Re: Dimension of sequences
- Posted by Fernando Bauer <fmbauer at hotma?l.com> Sep 19, 2007
- 615 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