OpenEuphoria

Re: Dimension of sequences

• Posted by Fernando Bauer <fmbauer at hotma?l.com> Sep 19, 2007
• 759 views

Igor Kachan wrote:
> 
> Hello Fernando!

Hello Igor!

> 
> Fernando Bauer wrote:
> > 
> > Igor Kachan wrote:
> > >
> 
> [snipped]
> 
> > > Ok, suppose, we now have all these new definitions -
> > > 'rectangular sequence' (RS), 'non-rectangular sequence' (NRS),
> > > 'dimension of RS', 'dimension of NRS'.
> > 
> > 'non-rectangular sequence' (NRS) = all sequences that aren't RS.
> > 'dimension of RS' = maximum depth of the sequence.
> > 'dimension of NRS' = that is the question!
> 
> Let's see the refman.doc file now.
> 
> Robert Craig wrotes:
> 
>  "Sequences can be nested to any depth, i.e. you can have sequences within
>   sequences within sequences and so on to any depth (until you run out of
>   memory)." 
> 
> I see Rob cares just about *maximum* depth here, so his definition
> of depht, documented in refman.doc, is strongly equivalent to your
> definition of 'dimension of RS'.
> Same thing, you just introduce some new term, synonym.
> 
> No?

Ok. We can use "depth" as synonym of "dimension" as you prefer. Then my question
is:
What is the depth of a NRS? How can I obtain it? For now, I only know the depth
of a RS.

> 
> Then, I do not think now that the 'rectangular' word is very
> good for your purpose, maybe, 'regular', as some short
> for 'regularly nested', is better.
> 
Ok. But I think "rectangular" is sligthly more precise than "regular", since I
could think that the following sequence is regular:
repeat({1,{1,1}},n) where n is any integer number. And that sequence is NRS.
Well, this is only a definition problem.

> > > So what?  What will we do with all these new terms, with
> > > all these new notions, with all these new concepts?
> > 
> > First of all, they facilitate our communication, since we don't have to say
> > that whole definition phrase.
> > Second, the terms RS and NRS can represent types in Euphoria, like vector or
> > matrix, and so can be checked.
> > Some algorithms can function with one and not with other type, etc..
> 
> Ok, but for now I do not see some real place for the 'dimension' word
> here. Length & Depth. These old good words are very clear in 
> the specific EU context. 

Ok. But the Depth concept is not so clear as it seems, since nobody defined what
it is for NRS yet.

[snipped]

> Regards,
> Igor Kachan
> kinz at peterlink.ru

Regards,
  Fernando