#6189: 'integrate' produces incorrect answer
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Reporter: emchristiansen | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone:
Component: calculus | Keywords: integrate, integral, incorrect
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Affects:
x64 Ubuntu 9.04 (Jaunty)
Sage 4.0, compiled from source, and updated (sage -upgrade) as of this
posting
By simply casting a number using 'n()', I can cause integrate to return a
vastly different result. See below:
{{{
var = sage.calculus.calculus.var
def NormalPDF(x,mu,sigma):
return 1/sqrt(2*pi*sigma^2)*exp(-1/(2*sigma**2)*(x-mu)^2)
x = var('x')
mu = var('m')
sigma = var('s')
assume(sigma>0)
child1 = NormalPDF(x,0,1)
child2 = NormalPDF(x,n(0),n(1))
parent = NormalPDF(x,mu,sigma)
# this expansion helps Sage to do the integral
integrand1 = ((parent-child1)^2).expand()
integrand2 = ((parent-child2)^2).expand()
int1 = integrate(integrand1,x,-infinity,infinity)
int2 = integrate(integrand2,x,-infinity,infinity)
print "THIS EXPRESSION:"
print int1
print "\nSHOULD BE VERY SIMILIAR TO THIS EXPRESSION:"
print int2
print "\nMAKING THIS NUMBER:"
print int1.subs({mu:0,sigma:1}).n()
print "\nVERY SIMILAR TO THIS NUMBER:"
print int2.subs({mu:0,sigma:1}).n()
}}}
The above produces the output:
{{{
THIS EXPRESSION:
1/2*((s + 1)*sqrt(s^2 + 1)*e^(1/2*m^2/(s^2 + 1)) -
2*sqrt(2)*s)*e^(-1/2*m^2/(s^2 + 1))/(sqrt(s^2 + 1)*sqrt(pi)*s)
SHOULD BE VERY SIMILIAR TO THIS EXPRESSION:
1/2*(sqrt(0.5*s^2 + 0.5)*e^(1/2*m^2/(s^2 + 1)) -
sqrt(2)*s)*e^(-1/2*m^2/(s^2 + 1))/(sqrt(0.5*s^2 + 0.5)*sqrt(pi)*s)
MAKING THIS NUMBER:
0.000000000000000
VERY SIMILAR TO THIS NUMBER:
-0.116847488627555
}}}
Mathematica claims the correct integral is:
{{{
\frac{1+\sigma }{2 \sqrt{\pi } \sigma }-\frac{\sqrt{2} e^{-\frac{\mu
^2}{2+2 \sigma ^2}}}{\sqrt{\pi +\pi \sigma ^2}}
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6189>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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