Re: The current proposal
Is it reasonable that a mathematically defined object, which
may be the result of legal operations such as intersection,
is used to indicate something else, is used as a flag?
Can you give an example of what you mean here?
For f(x):=(x^2-1)/(x-1), f(1) is not mathematically defined.
Yes, the mathematically defined object is the empty set. In our
example, F([1,1])=Empty, but Intersection([1,2],[3,4])=Empty
as well. Similarly,
Union( F([1,1]) , F([2,2]) ) = [3,3] and
Union( Intersection([1,2],[3,4]) , F([2,2]) ) = [3,3] .
The difference is that in the first case a flag is set, in the
second it is not. It may be not unlikely for users to forget
to check the flag.
I can only say that, on your request Arnold, I put the possiblity
to ignore input-out-of-range into INTLAB, together with a flag to
be inspected. However, I forgot to check this flag in verifynlss,
my nonlinear system solver in INTLAB.
So before correcting this, results might be wrong. I think it is
not unlikely that this, to forget to check the flag, happens to
me again because in my applications I hardly need this ability.
This may be different in your applications.
Similarly, when printing one of the above results, I do not see
the flag and may conclude that nothing peculiar happened.
In a nutshell, it may be wise to define NaN to be the default
answer if some invalid input occurred. This is always safe. In
addition there may be an expert mode to your desire.
Cheers, Siegfried
--
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
Schwarzenbergstr. 95
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Germany
phone +49 40 42878 3027
fax +49 40 42878 2489
http://www.ti3.tu-harburg.de
and
Visiting Professor at Waseda University
Faculty of Science and Engineering
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