Question: INTERVAL membership

This doesn't work directly:

is(RootOf(_Z^3-_Z-1, index = 1)+RootOf(_Z^3-_Z-1, index = 2) = 0);
                                      FAIL

But Maple can compute the bounding interval for a polynomial RootOf (convert(..., RootOf, form=interval)), and evalrC can perform operations on complex intervals:

evalrC(RootOf(_Z^3-_Z-1, index = 1)+RootOf(_Z^3-_Z-1, index = 2));
       INTERVAL(0.6623589782, 0.5622795119, 0.6623589795, 0.5622795122)

evalrC(Re(%));
Error, (in evalrC/INTERVAL) not implemented yet: 4

Re and Im are obviously positive though. Why doesn't Maple try to do that automatically, and also, how do I check if the point is inside the interval? (Without writing my own function to handle real intervals, unions of real intervals, and complex intervals.)

 

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