Combining symbolic integral expressions

Consider the example

syms a b x y f(x) g(x)
I =  @(x)int( f(x), x, a, b)
J =  @(x)int( g(x), x, a, b)
K = combine(I(x)*I(y) + J(y)*J(x),'int')
L = int(int(f(x)*f(y) + g(x)*g(y),x,a,b),y,a,b)

How can I get matlab to simplify K such that it results in L? Also I noticed that matlab seems to think that the two are different since

logical(K == L)

returns 0; on the other hand it thinks they are the same since

simplify(K-L,100)

also returns 0.

Answer 1

[Naman Chaturvedi]

Hi Randolf,

To check the validity of K==L, you must expand the equation and then simplify it as shown:

>> logical(simplify(expand(K))==simplify(expand(L)))

ans =

    logical

     1

As stated in this doc of 'logical'.

Do not use logical to check equations and inequalities that require simplification or mathematical transformations. For such equations and inequalities, logical might return unexpected results. For example, logical does not recognize mathematical equivalence of these expressions:

syms x
logical(sin(x)/cos(x) == tan(x))

ans =
  logical
   0

To test the validity of equations and inequalities that require simplification or mathematical transformations, use isAlways:

isAlways(sin(x)/cos(x) == tan(x))
ans =
  logical
     1

Using isAlways to check K and L,

isAlways((K) == (L))

ans =

    logical

     1

HTH

[Randolf Scholz]

Dear Naman, thank you for your reply. Unfortunately it doesn't answer my main question which is how can I get MATLAB to simplify the expression K towards the expression L. Ideally I would like it to automatically simplify sums of squares of integrals.