Re: motioin43 amended
Jürgen,
Some "if" cases overlaps in current definitions.
One case gives an intended result and the other case gives incorrect result for some inputs.
I guess that it is possible to simplify both definitions so that "if" cases don't overlap.
divPair([a],[b]) can be simplified to three cases:
(3) ([a],[b])->([-oo,sup(a)/sup(b)] , [sup(a)/inf(b),+oo]) if ([a] < 0 and 0 \subset [b])
(4) ([a],[b])->([-oo,inf(a)/inf(b)] , [inf(a)/sup(b),+oo]) if ([a] > 0 and 0 \subset [b])
(8) ([a],[b])->(div([a],[b]),\empty) otherwise
mulRevPair([b],[c]) can also contain only three cases:
(11) ([b],[c])->([-oo,sup(c)/sup(b)] , [sup(c)/inf(b),+oo]) if ([c] < 0 and 0 \subset [b])
(12) ([b],[c])->([-oo,inf(c)/inf(b)] , [inf(c)/sup(b),+oo]) if ([c] > 0 and 0 \subset [b])
(14) ([b],[c])->(mulRev([b],[c]),\empty) otherwise
Also look at signature of mulRev in John's draft.
mulRev(b, c, x)
mulRev(b, c)
a in your definition plays role of c in John's definition.
It is good if mulRevPair and mulRev have consistent argument order.
So I suggest to name arguments in mulRevPair definition
either mulRevPair([b],[a]) or mulRevPair([b],[c]).
-Dima
----- Исходное сообщение -----
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Отправленные: Среда, 24 Апрель 2013 г 0:25:21 GMT +04:00 Абу-Даби, Маскат
Тема: Re: motioin43 amended
Am 23.04.2013 14:32, schrieb Dmitry Nadezhin:
> Jürgen,
>
> 1) I think that (3) and (10) have typos:
> <<<
> if ([a] = \empty || [a] = \empty)
> ===
> if ([a] = \empty || [b] = \empty)
>>>>
you're right
>
> 2) The definition gives divPair([0,0], [0,0]) = ([0,0], \empty) according to (6).
> Is this intentionally ?
yes but b=[0,0] has to be excluded from that case 0 \subset b
>
> I expect that divPair([0,0], [0,0])=(\empty, \empty)
that is (7)
.
> This can be obtained if we remove (6) and (7) from definition of divPair.
>
> 3) The definition gives mulRevPair([0,1],[0,1]) = ([0,+oo), \empty) according to (14).
> I expect that
> mulRevPair([0,1],[0,1])={x \in R | \exists a in [0,1], \exists b in [0,1], b*x = a } =(-oo,+oo)
= mulRev([0,1],[0,1]) clearly mulRev(a,b) has to be the default
Jürgen
>
>
> -Dima
>
>
> ----- Исходное сообщение -----
> От: wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx
> Кому: rbk@xxxxxxxxxxxxx, George.Corliss@xxxxxxxxxxxxx, stds-1788@xxxxxxxxxxxxxxxxx
> Отправленные: Вторник, 23 Апрель 2013 г 15:30:16 GMT +04:00 Абу-Даби, Маскат
> Тема: motioin43 amended
>
> Baker, George
> please find attached an amended verion of the divPair motion.
> ready for voting. thanks to Vincent L. and Dima N
> Jürgen
>
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