In version "reduce-algebra-20101007", setting "off nat;", I am confused about the treatment of complex numbers in "rounded" mode, with or without "complex" mode. In particular, with "on rounded", "sqrt(s^2);" gives "abs(s)", considering that "s" could have a non-zero imaginary part, and "sqrt(2*(s^2));" gives "1.41421356237*abs(s)", which is reasonable, but then "sqrt(2/(s^2))" gives "(2/s**2)**0.5", while in "rounded" mode, which seems like a bug.

Am I missing something? Should there be any difference between a quotient and a product here? It seems to me that, in "rounded" mode, the square-root of the numerator can be taken, even on the chance that "s" could be complex.

And then, this failure to evaluate the numerical quantities becomes annoying when trying to simply find some numeric result. For instance, "(2*pi)*sqrt((2*e)/(s^2));" gives "6.28318530718*(5.43656365692/s**2)**0.5", instead of simply "14.6501512067/abs(s)", which would be more useful.

James