Re: Motion 10v2 released; and atan2

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Nate Hayes wrote:
> John Pryce wrote:
> > I have a related query here. For any box B that straddles the branch
> > cut, peeking no matter how slightly into both the y<0 and y>=0
> > regions for some x<0, we get
> >     atan2([ylo,yhi],[xlo,xhi]) = [-Pi,Pi].
> > If what we REALLY want is "an interval extension of the point
> > function that is the Principal Value atan2 as above" then that is
> > fine. But for applications to do with "winding" (continuous change of
> > angle on a path that loops round the origin) one would like an atan2
> > that is about the incremental, continuous, change in angle across box
> > B -- and is not always limited to (-Pi,Pi].
> >
> > Has anyone got a suitable definition? Arnold, it looks the sort of
> > thing for you. 

Atan2 is defined as the (not everywhere continuous) principal value,
so we should stick to that.

Going to interval arithmetic on Riemann surfaces (the next natural
step) is really meaningful only if one evaluates complex expression
in some complex interval arithmetic, and is much beyond what the 
standardization committee can or should do.


Arnold Neumaier