On 04/04/2013 06:27 AM, Prasoon Shukla wrote:
I think I have a fair idea of what the class may behave like. Let's
have a vector field like so (an example):
*v*(x, y, z) = /f (x, y, z) /*i *+ /g (x, y, z) /*j *+ /h (x, y, z) /*k*
*
*
Just and example in rectangular coordinates using variables x, y and z.
Now, we can have a class, say ParamSpace(). Let us define a spherical
surface like so:
/p = ParamRegion(x=5*sin(u)*cos(v), y=5*sin(u)*sin(v), z=5*cos(u),
params=[u, v], bounds=[(u, 0, PI), (v, 0, 2*PI) ])/
This object can then be passed to Vector.integrate() and can serve as
the container for defining the region of integration.
Obviously, one problem is how to implement multiple patches. I am
still thinking on it.
After this, the next step is the integration itself. This means I need
to add functionality to the integration module so that it can handle
multiple integrals too. (I couldn't find any such functions already
existing in SymPy. Is there any implementation of it?).
Another problem is with vector calc theorems. For example, if you have
a contour for a line integral, what area do you choose for applying
the Stokes theorem (as the area can be any that has the contour as its
boundary)? Similarly for Gauss theorem too. I am still thinking in
this direction. Will post here when something occurs to me.
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You might want to let i,j, and k be sympy noncommuting symbols then you
automatically get vector addition, subtraction, and multiplication by a
scalar and could write -
/p = ParamRegion(r=5*sin(u)*cos(v)*i+5*sin(u)*sin(v)*j+5*cos(u)*k,
params=[u, v], bounds=[(u, 0, PI), (v, 0, 2*PI) ])
change of coordinates becomes proper substitutions for i,j,k in terms of
i',j',k'.
Practically speaking with stokes theorem a surface would be defined
first and the closed contour would lie on the surface, not the other way
around.
/
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