Question: How to extract concrete roots from general solution?

December 18 2013 Markiyan Hirnyk 5663


Up to Maple Help, the relatively new command SolveTools[Engine] with the
allsolutions option returns parameterized solutions for non-algebraic equations which may have infinitely many solutions. The question arises: how to extract these?
For example,
sol := SolveTools:-Engine({tan(x) = x}, [x], allsolutions);
[{x = RootOf(-tan(_Z)+_Z)}]
I want to extract the third positive solution (by its value), trying
[{x = -4.493409458}], [{x = 0.}]
Is it possible at all?

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