My specific problem is that it would have been a lot faster for me to
just evaluate this integral by hand, as at least I would have the
answer by now.
I don't really know what to say at this point except that sage could
be a lot easier to use right now than it currently is. I bring up this
example as something perhaps that could be improved upon
sage: var('m r a R')
sage: forget()
sage: assume(m>=0)
sage: assume(m,'integer')
sage: assume(R>0)
sage: assume(a>0)
sage: assume(R<a)
sage: integrate(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4),r)
Traceback (click to the left of this block for traceback)
...
Is 2*m-3 zero or nonzero?
I'll leave this next link just to make the point that other CASes
aren't quite as pedantic as sage likes to be,
http://www.wolframalpha.com/input/?i=int+1%2Fr^%282*m%2B2%29*%282*%28r%2Fa%29^2-%28r%2Fa%29^4%29+dr
Bottom line, sage currently has to be coddled excessively via
assumptions into giving any result at all, verses system which give
results which may happen to be incorrect for certain values. Ideally,
sage should give results with caveats included, but at the very least,
sage should not need to be spoonfed to the extent it currently has to
be just to get back basic results.
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