Find Child Subexpressions of Symbolic Expression

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Erivelton Gualter
Erivelton Gualter 2019-4-12
评论： Walter Roberson 2019-4-14
I believe the function children might have a problem. Acording to the documentation it returns a cell array containing the child subexpressions of each expression in A.
For example:
syms x y
children(x^2 + x*y + y^2)
It will return:
[ x*y, x^2, y^2]
However, for the following:
children(x*y)
it return:
[ x, y]
I believe it should return:
x*y
Is it a bug ? Or am I missing something?

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Walter Roberson
Walter Roberson 2019-4-12
You are missing something.
x^2 + x*y + y^2
is internally
_plus(_power(x, 2), _mult(x, y), _power(y,2))
children() removes the outer layer call and returns its arguments, giving back what would be internally
matrix([_power(x, 2), _mult(x, y), _power(y,2)])
which the interface translates back to
[x^2, x*y, y^2]
And likewise,
x*y
is internally
_multi(x,y)
children() removes the outer layer call and returns its arguments, giving back what would be internally
matrix([x, y])
which the interface translates back to
[x, y]
The children() call does not just find operands of additions and declare anything non-addition to be indivisible: it removes the outermost operation, no matter what it is. For example, children(sin(x*pi/2)) would remove the sin() giving you back x*pi/2
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Erivelton Gualter
Erivelton Gualter 2019-4-12
编辑：Erivelton Gualter 2019-4-12
My only issue happens when I have some of the following expressions for instance:
  • x*y , which results in [x,y], But I would like only x*y
  • sin(x) , which results in x, but again, I would like ony the sin(x)
  • x^2 , which resuls in [x,2], but I wanted only x^2.
For the expression you asked, I am solving like the following code,which is fine. The output for this case totally works for me, which is: [ x*sin(x - y), y*sin(x - y)]
syms x y
F = (x+y)*sin(x-y);
F = expand(F, 'ArithmeticOnly', true)
CF = children(F)
Basically, this piece of code I just provided do what I want; however, when I have elements such as x*y, sin(x), x^2 it removes this undesired layer. I would like to keep it just return these expression as they are.
In conclusion, I want to expand the symbolic equation (only in simple arithmetic) [1] and then get the sum parts of the element.
So, responding your question:
(x+y)*sin(x-y) ---> [ x*sin(x - y), y*sin(x - y)]
(x+y) --> [x,y]
But, the piece of code already provide it.
By the way, I am using R2018b. I just tried the R2019a online, but as expected it had the same output.
Walter Roberson
Walter Roberson 2019-4-14
In R2018b the only way to proceed is to write MuPAD code that you evaluate using evalin(symengine) or feval(symengine) . The MuPAD code would have to know how expressions are internally represented.
R2019a added additional ways of examining sub-expressions without having to use MuPAD code.

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