Re: Bug in Sum on symbolic differentiation
- To: mathgroup at smc.vnet.net
- Subject: [mg30732] Re: Bug in Sum on symbolic differentiation
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sat, 8 Sep 2001 02:56:30 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <9nam6l$nqb$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, for me q /: D[q[i_], q[j_]] := KroneckerDelta[i, j] Unprotect[Sum] HoldPattern[Sum[a_D, b__]] := Sum[Evaluate[a], b] Protect[Sum] work fine. But you should keep in mind that the exchange of the summation and the derivative may destroy the convergence of an infinite sum. Regards Jens ChiaMing Yu wrote: > > Dear Sir, > > Excuse me! > When I want to differentiate through a Sum, such as (in LaTeX format): > d (\Sum^n_{i=1} q_i) / d q_i > > The answer should be "1", because in the above equation, (d q_i) means > differentiate > respect to q_1, or q_2, or q_3, ..., etc, one and only one variable of the > possible-variable > set {q_i | i=1, .., n}. > > But when I excute following command, Mathematica give me the wrong answer > "n", > D[ Sum[q[i], {i,1,n}], q[i] ] > > It may because Mathematica first differentiate the inner expression of > Sum[], that is q[i], > respect to q[i] and get the result 1, then Mathematica Sum these 1 with n > times, that is > Sum[1, {i,1,n}], and return the output to be "n". > > When we assign a specific number to n, for example n=10, the operation will > be fine, > for example, > D[Sum[x[i], {i, 1, 10}], x[5]] > > But when the variable n is Not assign any number, the situation described > previously will > appear. This may imply the limitation of Sum[] on symbolic operation, > espetially differentiation opration. How can I refine the situation and get > my right answer "1" from Mathematica? > > Thank you for any suggestion! > > Chia-Ming Yu, September 5, 2001 > National Taipei University