simplify() has no effect

Question

I used the following snippet to simplify an equation:

syms P Q R S T U V A B C D E F G X Y
simplify((X - A)^2 + (Y - B)^2 - (X - B)^2 - (Y + A)^2)

Which gives me the result:

2*B*X - 2*A*Y - 2*A*X - 2*B*Y

On the other hand,

simplify((X - A)^2 + (Y - B)^2 - (X - B)^2 - (Y + 2*A)^2)

gives the same result after just re-ordering:

(A - X)^2 - (B - X)^2 - (2*A + Y)^2 + (B - Y)^2

What changed between these two equations? Am I not using the function correctly?

Any help would be appreciated.

Answer 1

As per the documentation, you can increase the amount of simplification "steps" using:

simplify(expr,'Steps',nSteps); % e.g. nSteps = 50

You can also try other functions (combine, expand, factor, ...) for rearranging an expression.

I have the Maple symbolic toolbox for MATLAB and I get different results than you:

>> syms P Q R S T U V A B C D E F G X Y
>> simplify((X - A)^2 + (Y - B)^2 - (X - B)^2 - (Y + A)^2)

ans =

                         (-2 X - 2 Y) A + 2 B (X - Y)

>> simplify((X - A)^2 + (Y - B)^2 - (X - B)^2 - (Y + 2*A)^2)

ans =     
                         2
                     -3 A  + (-2 X - 4 Y) A + 2 B (X - Y)

In conclusion - it works as expected, you should give other functions/tools a try.