working with sums

*To*: mathgroup at yoda.physics.unc.edu*Subject*: working with sums*From*: mwl at trantor.jpl.nasa.gov (Martin W. Lo)*Date*: Wed, 3 Mar 93 10:44:34 PST

Dear Mathgroup, 1.) I'm trying to work with sums and can't get the algebra to work. For example: In[1]:= << Algebra`SymbolicSum` In[2]:= s=Sum[a*x[i],{i,1,n}] Out[2]= Sum[a x[i], {i, 1, n}] In[3]:= s/a Sum[a x[i], {i, 1, n}] Out[3]= ---------------------- a Of course, the function x[i] is not defined, but surely this simple factor out to be possible? Using Expand and Simplify do nothing. Although, differentiation with respect to a works: In[4]:= D[s,a] Out[4]= Sum[x[i], {i, 1, n}] Is there some way to make this work? Or do I have to use Map and get at the expression at specific levels? 2.) What is the difference between Sum and SymbolicSum? This is what I get with SymbolicSum (doing the same operations above): In[5]:= ss=SymbolicSum[a*x[i],{i,1,n}] Out[5]= SymbolicSum[a x[i], {i, 1, n}] In[6]:= ss/a SymbolicSum[a x[i], {i, 1, n}] Out[6]= ------------------------------ a In[7]:= D[ss,a] (1,0) Out[7]= {x[i] SymbolicSum [a x[i], {i, 1, n}], (1,0) > x[i] SymbolicSum [a x[i], {i, 1, n}], (1,0) > x[i] SymbolicSum [a x[i], {i, 1, n}]} What does this last result mean? Does one have to specify the function x in some way? I need it to be arbitrary. Thanks in advance. Martin Lo jpl 818-354-7169 mwl at trantor.jpl.nasa.gov