Re: Motion 11
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Dear Vincent,
Vincent Lefevre wrote:
> On 2010-02-16 10:11:46 +0100, Frédéric Goualard wrote:
>> I do not know enough about modal interval arithmetic to have any
>> definitive argument about that. However, I doubt you can easily obtain
>> the same results as with reverse division. Once again, consider my example:
>>
>> A=[0,2]
>> B=[-1,1]
>> C=[1,1]
>>
>> with \circ=\times
>>
>> and compute \times_1^-(B,C,A) = hull({x\in[0,2]\mid\exists b\in[-1,1],
>> x\times b\in[1,1]})
> [...]
>
>> No, because Corollary 1 is false.
>> You just have to consider the example above. [...]
>
> Corollary 1 seems perfectly correct to me. If the example you're
> talking about is the example above, then you don't have the same
> definition as in Motion 11, where there's no "hull"!
>
My mistake. My original message was referring to the first version of
Motion 1, where there was some "hull" involved. Marco has modified
Motion 11 since then to take into account my remark.
Then again, I believe that abandoning "Hull" as done in the current
version of Motion 11 removes the problem with Corollary 1 only to
introduce new difficulties since we are no longer restricted to
intervals and that we would have to consider possibly infinite unions of
intervals when time to consider trigonometric inverse functions comes.
F.
- --
Frédéric Goualard LINA - UMR CNRS 6241
Tel.: +33 2 51 12 58 38 Univ. of Nantes - Ecole des Mines de Nantes
Fax.: +33 2 51 12 58 12 2, rue de la Houssinière - BP 92208
http://goualard.frederic.free.fr/ F-44322 NANTES CEDEX 3
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