Here is an example that shows the difference between remove_RootOf and allvalues.
is rewritten by remove_RootOf as:
An example with nested RootOfs
If we now evaluate the integral, the resulting solution is
One RootOf can be removed in the expression above (and the solution can be further evaluated using allvalues).
Here, the sum over the Roots of the third degree polynomial is equal to zero.
A second order ODE example in which three solutions with RootOf are returned by dsolve
Although remove_RootOf is mainly useful for manipulating nonlinear ODE solutions, it can also be of help with solutions to linear ODEs, for instance when allvalues fails in evaluating the RootOfs.