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Re: Branch & bound for not everywhere defiend constraints

On 7 Sep 2009, at 17:22, Nate Hayes wrote:

Vincent Lefevre wrote:

On 2009-09-07 10:36:36 +0200, Arnold Neumaier wrote:

Vincent Lefevre schrieb:

On 2009-09-02 11:26:21 +0200, Arnold Neumaier wrote:

Vincent Lefevre schrieb:

One could also have a flag attached to the returned interval.
Alternatively, one could have a function telling whether X' is
included in the domain of f.

The latter can in general be found out only by evaluating;
so this would double the work whenever one needs both the
evaluation and the domain check.


I would have said the opposite, i.e. that the latter doesn't need
evaluation in general. For instance, if the domain is R, then the
result is always TRUE. For the division, the result is TRUE iff
the second argument doesn't contain 0.


I meant the domain of a whole expression.


OK, but then, this is out of the scope of the standard, isn't it?


Yes.
No. Isn't there a misunderstanding going on here? As I outlined in my email yesterday, we IMPLEMENT some kind of possiblyUndefined feature in the elementary functions which has the CONSEQUENCE for more complicated functions (whole expressions) of providing a sufficient -- though not necessary -- test that the hypotheses of a fixed-point theorem have been satisfied: 
  If "possiblyUndefined" wasn't raised, we know for
  certain that the complicated function is defined
  everywhere on the input box.
And is continuous -- we need to include this in the definition of possiblyUndefined for the elementary functions, at least for this application. 

John