Re: Symbolic Integration of Sums
- To: mathgroup at smc.vnet.net
- Subject: [mg79182] Re: Symbolic Integration of Sums
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 20 Jul 2007 03:31:29 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <f7n4pv$286$1@smc.vnet.net>
Peter wrote: > I am having trouble figuring out how to Mathematica to recognize sums when I > take derivates. > > Here is a very simple example, define > > portM = Sum[w[i] m[i], {i, 1, n}] > > Then, if I try to take the derivative of portM wrt say w[1] I get 0 > instead of m[1]. > > D[portM, w[1]] --> returns 0 > > If I spell the sum out explicitly using say for n=10: > > portM = Sum[w[i] m[i], {i, 1, 10}] > > I get the correct answer but this is often messy with the real > problems I am working with and it also removes the ability to work > with the length of sum in the other parts of the analysis I am doing. > > Is using Sum in this way simply a level of abstraction more than Mathematica > can do or am I asking it the wrong question? > > Many thanks. Adapted from the thread, "partial derivative of a sum", http://forums.wolfram.com/mathgroup/archive/2005/Aug/msg00572.html In[1]:= sumD[j_Integer, n_Integer] := If[j > n, 0, D[Sum[w[i]*m[i], {i, 1, n}], w[j]]] sumD[j_Integer, Infinity] := m[j] sumD[1, 10] Out[3]= m[1] The function above might or might not suit your needs, but it is a good started. Also, the thread titled "Derivative of Sum" might be of interest. See http://forums.wolfram.com/mathgroup/archive/2004/May/msg00055.html Regards, Jean-Marc