OpenEuphoria

Re: Dimension of sequences

• Posted by Fernando Bauer <fmbauer at ?otma?l.com> Sep 15, 2007
• 645 views

Igor Kachan wrote:

Hello Igor! Thanks for the reply.
> 
> Fernando Bauer wrote:
> > 
> > Derek Parnell wrote:
> > 
> > Hi Derek. Thanks for your reply.
> > 
> > > A sequence doesn't have a 'dimension' in geometrical sense. A sequence is
> > > not
> > > a geometric object.
> > 
> > A vector or a matrix aren't geometric objects in mathematics or in
> > programming
> > either, however they
> > have a dimension, as you know.
> 
> Yes, but their 'dimension' is just a special term, which means
> just number of members. And at all another thing, if, for example,
> some vector describes x-y-z coordinates of some point
> in some 3-dimensional space. 

I think you misunderstood what I've tried to ask. Probably you didn't read the
initial post.
Let's use Euphoria to describe better:

include genfunc.e
atom a
sequence seq1D, seq2D, seq3D
-- an atom
a = 1
-- a 1D sequence
seq1D = repeat(a, 2)
-- a 2D sequence
seq2D = repeat(seq1D, 2)
-- a 3D sequence
seq3D = repeat(seq2D, 2)

-- for rectangular sequences MaxDepth() compute the dimension
procedure ShowDimension(object o)
puts(1,"Dimension of ")
print(1, o)
printf(1," = %d\n",MaxDepth(o))
end procedure

ShowDimension(a)
ShowDimension(seq1D)
ShowDimension(seq2D)
ShowDimension(seq3D)

I think my concept of dimension is like Rank concept in the J language.
What I'm trying to ask is: What is the dimension for non-rectangular sequences?

> 
> > > Why do you need to know the 'dimension' of a sequence? I mean if you knew
> > > that
> > > a given sequence has a dimension of 'x', what would you use 'x' for? 
> > It is a theoretical question. Maybe there are rules or functions (e.g.
> > compression
> > factor?) that depends on this parameter. Why do the mathematicians and
> > physicists
> > calculate dimensions of fractal objects?
> 
> There is very simple theory of Euphoria sequences in Euphoria
> documentation, firsthand about EU sequences.
> These sequences have 'length', and nothing more.
> But any member of any sequence can be a sequence itself
> with its own length.
> This 'length' is just number of members.
> See, 'dimension' of vector is equal to 'length' of sequence.
I think my "dimension" is your "number of dimensions". See the code above.

> So, your question is not 'theoretical' one, but is just some
> question about sense of some terms in Euphoria.
> This is a question about multimeaning of the word 'dimension',
> I think.
> Another thing that EU sequences can describe any
> multidimensional real and unreal objects and things,
> thanks to very flexible nature of these sequences.
>  
> > > Are you asking the right question?
> > I think yes, since I understand your response as option e) (the concept does
> > not apply to). I don't know the answer.
> 
> I think, the answer may be simple enough - dimension of
> Euphoria sequence is just its length.
See above other concept or meaning of "dimension", which is what I'm trying to
ask about.

> 
> But we must not confuse sequence itself and thing,
> which is described with that sequence.
> 
> Regards,
> Igor Kachan
> kinz at peterlink.ru

Regards,
  Fernando