Also, I just found out that Interval supports negative fractional
power, but not negative integer power.
AIntervalCategory does not support both.
In AIntervalCategory, negative powers could be added, but only
conditionnally in the same place where
inv(x : %) : % ==
contains?(x, 0$R) => error "inv: interval contains 0"
interval(inv sup x, inv inf x)
is implemented.
For fractional powers, I am a bit hesitant. I introduced
AIntervalCategory to be able to compute with intervals also for more
general rings than just those that inherit from FloatingPointSystem.
However, I don't think it would be a problem to add the default
implementation
if R has Join(OrderedRing, Field, RadicalCategory) then
((x : %) ^ (n : Fraction Integer)) : % == ...
to AIntervalCategory.
Luckily, FloatingPointSystem fulfills this condition.
Ralf
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