Indeed. Thank you for this tips.
Julien
On Tuesday, March 31, 2015 at 8:17:36 AM UTC+2, Kalevi Suominen wrote:
>
>
>
> On Tuesday, March 31, 2015 at 2:40:34 AM UTC+3, Julien Hillairet wrote:
>>
>> Dear all,
>>
>> First of all, many thanks for Sympy, which is a great tools !
>>
>>
>> I try to integrate a product of two sinus functions such as :
>>
>> f(x) = sin(pi*n/L*x) * sin(pi*m/L*x)
>>
>> where n and m are two positive integer (and L>0). I've found the correct
>> expected values (L/2 if m=n, 0 otherwise). But if I make a small change of
>> variable, moving x to x+L/2, then Sympy fails to provide me an answer. Is
>> there a way to "help" Sympy finding the correct solution ?
>>
>> An example is below :
>>
>> ----
>>
>> z = symbols('z')
>> m, n = symbols('m n', positive=True, integer=True)
>> L = symbols('L', positive=True, real=True)
>>
>> def e1(z, n, L):
>> k_n = n*pi/L
>> return sin(k_n*(z))
>>
>> def e2(z, n, L):
>> k_n = n*pi/L
>> return sin(k_n*(z+L/2))
>>
>> Imn1 = integrate(fu(e1(z, n, L)*e1(z, m, L)), (z, 0, L))
>> Imn2 = integrate(fu(e2(z, n, L)*e2(z, m, L)), (z, -L/2, L/2))
>>
>> ---
>>
>> In [16]: Imn1
>> Out[16]: Piecewise((L/2, m == n), (0, True))
>>
>> In [17]: Imn2
>> Out[17]: Integral(sin(pi*m*(L/2 + z)/L)*sin(pi*n*(L/2 + z)/L), (z, -L/2,
>> L/2))
>>
>> Best regards,
>>
>> Julien
>>
>
> It seems that SymPy can compute the integral if you write sin(pi*m/2 +
> pi*m*z/L) instead of
> sin(pi*m*(L/2 + z)/L). Apparently its pattern matching does not cover the
> latter form. (fu will
> not be needed.)
>
> Kalevi Suominen
>
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