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Re: Neumaier-Pryce proposed decoration system (v03.2)

Dominique,

I don't quite follow. Can you clarify?

If we have the tracking results (by motion 25):

   sqrt([1,4])
       = sqrt(([1,4],D3))    // promote input to "best" decoration
       = (sqrt([1,4]),inf(S(sqrt,[1,4]),D3))
       = ([1,2],inf(D3,D3))
       = ([1,2],D3)

   sqrt(Empty)
       = sqrt((Empty,D4))   // promote input to "best" decoration
       = (sqrt(Empty),inf(S(sqrt,Empty),D4))
       = (Empty,inf(D4,D4))
       = (Empty,D4)

then we also have:

   Empty \subset [1,4]    and    D4 \subset D3

or, in motion 26 terms:

   Empty \subset [1,4]    and    ein \subset dac

so the tracking results are consistent with FTDIA.

Or were you making some other point?

Nate
----- Original Message ----- From: "Dominique Lohez" <dominique.lohez@xxxxxxx> 
To: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
Cc: "John Pryce" <j.d.pryce@xxxxxxxxxxxx>; "stds-1788" <stds-1788@xxxxxxxxxxxxxxxxx> 
Sent: Thursday, June 16, 2011 5:06 AM
Subject: Re: Neumaier-Pryce proposed decoration system (v03.2)



Nate, John , p1788,


IMHO the most significant comparison is between     decorated interval s

sqrt([1,4]) = ([1,2], saf)
sqrt(Empty)= (Empty,saf)

and we have
(Empty, saf) > ( [1,2], saf)

We only need such a comparison


Dominique


Nate Hayes a écrit :

Dominque Lohez wrote:

John, Nate,

My position is that the case ein should be merged with safe by removing
the restriction that for saf the input is not empty;


Using terms as per my last e-mail, returning D3/dac for an operation like
   sqrt( Empty )
is overly-conservative, since by the containment order "ein" is a more optimal "enclosure" of the decoration result; similarly, D3 is not the "best" decoration by the linear quality order (D4 is). 

Nate





--
Dr Dominique LOHEZ
ISEN
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Email: Dominique.Lohez@xxxxxxx