Decision tree regression: Polynomials unnecessary? I am testing out different models for a regression task.
When using OLS, Ridge and Lasso, I use different polynomial degrees of the explanatory variables.
Example: For two variables x and y, degree 2 would give the explanatory variables x, x^2, xy, y, y^2. 

When using decision tree, however, I am not sure whether it makes sense to use any any higher degrees than 1 as explanatory variables. Example: Does it make sense to test for x^2, xy and y^2 when applying a decision tree regressor?

The reason I ask, is that the decision tree regressor is a non-linear regressor. On the one hand this could perhaps be an arguement it not making sense to include higher order polynomials, as the decisoin tree already can deal with non-linearity.
Since CARTs (Classification And Regression Tree) are a non-parametric algorithm, they should be able to find interactions between variables and non-linear behaviors. 

Nevertheless, building polynomials can help them have a better performance.