Why doesn't SymPy integrate this function?

Question

I have the following:

x,x1,x2,t=symbols('x x1 x2 t')
f=t*x1*x2*(x-t)**(-0.5)
integrate(f,t)

I can integrate with respect to x , x1 and x2 , but when I try to integrate with respect to t (which is what I want) I get the following error

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py", line 1295, in integrate
    risch=risch, manual=manual)
  File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py", line 486, in doit
    conds=conds)
  File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py", line 908, in _eval_integral
    h = meijerint_indefinite(g, x)
  File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/meijerint.py", line 1612, in meijerint_indefinite
    res = _meijerint_indefinite_1(f.subs(x, x + a), x)
  File "/usr/local/lib/python2.7/dist-packages/sympy/integrals/meijerint.py", line 1677, in _meijerint_indefinite_1
    r = hyperexpand(r.subs(t, a*x**b), place=place)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/hyperexpand.py", line 2473, in hyperexpand
    return f.replace(hyper, do_replace).replace(meijerg, do_meijer)
  File "/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py", line 1408, in replace
    rv = bottom_up(self, rec_replace, atoms=True)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/simplify.py", line 999, in bottom_up
    rv = F(rv)
  File "/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py", line 1393, in rec_replace
    new = _value(expr, result)
  File "/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py", line 1336, in <lambda>
    _value = lambda expr, result: value(*expr.args)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/hyperexpand.py", line 2470, in do_meijer
    allow_hyper, rewrite=rewrite, place=place)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/hyperexpand.py", line 2355, in _meijergexpand
    t, 1/z0)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/hyperexpand.py", line 2281, in do_slater
    t, premult, bh, rewrite=None)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/hyperexpand.py", line 2038, in _hyperexpand
    ops += devise_plan(func, formula.func, z0)
  File "/usr/local/lib/python2.7/dist-packages/sympy/simplify/hyperexpand.py", line 1615, in devise_plan
    raise ValueError('Non-suitable parameters.')
ValueError: Non-suitable parameters.

What does this error mean?

Answer 1

Many of SymPy's routines struggle to handle floating point numbers, especially in exponents. Use rational numbers whenever possible. More discussion in common gotchas and pitfalls .

>>> x,x1,x2,t=symbols('x x1 x2 t')
>>> f=t*x1*x2*(x-t)**(-Rational('0.5'))
>>> integrate(f,t).simplify()
Piecewise((2*sqrt(x)*x1*x2*(-I*t**2*sqrt((t - x)/x) - I*t*x*sqrt((t - x)/x) + 2*t*x + 2*I*x**2*sqrt((t - x)/x) - 2*x**2)/(3*(t - x)), Abs(t/x) > 1), (2*sqrt(x)*x1*x2*(-t**2*sqrt((-t + x)/x) - t*x*sqrt((-t + x)/x) + 2*t*x + 2*x**2*sqrt((-t + x)/x) - 2*x**2)/(3*(t - x)), True))

Not the nicest answer, but it's an answer. If you know that x and t are, say, positive, it might help in simplification to declare it as such from the beginning. There are also two cases depending on Abs(t/x) being greater than 1 or not.

Ways to create the rational exponent 1/2:

• Rational(1, 2)
• Rational('0.5')
• S(1)/2
• or just use sqrt function, which has the same effect.