Decompose Expression into Segments

Questions
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1

Say I have an expression

test = 3 x1^2 - 2 x3^-3

and I would like to decompose the expression into

{3 x1^2, -(2/x3^3)}

I can do that by using List @@ test on Mathematica.

However, the problem I face is that when the expression is test = x1^2, i get {x1, 2} and for test = (3 x1^2) i get {3, x1^2} instead of {x1^2} and {3x1^2} respectively.

The added information I have is the list of variables. For example, if test = x1^2 I have the list of variables, which is {x1}. And for test = 3 x1^2 - 2 x3^-3, I have {x1,x3}

Is there any other way to get what I want?

Thanks

2

I’m guessing you want to divide up “terms” and not divide up “factors”, i.e, divide up + and - but not * and / and ^

In[1]:= 3 x1^2 - 2 x3^-3 /. Plus -> List

Out[1]= {3 x1^2, -(2/x3^3)}

In[2]:= x1^2 /. Plus -> List

Out[2]= x1^2

In[3]:= 3 x1^2 /. Plus -> List

Out[3]= 3 x1^2

But if you start having even more complicated expressions then you might run into trouble with things like this

In[4]:= x^(2 a + b) /. Plus -> List


Out[4]= {x^(2 a), x^b}

and it isn’t clear whether that is what you would want or not.

If that is not what you would want to happen then you might consider substituting for Plus only at the topmost level.

3

Are you considering polynomials only? Then would MonomialList be enough?

MonomialList[a x^2 + b x y + c y^2, {x, y}]
Out[]= {a x^2, b x y, c y^2}