[std-interval] More on interval computations as proofs

Ron Avitzur avitzur at PacificT.com
Sat Sep 30 11:00:53 PDT 2006


>>>  The discussion showed that Standard functions MUST set a flag when
>>>  the argument interval is not completely contained in the domain of
>>>  the function. Otherwise (i.e without the flag) verification of the
>>>  result with fixed points or other assertions that need continuity is
>>>  not possible
>>
>>  For my graphics application of intervals, as well, it is also
>>  sometimes necessary to track both continuity of functions and
>>  the domain over which they are well-defined.
>
>Could you please provide more details on your needs for detecting
>discontinuities?  I don't see many functions considered here which
>are not continuous on there definition domain, so maybe we only
>need special treatment instead of a general scheme.

A trivial example is at <http://www.PacificT.com/Examples/discontinuity/>
and a more interesting one at <http://www.PacificT.com/Examples/branchcut/>.

In both cases, sections of the surface are spurious, connecting parts of
the function across a discontinuity. In the first case it is sufficient
to flag division by zero to detect the error. The second case needs to
detect the discontinuity in the complex sqrt which is outside the scope
of this proposal.


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