Re: atan2_sharp() -- a Motion?
Folk
On 2014 Feb 20, at 14:14, Michel Hack wrote:
> (This is just a quick reply to John Pryce -- I have not yet had time
> to dig deeper than I have so far. I'd really appreciate some help.)
Yes please someone. I appeal to Siegfried: you have done complex intervals in INTLAB, so you should have the needed insights.
> On whether atan2_sharp() can be programmed using case() and the two
> or three shifted-range atan2x() functions: I suppose I should try,
> and identify the sticking point. If it's not possible, could we
> still prove the FT(D)IA?
My belief is yes. That is, suppose
- A multivalued function has several branches, each separately "nice" (smooth etc.) on its domain.
- The famous "some algorithm" chooses a branch for any given input box XX...
- and decorates according to the behaviour of the chosen branch on XX.
Then the FT(D)IA should work.
But I'm not sure if the case of XX containing the singularity at (0,0) messes this up.
Also, what about the possibility of XX contained in YY, and the algorithm choosing a branch for case YY that's incompatible with that for case XX?
> And if not, is that the death knell?
I fear it is.
John Pryce