isequaln() is testing symbolic objects for equality as stated in the documentation. However, this is not the case with the following script.
syms a
f1=cos(a)^2;
f2=1-sin(a)^2;
isequaln(f1,f2)
ans =
logical
0
MATLAB does not return the correct answer. What does MATLAB do when comparing equality for symbolic expressions, compare strings (i.e. a typical scenario for regular expressions), or something else?
At the bottom of the documentation page, there is a section called "Tips", which contains the following item:
isequaln(A,B)checks ifAandBare the same size and their contents are syntactically the same expression, treating NaN values as equal. To check whether the mathematical comparisonA == Bholds for all values of variables inAandB, useisAlways(A == B).
(emphasis mine)
isAlways does what you want:
syms a
f1 = cos(a)^2;
f2 = 1-sin(a)^2;
isAlways(f1 == f2)
This outputs true.
Alternatives:
>> simplify(f1-f2)
ans =
0
>> simplify(f1==f2)
ans =
symtrue