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Integration error #7383

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asmeurer opened this Issue Apr 8, 2014 · 0 comments

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asmeurer commented Apr 8, 2014

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Hello,

I was double-checking an integral with sympy, and noticed that the software comes up with the wrong answer. The integrand has five terms, which can be collected into three groups. Two of the groups -- Ec1 and Ec2 -- cancel after integrating over z. Strangely, sympy gets the answer right if you ask it to integrate the groups separately.

x, z, R, a = symbols('x z R a')
r = sqrt(x**2 + z**2)
u = erf(a*r/sqrt(2))/r
Ec = diff(u, z, z).subs([(x, sqrt(R*R-z*z))])
compare
>>> simplify(integrate(Ec, (z, -R, R)))
-2*sqrt(2)*a*(R**2*a**2 + 3*R**2 - 3)*exp(-R**2*a**2/2)/(3*sqrt(pi)*R**3)
to the analytical answer
-2*sqrt(2)*R*a**3*exp(-R**2*a**2/2)/(3*sqrt(pi))
in particular, Ec = Ec1 + Ec2 + Ec3, where
Ec1 = sympify('3*z**2*erf(sqrt(2)*a*sqrt(R**2)/2)/(R**2)**(5/2) - erf(sqrt(2)*a*sqrt(R**2)/2)/(R**2)**(3/2)')
Ec2 = sympify('+ sqrt(2)*a*exp(-R**2*a**2/2)/(sqrt(pi)*R**2) - 3*sqrt(2)*a*z**2*exp(-R**2*a**2/2)/(sqrt(pi)*R**4)')
Ec3 = Ec - Ec1 - Ec2 # -sqrt(2)*a**3*z**2*exp(-R**2*a**2/2)/(sqrt(pi)*R**2)

simplify(integrate(Ec1, (z, -R, R))) # -> 0
simplify(integrate(Ec2, (z, -R, R))) # -> 0

integrate(Ec3, (z, -R, R))

skirpichev added a commit to diofant/diofant that referenced this issue Dec 28, 2015

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