Find Child Subexpressions of Symbolic Expression

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?

Answer 1

[Walter Roberson]

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

[Erivelton Gualter]

Thank you Walter,

Unfortunatley, it is not clear on the documentation.

Do you know if is there any way I can get only the operands of additions? Or do I need to write my own algorithm for this task?

[Walter Roberson]

What release are you using? The possibilities increased in R2019a.

What result would you want for (say) (x+y)*sin(x-y) ?

What result would you want for x-y ?

[Erivelton Gualter]

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]

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.