Here, frac is multivariate, i.e it depends on more than one variable. So,
you need to explicitly tell the apart function for which variable should it
perform the decomposition.
Eg. No need to give x as the second argument
In [21]: apart(1/((x+1)*(x+2)))
Out[21]:
1 1
- ───── + ─────
x + 2 x + 1
x is required here (multivariate)
In [22]: apart(y/((x+1)*(x+2)), x)
Out[22]:
y y
- ───── + ─────
x + 2 x + 1
On Monday, 15 June 2015 22:44:40 UTC+5:30, Hugh wrote:
>
> Hello,
>
>
> There is this block of code in the tutorial
> <http://docs.sympy.org/latest/tutorial/simplification.html>:
>
> >>> l = []
> >>> frac = apart(frac, a0)
> >>> frac
> a₂⋅a₃⋅a₄ + a₂ + a₄
> a₀ + ───────────────────────────────────────
> a₁⋅a₂⋅a₃⋅a₄ + a₁⋅a₂ + a₁⋅a₄ + a₃⋅a₄ + 1
> >>> l.append(a0)
> >>> frac = 1/(frac - a0)
> >>> frac
> a₁⋅a₂⋅a₃⋅a₄ + a₁⋅a₂ + a₁⋅a₄ + a₃⋅a₄ + 1
> ───────────────────────────────────────
> a₂⋅a₃⋅a₄ + a₂ + a₄
>
>
>
> I've read the documentation on apart() and factor() but I still don't
> understand the purpose of putting a0 as the second argument to the call to
> apart(). Also, leaving out a0 produces a NotImplementedError:
> multivariate partial fraction decomposition error. and replacing a0 with
> other symbols like a1, a2, etc works fine. But I still don't understand
> what's going on. Please help.
>
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