I guess my (perhaps naive) view of this is that
the symbolic simplifications we make may depend on
the branch cut definitions as well, and the numeric
values, while important, are incidental to the
branch cut problem.
For purposes of contour integration (at least) it
is traditional to move the branch cuts [conceptually]
to convenient locations depending on the application.
I suppose equation-solving (functional inverses generally)
need to occasionally grapple with branch cut definitions.
I think this is mostly "I agree with Barton" but it would
not be a bad thing for us to SET standards, if we can figure
out what makes best sense for a CAS.
RJF
Barton Willis wrote:
>(1) In my experience (mathematical physics, education, ...)
>there are no agreed on values for the inverse trig functions
>on their branch cuts. The definitions given in various
>CL specifications are not standard in mathematics, physics, or
>education. Further A&S do not define the inverse trig functions on
>the branches.
>
>
....