*To*: mathgroup@smc.vnet.net*Subject*: [mg11145] dummy indices / variables (was my own sum)*From*: Richard Easther <easther@het.brown.edu>*Date*: Mon, 23 Feb 1998 21:41:04 -0500*Organization*: High Energy Theory Group, Physics Dept, Brown University*References*: <6cakf2$fac@smc.vnet.net> <6cn9ig$bfq@smc.vnet.net>

Daniel Lichtblau wrote: > > Thomas Lemm wrote: > > > > I want to implement another type of Sum to treat expressions in a > > "physical" manner. But I need to know how Mathematica tackles the > > Problem: > > > > Sum[F[x],{x,-a,a}]==Sum[F[y],{y,-a,a}] > > > > Help welcome > > > > Thomas Lemm > > > > Lemm@stud-mailer.uni-marburg.de > > Not sure exactly what you have in mind, but if you want to just have > dummy summation variables replaced by a standard variable, call it > 'local', you could do as below. > > In[10]:= mySum[a_,{x_,y_,z_}] := Block[{local}, > ReleaseHold[Hold[Sum[a, {local,y,z}]] /. x->local]] > > In[11]:= mySum[F[x],{x,-a,a}] > Out[11]= Sum[F[local], {local, -a, a}] > > In[12]:= mySum[F[x],{x,-a,a}]==mySum[F[y],{y,-a,a}] Out[12]= True This touches on a problem that I am tackling at the moment, which is coming up with a method to let Mathematica recognise (and then perform simplifications upon) equivalent expressions with dummy indices. For instance, Sum[f[a],{a,1,m}] + Sum[f[b],{b,1,m}] // FullSimplify does not recognise that the two sums are identical, and misses what (to a human being, at least!) is a trivial simplification. What I am wondering is whether a) It is possible to extend Simplify or FullSimplify by specifying rules that would allow them to spot expressions such as integrals or sums which differed only in their dummy index, especially in cases where you have more than one dummy index, and complicated integrands. b) Or, for that matter, how would you implement a "MySimplify" which worked with a small subset of possible simplifications (including simplifying over dummy indices)? Any comment most appreciated! Richard Easther PS If anyone is keeping track, I would add the ability to recognise dummy indices to the wish-list for the next version of mathematica!