quintuple summation using a for loop

Ive tried setting the sum to an empty cell and filling it and not declaring it and I do not know what to do or whats wrong and why it will not give me an answer different than the inital declaration.

syms i j k l p q
U = ((-1)^j)*a' - ((-1)^i)*a;
V = ((-1)^j)*a' - ((-1)^i)*a;
W = ((-1)^j)*a' - ((-1)^i)*a;
r = sqrt(U*U+V*V+W*W);
Phi = -U*W*log(r-U)-V*W*log(r-V)+U*V*atan((U*V)/(r*W))-r*W;
 for  i = 0:1
     for  j = 0:1
         for  k = 0:1
             for  l = 0:1
                 for  p = 0:1
                     for  q = 0:1
                         sum = sum + (((-1)^(i+j+k+l+p+q))*Phi);
                         disp(sum)
                     end 
                     disp(sum)
                 end    
                 disp(sum)
             end  
             disp(sum)
         end   
         disp(sum)
     end    
     disp(sum)
 end
 disp(sum)

[Wyatt Panaccione]

Attached is the equation I am attempting to emulate.

[Walter Roberson]

You do not initialize sum to sym(0)

Note: we recommend against naming a variable sum: it happens a lot that people want to use the function sum in the same code they used sum as a variable. And it confuses readers.

Note: we would need your a to test this.

[Wyatt Panaccione]

%% Inputs
a = 0.035;%length of up/low magnet
b = 0.014;%width of up/low magnet
c = 0.007;%height of up/low magnet
am = .03;%length of middle magnet
bm = .01;%width of middle magnet
cm = 0.01;%height of middle magnet

%% Negative K
syms iw jw k l p q
U = ((-1)^jw)*am - ((-1)^iw)*a;
V = ((-1)^l)*bm - ((-1)^k)*b;
W = ((-1)^q)*cm - ((-1)^p)*c;
r = sqrt(U*U+V*V+W*W);
Phi = -U*W*log(r-U)-V*W*log(r-V)+U*V*atan((U*V)/(r*W))-r*W;
sum =[0];
 for  iw = 0:1

     for  jw = 0:1
         for  k = 0:1
             for  l = 0:1
                 for  p = 0:1
                     for  q = 0:1
                         sum = sum + (((-1)^(iw+jw+k+l+p+q))*Phi);
                         disp(sum)
                     end
                 end
             end
         end
     end
 end

 disp(sum)

[Wyatt Panaccione]

Here is the entire code

Answer 1

[David Goodmanson]

Hello Wyatt,

The sum comes out zero because it is, in fact, zero. Each term in the desired sum is

((-1)^(iw+jw+k+l+p+q))*constant;

Each of the indices is +-1. Their sum is either even or odd.

When it's even, the term contributes (-1)^even = +constant to the desired sum.

When it's odd, the term is contributes (-1)^odd = -constant to the desired sum.

There are 2^6 instances of (iw+jw+k+l+p+q), and half of those sums are even, half odd as you can check. So the desired sum ends up as zero.

It would be better if you went with Walter's recommendation and used something other than 'sum' for the sum variable. 'Sum' would work fine.