http://www.mapleprimes.com/questions/126733-Splitting-Nested-Sums-Into-A-Set-Of-Single-Sums en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 09:51:40 GMT Thu, 11 Jun 2026 09:51:40 GMT The latest answers and comments added to the Question, Splitting nested sums into a set of single sums http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/126733-Splitting-Nested-Sums-Into-A-Set-Of-Single-Sums http://www.mapleprimes.com/questions/126733-Splitting-Nested-Sums-Into-A-Set-Of-Single-Sums?ref=Feed:MaplePrimes:Splitting nested sums into a set of single sums:Comments#answer126755 <p>I'm afraid I don't understand you.&nbsp; <br>Sum(Sum(x[i]*x[j], i=1..n),j=1..n) is the one that factors as Sum(x[i],i=1..n)*Sum(x[j],j=1..n).&nbsp; <br>The sum for j &lt;&gt; i does not factor.&nbsp; </p> <p>Unfortunately, Maple does not seem to have very good tools for this kind of elementary symbolic manipulation of sums.&nbsp;</p> <p>I'm afraid I don't understand you.&nbsp; <br>Sum(Sum(x[i]*x[j], i=1..n),j=1..n) is the one that factors as Sum(x[i],i=1..n)*Sum(x[j],j=1..n).&nbsp; <br>The sum for j &lt;&gt; i does not factor.&nbsp; </p> <p>Unfortunately, Maple does not seem to have very good tools for this kind of elementary symbolic manipulation of sums.&nbsp;</p> 126755 Tue, 18 Oct 2011 04:07:33 Z Robert Israel Robert Israel http://www.mapleprimes.com/questions/126733-Splitting-Nested-Sums-Into-A-Set-Of-Single-Sums?ref=Feed:MaplePrimes:Splitting nested sums into a set of single sums:Comments#comment126771 <p>Thank you for the reply. I am sorry, it is tricky to show the steps without a LaTex-type mathematics typsetting environment.</p> <p>What I need is to split a double nested sum into two parts, one where the indecies are equal to each other, and one where they are not equal to each other. This is of course trivial as your indecies are either the both the same or different, but gets more complicated with 3 nested sums. For 3 sums you get 5 single sum terms after splitting the sum, one where all the indecies are the same, one where they are all different, and thre terms where two indecies are the same but one is different.As you can imagine, when you get to high orders of nested sums, the number of terms in an expansion gets very high. For my problem there are 105 single sums that need to be manipulated, expanded and then simplified, and they are not simple. The starting equation is however simply a triple nested sum squared minus a triple nested sum - something that is easy enough to type into maple if it can do the expansion for me</p> <p>You may however have answered my question, if maple cannot eaily symbolically manipulate sums, trying to get it to do this may be rather tricky!</p> <p>Unless anyone else knows a shortcut (or even, dare I ask, an alternative program that can do what I am looking for?)</p> <p>Thanks</p> <p>Thank you for the reply. I am sorry, it is tricky to show the steps without a LaTex-type mathematics typsetting environment.</p> <p>What I need is to split a double nested sum into two parts, one where the indecies are equal to each other, and one where they are not equal to each other. This is of course trivial as your indecies are either the both the same or different, but gets more complicated with 3 nested sums. For 3 sums you get 5 single sum terms after splitting the sum, one where all the indecies are the same, one where they are all different, and thre terms where two indecies are the same but one is different.As you can imagine, when you get to high orders of nested sums, the number of terms in an expansion gets very high. For my problem there are 105 single sums that need to be manipulated, expanded and then simplified, and they are not simple. The starting equation is however simply a triple nested sum squared minus a triple nested sum - something that is easy enough to type into maple if it can do the expansion for me</p> <p>You may however have answered my question, if maple cannot eaily symbolically manipulate sums, trying to get it to do this may be rather tricky!</p> <p>Unless anyone else knows a shortcut (or even, dare I ask, an alternative program that can do what I am looking for?)</p> <p>Thanks</p> 126771 Tue, 18 Oct 2011 16:28:16 Z jimbo_cambridge jimbo_cambridge