Consider the following simple calculation with Ore algebras:

DA:=Ore_algebra[skew_algebra](euler=[theta,z]):
Ore_algebra[skew_power](sqrt(3)*theta,2,DA);
Error, (in Ore_algebra:-skew_power) skew polynomial must be member of the algebra

The error is due to the square root which is not recognized as a member of the algebra even though it is only a number. There seems to be no option to remedy this issue. Is there another solution ?

I have a particular system of partial differential equations to which I want to apply a change of variables involving square roots using PDEtools[dchange]. The result turns out to be not in a simple form due to the square roots. Why is this so ? Is there a better way solving the problem than the one I am suggesting below ? The system of partial differential equations of interest is the following: