Here's a slight variation on the sympy tutorial examples that gives an
error:
In [1]: f = 1/x + 1/y + 1/z
In [2]: f.together()
Out[2]:
x⋅y + x⋅z + y⋅z
───────────────
x⋅y⋅z
In [3]: f.together().apart()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
/home/jlh/<ipython-input-3-079c454de460> in <module>()
----> 1 f.together().apart()
...
NotImplementedError: multivariate partial fraction decomposition
In [4]:
Note that in this case a simple 'apart' function can be made from
num,den = f.together().as_numer_denom()
sum([n/den for n in num.as_ordered_terms()])
but there should be a general multivariate inverse to 'together'. I
don't see an issue for this problem yet but I'm happy to make one.
There's already a 'partial_fraction()' method in Sage that works with
many variables (you can give a string of vars as an argument, as in
"f.partial_fraction('xyz')"), and it makes sense to offer both 'apart'
and 'together' in any cases where you offer one of them. Especially,
in the tutorial, there is an immediate one variable example of the
inverse of 'apart' and 'together', and then an example of multivariate
'together', after which one naturally tries the multivariate 'apart'
and gets the NotImplementedError.
Has anyone started work on such a decomposition function?
John Hoebing
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