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Problems with the interval-valuation of an expression

An important point is that not all expressions can be evaluated using
interval arithmetics. Namely constraints that prohibits the interval
evaluation of an expression are:

- denominator that may include 0
- argument of square should be positive
- argument of arcsin and arccos should be included in [-1,1]
- argument of log,ln,log10 should be positive
- argument of arccosh should be greater than 1
- argument of arctanh cannot include the interval [-1,1]
- argument of where is not an integer should be
- argument of should not be too large to avoid
overflow problem.

If such situation occurs a fatal error will be generated at run time.
Hence such special cases has to be dealt with carefully.
ALIAS-Maple offers the possibility of dealing with such problem. For
example the procedure `Problem_Expression` allows one to
determine what constraints should be satisfied by the unknowns so that
each equations can be interval evaluated, see the ALIAS-Maple documentation.
If you use your own evaluation procedure and are
aware of evaluation problems and modify the returned values if such
case occurs it will be
a good policy to set C++ flags `ALIAS_ChangeF`, `ALIAS_ChangeJ` to 1 (default value 0) if a change occurs.
Currently the interval Newton scheme that is embedded in some of the
solving procedures of `ALIAS` will not be used if one of these
flags is set to 1 during the calculation.

** Next:** Dealing with infinity
** Up:** Interval Analysis
** Previous:** Implementation
** Contents**
Jean-Pierre Merlet
2012-12-20