There was a discussion of the principal value of square root on this list some time back, making the point that for positive real numbers the positive square root is the value of the standard function. In the complex plane it is desirable to define the principal value at every point so as to produce a minimum of surprises, such as sudden jumps at discontinuities. However, there must necessarily be a line of discontinuity. Similarly for other complex-valued functions, particularly the trig and inverse trig functions, some of which are infinite-valued.
It turns out that the domain and range and the location of the cut lines have to be worked out separately for different functions. Mathematical practice is not entirely consistent in making these decisions, but in programming, there seems to be widespread agreement that the shared definitions used in the APL, Common LISP, and Ada standards are the best available. Do we want to get into all of this in Perl6? -- Edward Cherlin Generalist & activist--Linux, languages, literacy and more "A knot! Oh, do let me help to undo it!" --Alice in Wonderland http://cherlin.blogspot.com
