Re: motion divPair
Juergen,
1) Comments on divPair operation.
1.1)
> Only for the division a/b when b contains zero, the resulting sets are not necessarily
> intervals, there may be 2 semi-infinite intervals.
The range of "div" operation is not necessarily interval or 2 semi-infinite intervals,
because it is not necessarily closed set:
a=[1,1] b=[1,+oo) ==> Rng(div | a x b) = (0,1]
a=[1,1] b=[-1,1] ==> Rng(div | a x b) = (-oo,0) U (0,+oo)
Maybe such wording ?
Only for the division a/b when b contains zero, the range is not necessarily connected
set, it may consists of 2 semi-infinite sets.
1.2) First line of definition of divPair:
(a, b) → ([-oo, inf(a)/sup(b)], [inf(a)/inf(b), +oo]) if (a < 0) ∧ (0 ⊂ b)
Is this more correct ?
(a, b) → ([-oo, sup(a)/sup(b)], [sup(a)/inf(b), +oo]) if (a < 0) ∧ (0 ⊂ b)
1.3) The third line of definition of divPair returns Entire that is not the tightest hull.
The tightest hull in this case is either [0,0] or Empty.
Why do you want to define divPair in such a way ?
Can the third line be omited in favour of the fourth line ?
1.4) The paragraph about decorated version.
When the denominator doesn't contain 0, the second result interval is empty.
It can't be dac- or com- decorated. Possible wording:
As a division divPair shall have a version for decorated intervals setting the local
decoration of nonempty result intervals to trv, if the denominator contains 0, and to dac or com, if not.
The local decoration of empty result intervals is trv.
2) The question on mulRevPair operation.
The information returned by mulRevPair can be obtained by two ternary mulRev operations:
mulRev(b,a,(-oo,0]) and mulRev(b,a,[0,+oo)).
What is the advantage of new operation ?
-Dima
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Отправленные: Суббота, 30 Март 2013 г 20:12:56 GMT +04:00 Абу-Даби, Маскат
Тема: motion divPair
P1788
please find attached a motion completing our functional interface
happy easter
Jürgen
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