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