Status: Accepted
Owner: asmeurer
CC: [email protected]
Labels: Type-Defect Priority-Medium Integration
New issue 2332 by asmeurer: Problem with substituting a term in an Integral
http://code.google.com/p/sympy/issues/detail?id=2332
Sorry I couldn't make this simpler. I don't have time to debug it further
right now. Basically, subs is not replacing the integrand in the below
expression for some reason.
In [201]: print a
f(t) == C1*sin(t*lambda_n**(1/2)) + C2*cos(t*lambda_n**(1/2)) +
C3*sin(t*lambda_n**(1/2)) + C4*cos(t*lambda_n**(1/2)) +
Integral((c*lambda_n**(1/2)*sin(t) - c*lambda_n*(-1)**n -
c*l*(-1)**n*exp(-t)/lambda_n)*cos(t*lambda_n**(1/2))/(-lambda_n**(1/2)*cos(t*lambda_n**(1/2))**2
- lambda_n**(1/2)*sin(t*lambda_n**(1/2))**2), t)*sin(t*lambda_n**(1/2)) -
Integral((c*lambda_n**(1/2)*sin(t) - c*lambda_n*(-1)**n -
c*l*(-1)**n*exp(-t)/lambda_n)*sin(t*lambda_n**(1/2))/(-lambda_n**(1/2)*cos(t*lambda_n**(1/2))**2
- lambda_n**(1/2)*sin(t*lambda_n**(1/2))**2), t)*cos(t*lambda_n**(1/2))
In [202]: print b
(c*lambda_n**(1/2)*sin(t) - c*lambda_n*(-1)**n -
c*l*(-1)**n*exp(-t)/lambda_n)*cos(t*lambda_n**(1/2))/(-lambda_n**(1/2)*cos(t*lambda_n**(1/2))**2
- lambda_n**(1/2)*sin(t*lambda_n**(1/2))**2)
In [203]: b in a
Out[203]: True
In [206]: print trigsimp(b)
-(c*lambda_n**(1/2)*sin(t) - c*lambda_n*(-1)**n -
c*l*(-1)**n*exp(-t)/lambda_n)*cos(t*lambda_n**(1/2))/lambda_n**(1/2)
In [207]: trigsimp(b) == b
Out[207]: False
In [208]: print a.subs(b, trigsimp(b))
f(t) == C1*sin(t*lambda_n**(1/2)) + C2*cos(t*lambda_n**(1/2)) +
C3*sin(t*lambda_n**(1/2)) + C4*cos(t*lambda_n**(1/2)) +
Integral((c*lambda_n**(1/2)*sin(t) - c*lambda_n*(-1)**n -
c*l*(-1)**n*exp(-t)/lambda_n)*cos(t*lambda_n**(1/2))/(-lambda_n**(1/2)*cos(t*lambda_n**(1/2))**2
- lambda_n**(1/2)*sin(t*lambda_n**(1/2))**2), t)*sin(t*lambda_n**(1/2)) -
Integral((c*lambda_n**(1/2)*sin(t) - c*lambda_n*(-1)**n -
c*l*(-1)**n*exp(-t)/lambda_n)*sin(t*lambda_n**(1/2))/(-lambda_n**(1/2)*cos(t*lambda_n**(1/2))**2
- lambda_n**(1/2)*sin(t*lambda_n**(1/2))**2), t)*cos(t*lambda_n**(1/2))
In [209]: trigsimp(b) in a.subs(b, trigsimp(b))
Out[209]: False
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