The trac ticket <http://trac.sagemath.org/sage_trac/ticket/4039>
points out that there are two ways in Sage to do partial fraction
decompositions and recommends choosing only one of them. I might be
able to write a patch for this, but I don't know how to choose between
them, so I thought it would make sense to discuss the issue here
first. One way returns a formal sum:
(x - 3)/((x +1)*(x-1)) --> 2/(x + 1) - 1/(x - 1)
The other way returns a tuple:
(x - 3)/((x +1)*(x-1)) --> (0, [-1/(x - 1), 2/(x + 1)])
(The '0' is the 'whole' piece, followed by a list of the fractional
parts.)
So, which is preferable? I actually think it's reasonable to have
both, but I would suggest that f.partial_fraction_decomposition()
should return a formal sum, while
f.partial_fraction_whole_and_parts(), or f.partial_fraction_tuple(),
or something like that, should return a tuple.
(The actual focus of the ticket is that there should be one name, not
two: partial_fraction and partial_fraction_decomposition. Patching
this is easy, of course, and I would suggest keeping the longer name.
The issue of list vs. formal sum is also mentioned, and that's what
needs discussing.)
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