Comparison of symbolic expressions

Welcome.

A certain set of symbolic calculations is performed in two different ways. After that, you need to compare the results (we want them to be equal). But using " eq " or "= = " you can't get the desired result. You can use a trick and subtract or divide the results, but this method does not always work correctly.

Is there a function for comparing symbolic calculations?

Example:

Answer 1

[KSSV]

syms a b
c = a+b ;
d = b+a ;
isequal(c,d)

ans = logical
   1

[John D'Errico]

syms theta
isequal(sin(theta)^2 + cos(theta)^2,1)

ans = logical
   0

Even worse, we see that while rewrite can seemingly improve this first counter-example, isequal still fails.

rewrite(sin(theta)^2 + cos(theta)^2,'sin')

ans = 

1

isequal(rewrite(sin(theta)^2 + cos(theta)^2,'sin'),1)

ans = logical
   0

The reason being that 1 and 1 are counter-intuitively not always seen to be equal, at least by isequal.

For this one, a carefully applied expand would have helped.

syms x
isequal((x+1)^3,x^3 + 3*x^2 + 3*x + 1)

ans = logical
   0

[reincornator]

isequal(expand((x+1)^3),x^3 + 3*x^2 + 3*x + 1)

Answer 2

[Walter Roberson]

isAlways(c == d, 'Unknown', false)

[reincornator]

Thanks!

syms a b c
d=c*(a+b);
e=c*b+c*a;
j=a*b;

isAlways(e == d, 'Unknown', 'false')
isAlways(j == d, 'Unknown', 'false')