On Wed, Mar 14, 2012 at 2:22 PM, john.hoebing <jlhs...@gmail.com> wrote:
> 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
Not as far as I know. The algorithm for multivariate partial fraction
decomposition is not implemented. It's described in the paper
"Multivariate Partial Fraction Expansion" by David R. Stoutemyer, it
should not be too difficult to implement, given that we already have
the algorithms for univariate decomposition and for multivariate
factorization implemented.
Aaron Meurer
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