Added verification for PTC-BCR-3

[JoelManYunLee]

Modified reproducing.m to include verification for PTR-BCR-3 on Pg.22 eq 65.

b = dec2bin(2^5-1:-1:0)-'0';
b1=b(:,1);b2=b(:,2);b3=b(:,3);b4=b(:,4);ba=b(:,5);
LHS = min(b1.*b2.*b3.*b4);
RHS = min(1/2*(b1 + b2 + b3 + b4 - 2*ba).*(b1 + b2 + b3 + b4 - 2*ba - 1));
isequal(LHS, RHS);

[ndattani]

Well done @JoelManYunLee! I notice though that you're only verifying that the min(LHS) = min(RHS), whereas for PTR-BCR-3, we actually can show something more powerful which is that LHS = min_ba(RHS) where the minimization is over all auxiliary variables. I'd recommend to take a look at the code that was done here for PTR-BCR-4.

I would also encourage you to do the following:

• Test the equation in the "Summary" section for k = 8.
• Test the equation in the "Alternate forms" section for k=8.
• Expand the equation in the "Example" section and add it in a new line (with an equation number too). You can add this into the book's source code here.
• Once you're done the above step, then add "LaTeX" to your resume if you don't have it there already :) Please don't send me a new copy of the resume though.
• The expanded version of the "Example" should also be tested in reproducing.m.
• Once the added equation is in the book's PDF file, please show a screenshot of just that equation (not the full page) in a reply here, so that I can verify that the PDF looks good :)