Re: Why this can't be reduced by mathematica?!

*To*: mathgroup at smc.vnet.net*Subject*: [mg114197] Re: Why this can't be reduced by mathematica?!*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Fri, 26 Nov 2010 05:31:55 -0500 (EST)*References*: <iciul1$leo$1@smc.vnet.net> <iclfg0$ld0$1@smc.vnet.net>

On Nov 25, 11:58 am, Valeri Astanoff <astan... at gmail.com> wrote: > On Nov 24, 12:58 pm, olfa <olfa.mra... at yahoo.fr> wrote: > > > Hi Mathematica Community, > > > Reduce[s==Sum[a[index], {index, i + 1, N}] - Sum[a[index], {index, j + > > 1, N}] && > > j >= i,{s}] > > > the output should be s==Sum[a[index], {index, i+1, j }] > > > but it is not! > > Thank you. > > Good day, > > You can do it this way : > > 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[a[index], {index, i + 1, n}] - Sum[a[index], {index, j > + 1, n}]; > > In[3]:= s // myCombine // Simplify[#, j >= i] & > > Out[3]= Sum[a[index], {index, 1 + i, j}] > > -- > Valeri Here is the same one with some "protection" : myCombine[Sum[a_, {i_, i1_, i2_}] - Sum[a_, {i_, j1_, j2_}]] /; i1 == j1 || i2 == j2 := If[i2 == j2, Sign[j1 - i1], Sign[j2 - i2]]* (Sum[a, {i, Min[i1, j1], Max[i1, j1] - 1}] + Sum[a, {i, Min[i2, j2] + 1, Max[i2, j2]}]) v.a.