[sympy] Another GSoC Idea
Yuri Karadzhov
Now I'd ike to propose another idea for GSoC.
Idea: Implement algoryth to find symmetries of single equation or
system of ODE or PDE.
Aaron Meurer
(anyway, there will need to be a lot more details in the application).
Aaron Meurer
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Yuri Karadzhov
> I think this idea could work, but would like to see more details
> (anyway, there will need to be a lot more details in the application).
>
> Aaron Meurer
functionality
1. Generate infinitesimal operator of given variables
2. Calculate the extension of infinitesimal operator of given order
3. Calculate differential sequence of given equation (system of
equations)
4. Apply the infinitesimal operator to the equation (system of
equations)
5. Obtain system of determining equations
6. Calculate commutator and anticommutator of two operators
Then some additional functionality can be added
1. Obtain the classification and determining equations for the
classification problem
2. If tesor module allow – implement above functionality for arbitrary
order of dependent and independent variable e.g. x = (x_1,...,x_n), y
=(y_1,...,y_m), where n and m is unknown
3. If PDE module allow – solve the system of determining equations
4. If above is true – completely solve the classification problem in
simple cases
Brian Granger
<yuri.ka...@gmail.com> wrote:
> On Mar 22, 11:31 pm, Aaron Meurer <asmeu...@gmail.com> wrote:
>> I think this idea could work, but would like to see more details
>> (anyway, there will need to be a lot more details in the application).
>>
>> Aaron Meurer
>
> At least it is possible to implement basic the most routine
> functionality
> 1. Generate infinitesimal operator of given variables
> 2. Calculate the extension of infinitesimal operator of given order
> 3. Calculate differential sequence of given equation (system of
> equations)
> 4. Apply the infinitesimal operator to the equation (system of
> equations)
> 5. Obtain system of determining equations
> 6. Calculate commutator and anticommutator of two operators
For operators, commutators, etc., check out:
sympy.physics.quantum.operator|commutator|anticommutator
Cheers,
Brian
> Then some additional functionality can be added
> 1. Obtain the classification and determining equations for the
> classification problem
> 2. If tesor module allow – implement above functionality for arbitrary
> order of dependent and independent variable e.g. x = (x_1,...,x_n), y
> =(y_1,...,y_m), where n and m is unknown
> 3. If PDE module allow – solve the system of determining equations
> 4. If above is true – completely solve the classification problem in
> simple cases
>
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--
Brian E. Granger, Ph.D.
Assistant Professor of Physics
Cal Poly State University, San Luis Obispo
bgra...@calpoly.edu
elli...@gmail.com
Yuri Karadzhov
6. Classify algebra according to commutation relations and present the
table of commutation.
The other problems remain actual
> > For more options, visit this group athttp://groups.google.com/group/sympy?hl=en.
> --
> Brian E. Granger, Ph.D.
> Assistant Professor of Physics
> Cal Poly State University, San Luis Obispo
> elliso...@gmail.com