#9650: Adding support for differential forms
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Reporter: jvkersch | Owner: burcin
Type: enhancement | Status: needs_work
Priority: major | Milestone:
Component: symbolics | Keywords: forms, functions, symbolics
Author: jvkersch | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by jason):
* status: new => needs_work
Comment:
Wow, thanks! I'm not an expert in differential geometry, so I'm going to
have to rely on someone else to vet the theoretical design at this level.
Here are a few python comments, though:
* {{{all([is_SymbolicVariable(c) for c in coordinates])}}} should not
construct a list, so that short-circuiting can occur:
{{{all(is_SymbolicVariable(c) for c in coordinates)}}}
* Checking for {{{None}}} should be done with is (it's a lot faster that
way): {{{metric is not None}}}
I also added mention of two other mma packages to the wiki page, one of
which has a nice Integral command. Do you see us getting a command that
can integrate like the following commands indicate?
{{{
The area of the unit square is calculated by:
Integral[ d[x,y] , Chain[ {x -> s, y -> t}, {s, 0, 1}, {t, 0, 1}]].
The area of the circle of radius R is calculated by:
SetAttributes[R, Constant];
Integral[ d[x,y] , Chain[ {x -> r Cos[theta], y -> r Sin[theta]}, \
{r, 0, R}, {theta, 0, 2Pi}]].
Stokes Theorem:
Integral[ d @ ((x/2) d[y] - (y/2) d[y]) , Chain[ {x -> s, y -> t}, \
{s, 0, 1}, {t, 0, 1}]] ==
Integral[ ((x/2) d[y] - (y/2) d[y]) , Boundary @ Chain[ {x -> s, y -> \
t}, {s, 0, 1}, {t, 0, 1}]]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9650#comment:2>
Sage <http://www.sagemath.org>
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