Re: P1788/D9.2 draft (10.5.5)
Dear Dimitri,
On 27/05/2014 10:35, Dmitry Nadezhin wrote:
> Frederic,
>
> The relations X/Y = Z and X = ZY are not exactly equivalent.
>
> The tuple (x=0, y=0, z=1) belongs to the second relation, but it
> doesn't belong to the first relation.
Thank you for your answer. However, I beg to differ on this. As I
understand it, 0/0 is an indeterminate form, which means that any
value for z is admissible when x=0 and y=0. Hence, (x=0, y=0, z=1) should
be kept as a solution.
From the definitions in (5), (6), and (7) on Page 34 in Draft 9.2, I
can understand how the operators divRev1() and divRev2() are derived.
What I question is the legitimacy to do so in the first place.
>
> Also it seems to me that pow(X,Y,Z) == hull({z\in Z\mid \exists
> x\in X, \exists y\in Y: x^y = z}) powRev(Z,X,Y) == hull({x\in
> X\mid\exists y\in Y, \exists z\in Z: x^y = z}) powRev(Z,Y,X) ==
> hull({y\in Y\mid\exists x\in X, \exists z\in Z: x^y = z}) are three
> different operations (in contrast to mul). Please, explain if I
> miss something.
Yes, you are right on this one.
>
> -Dima
>
> ----- Original Message ----- From:
> Frederic.Goualard@xxxxxxxxxxxxxx To: mhack@xxxxxxx,
> stds-1788@xxxxxxxxxxxxxxxxx Sent: Friday, May 16, 2014 9:15:31 PM
> GMT +04:00 Abu Dhabi / Muscat Subject: Re: P1788/D9.2 draft
> (10.5.5)
>
> Dear Michel,
>
> On 16/05/2014 16:42, Michel Hack wrote:
>>> that the mulRev1/mulRev2 and powRev1/powRev2 dichotomy is not
>>> present.
>
>> There is only one mulRev, but there are divRev1 and divRev2.
>> We also need powRev1 and powRev2 because the pow(x,y) function is
>> not commutative.
>
>> You would use divRev1 to narrow X in the relation X/Y = Z and
>> divRev2 to narrow Y.
>
>> At least that's MY understanding.
>
> That is precisely my point. The *relation*
>
> X/Y = Z
>
> can be rewritten equivalently as
>
> X = ZY
>
> and then we are back to what I said in my previous mail.
>
> Best regards,
>
> F.
>
--
Frédéric Goualard LINA - UMR CNRS 6241
Tel.: +33 2 76 64 50 12 Univ. of Nantes - Ecole des Mines de Nantes
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