Derivative of summations

Question

I am using sympy from time to time, but am not very good at it. At the moment I am stuck with defining a list of indexed variables, i.e. n1 to nmax and performing a summation on it. Then I want to be able to take the derivative:

So far I tried the following:

numSpecies = 10
n = IndexedBase('n')
i = symbols("i",cls=Idx)
nges = summation(n[i],[i,1,numSpecies])

However, if i try to take the derivative with respect to one variable, this fails:

diff(nges,n[5])

I also tried to avoid working with IndexedBase.

numSpecies = 10
n = symbols('n0:%d'%numSpecies)
k = symbols('k',integer=True)
ntot = summation(n[k],[k,0,numSpecies])

However, here already the summation fails because mixing python tuples and the sympy summation.

How I can perform indexedbase derivatives or some kind of workaround?

Answer 1

With SymPy's development version, your example works.

To install SymPy's development version, just pull it down with git:

git clone git://github.com/sympy/sympy.git
cd sympy

Then run python from that path or set the PYTHONPATH to include that directory before Python's default installation.

Your example on the development version:

In [3]: numSpecies = 10

In [4]: n = IndexedBase('n')

In [5]: i = symbols("i",cls=Idx)

In [6]: nges = summation(n[i],[i,1,numSpecies])

In [7]: nges
Out[7]: n[10] + n[1] + n[2] + n[3] + n[4] + n[5] + n[6] + n[7] + n[8] + n[9]

In [8]: diff(nges,n[5])
Out[8]: 1

You could also use the contracted form of summation:

In [9]: nges_uneval = Sum(n[i], [i,1,numSpecies])

In [10]: nges_uneval
Out[10]: 
  10      
 ___      
 ╲        
  ╲   n[i]
  ╱       
 ╱        
 ‾‾‾      
i = 1     

In [11]: diff(nges_uneval, n[5])
Out[11]: 
  10      
 ___      
 ╲        
  ╲   δ   
  ╱    5,i
 ╱        
 ‾‾‾      
i = 1     

In [12]: diff(nges_uneval, n[5]).doit()
Out[12]: 1

Also notice that in the next SymPy version you will be able to derive symbols with symbolic indices:

In [13]: j = symbols("j")

In [13]: diff(n[i], n[j])
Out[13]: 
δ   
 j,i

Where you get the Kronecker delta.

If you don't feel like installing the SymPy development version, just wait for the next full version (probably coming out this autumn), it will support derivatives of IndexedBase.