> in final result so convertion from Expression(Complex(R)) to
> Expression(R) must properly handle imaginary unit (replace %i by
> sqrt(-1) if R is real).

Oh... maybe I'm wrong, but AFAIU, the Expression domain is somewhat
tailored towards a nice representation for integration. It is, in fact,
something like

  K(t1, t2, ..., tn)                      (*)

where the ti may have relations with the tj for j<i. Unfortunately, our
Expression domain, does not explicitly show this relations. Waldek, you
know certainly better than me that the integration code builds this
tower of fields somehow, but in fact it's always in Expression(R) or
maybe Expression(Complex(R)). Am I wrong?

It's probably too much of rewriting to actually get rid of Expression(R)
in the integration code and let it work with a tower of fields that is
explicitly constructed for the expression that is to be integrated.
What I mean is something like this

given integrand -->
build tower (*) and map integrand to that field -->
apply Risch's algorithm -->
transform the result back to Expression(X)

I.e. during Risch's algorith there would be no involvement of
Expression(X), but only some rational function fields. Isn't that all
what Risch's algorithm cares about?

Ralf

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