> 1) Why does not sqrt(a^2) return abs(a)?

OK, let's try with a being the imaginary unity.

(4) -> sqrt(%i^2)

   (4)  %i
                                           Type:
Expression(Complex(Integer))
(5) -> abs(%i)

   (5)  abs(%i)

FriCAS does not simplify abs(%i). So it's left unspecified.
You would probably not agree that abs(%i)=%i

> 2) Why does not FriCAS know that abs(a) > 0?

Because it is just an operator and a can be anything. What would you
want abs("Hello World!") to return?

> 3) How can one tell FriCAS that a>0 in the Gaussian integral? 
>     In Maxima this is done with assume. Maybe in FriCAS one could use 
> predicates.

I've no idea.

Ralf

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