I already new all that, but my question would be: "why
S.has_coerce_map_from(R) returns False?"

And the second question is "is there a command (or an easy way to
implement it) to recover QQ[x,y,z] from QQ[x][y][z] or any other
similar situation?"

I know how to deal with these cases by hand, but i am trying to write
a patch for computing discriminants, and there i need a way to
automatically do it. I think i could construct such a function if i
knew how to recognize if a given ring is a polynomial ring or not.

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