What am I doing wrong with apart()?

[Francesco Biscani]

Hello list,

I feel a bit embarrassed as probably I am doing something blatantly wrong, but I cannot understand what is going here. Consider this snippet (copy pasted from an Ipython notebook):

"""

import sympy

sympy.init_printing()

from sympy import Symbol,sqrt,cos,sin,solve,Function,atan,apart,S

# Some symbols

h,n,m,M,g,t,xi_s,eta_s = [Symbol(_) for _ in ['h','n','m','M','g','t',r'\xi',r'\eta']]

pxi,peta = [Symbol(_) for _ in [r'p_\xi',r'p_\eta']]

# A rational expression

foo = 32*eta_s**8*g*m/(eta_s**2+xi_s**2)**3-64*eta_s**6*g*m/(eta_s**2+xi_s**2)**2-23*g/2*eta_s**2*m-7*g/2*xi_s**2*m+(320*eta_s**4*g*m**2+peta**2+pxi**2)/(8*m*(eta_s**2+xi_s**2))

"""

Now if I do "foo_apart(xi_s)", it seems like there are two parts of the expression that disappear. (specifically, -23*g/2*eta_s**2*m-7*g/2*xi_s**2*m is not there any more). Indeed, if I do:

"""

foo.apart(xi_s).expand() == foo.expand()

"""

This returns False.

My brain is a bit fried at the moment :) So what am I overlooking here?

Cheers,

  Francesco.

[Francesco Biscani]

A much reduced testcase:

x,y = [Symbol(_) for _ in ['x','y']]

foo = 1/(x+y)-Rational(1,2)*x**2

print(foo.apart(x))

This prints:

1/(x + y)

If the Rational has an integral value, everything looks ok:

foo = 1/(x+y)-Rational(6)*x**2

print(foo.apart(x))

Output: -6*x**2 + 1/(x + y)

[Aaron Meurer]

It looks like a bug. If you do foo.expand() - foo.apart(xi_s).expand()
you get a term which is definitely not equal to zero.

Aaron Meurer

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[Chris Smith]

Check the version of SymPy that you are using. The development version gives

>>> var('x y')

(x, y)

>>> apart(1/(x+y)-Rational(1,2)*x**2)

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

  File "sympy\utilities\decorator.py", line 35, in threaded_func

    return func(expr, *args, **kwargs)

  File "sympy\polys\partfrac.py", line 123, in apart

    return apart(fc, x=x, full=full, **_options)

  File "sympy\utilities\decorator.py", line 35, in threaded_func

    return func(expr, *args, **kwargs)

  File "sympy\polys\partfrac.py", line 126, in apart

    "multivariate partial fraction decomposition")

NotImplementedError: multivariate partial fraction decomposition

[Aaron Meurer]

The foo.expand() - foo.apart(xi_s).expand() issue is there for me on
the master version of SymPy.

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/e7daf358-3af7-4c36-b088-9ed11d6c67b4%40googlegroups.com.

[Chris Smith]

issue opened at https://github.com/sympy/sympy/issues/9123