis would probably be more time consuming,
> but I think it would be a really interesting way to spend the Summer.
>
> I would have contacted you earlier, but I have been very busy putting
> together another proposal for Sage (also a Google Summer of Code
> organization). Would you please let me know if there is still interest on
> your part for this project.
Yes. I hope you understand that Google will support only one project
per student. We are interested even if you eventually end up doing
different project.
> Here is a little bit about my background: In addition to the coursework at
> my home university, I have taken coursework at the University of Maryland
> in Commutative Algebra, Geometric Analysis, Riemannian Geometry and
> Differential Topology. Most of my knowledge of ODE's comes from Lawrence
> Perko's Differential Equations and Dynamical Systems text (the first few
> chapters). Most of my knowledge of algebra (and Galois theory) comes from
> Dummit and Foote's graduate textbook.
Welcome.
It looks that you have quite adequate background. I would suggest
a little coding task (I suggested the same to other candidate who
apparently lost interest): write a Spad function which given a
linear ordinary differential operator returns true if the operator
has constant coefficients and false otherwise.
This can be done in few lines of code. The difficulty is to
find which operations are available and how to use them.
Let me add that FriCAS has special type for differential
opeartors namely 'LinearOrdinaryDifferentialOperator1'
(there are other, but this one is appropriate for
factorization).
Also, HyperDoc help browser which should pop up when you
start FriCAS in a GUI has a search box. Given type name
it you can get for example list of operations with
short descriptions and expected parameters.
--
Waldek Hebisch
[email protected]
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