🚀 go-pugleaf

Hi,
> In a complex domain, there are three possible answers, corresponding
> to the three roots of unity:
> 
> -3
> 
> 3 * (1 + sqrt(3)*I)/2
> 
> 3 * (1 - sqrt(3)*I)/2
An answer of the form given by Duval's "dynamic evaluation" seems the most
accurate.  That is, all three answers are given along with the value of the
surd needed to produce the answer.  This could lead to a combinatorial
explosion: an expression with four square-roots would have 16 possible
values.  Also there are other questions: if particular choices have been
made for sqrt(2) and sqrt(3), does this define sqrt(6) uniquely?

Cannot something be done with unknown powers of primitive roots of unity?
Of course, there must be a way of making sure the same power is associated
with each instance of a particular symbol.  So perhaps (-27)^(1/3) could
simplify to (-3)*w(3)^j  for j=0..2  where w(3) means a primitive 3rd root
of unity.  This would make sqrt(2)*sqrt(3) simplify to something like
psqrt(2)*psqrt(3)*w(2)^(j1+j2)  for j1=0..1  for j2=0..1
[psqrt is meant to be some fixed principal value]

John Abbott