Combining symbolic integral expressions

Question

Randolf Scholz 2018-9-4

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/417492-combining-symbolic-integral-expressions

评论： Randolf Scholz 2018-9-10

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.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Naman Chaturvedi 2018-9-7

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/417492-combining-symbolic-integral-expressions#answer_335856

在 MATLAB Online 中打开

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

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Randolf Scholz 2018-9-10

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.

请先登录，再进行评论。