Re: A Bug in symbolic summation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg113175] Re: A Bug in symbolic summation?*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Sat, 16 Oct 2010 13:13:03 -0400 (EDT)*References*: <i95tkd$65u$1@smc.vnet.net>

On 14 oct, 05:32, Fancy Airex <aoi... at gmail.com> wrote: > I wish to do a basic symbolic manipulation of two summations. > > > Sum[f[i], {i, 0, m}] - Sum[f[i], {i, 0, j}] > > but can't get the expected result > > > Sum[f[i], {i, j+1, m}] > > I also tried > > > Sum[f[i], {i, 0, m}] - f[0] > > but can't get the expected result > > > Sum[f[i], {i, 1, m}] > > Though when I replace m with any definite number everything works > fine. > > It seems that Mathematica can't change the minimum/maximum value of > the summation variable i above in symbolic calculation... > > I also tried another system, but failed to do such symbolic computation. > > Did I miss any point here? > > Best, > Rex My suggestion : In[1]:= myCombine[Sum[a_, {i_, i1_, i2_}] - Sum[a_, {i_, j1_, j2_}]] := Sum[a, {i, Min[i1, j1], Max[i1, j1] - 1}] + Sum[a, {i, Min[i2, j2] + 1, Max[i2, j2]}] In[2]:= s = Sum[f[i], {i, 0, m}] - Sum[f[i], {i, 0, j}] ; In[3]:= s // myCombine Out[3]= Sum[f[i], {i, 1 + Min[j, m], Max[j, m]}] In[4]:= % // Simplify[#, m > j] & Out[4]= Sum[f[i], {i, 1 + j, m}] -- Valeri Astanoff