Re: Dimension of sequences
Igor Kachan wrote:
Hello Igor! Thanks again for your considerations.
>
> Hello Fernando!
>
> Fernando Bauer wrote:
> >
> > 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</font></i>
> > > > > 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:
> >
> > }}}
<eucode>
> > 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)
> > </eucode>
{{{
> >
> > 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?
>
> Ok, good. I do understand your concept, be sure.
> But it is something new. There is no any theory under
> "dimension of Euphoria sequence".
>
> Euphoria sequence as it is is invented by Robert Craig
> and has just its length.
>
> So you are free to define some *new* & *useful* parameters
> of some *specific kind* of sequences and to name these
> parameters as you wish - 'dimension' or something else,
> say, 'length-depth'.
>
> I do not think, for now at least, that we have to
> care if the sequence is 'rectangular' or 'non-rectangular'.
> But I think that sequences can describe any rectangular
> and non-rectangular objects, and dimension of that
> described object, for example, may be some dimension
> of this describing sequence too.
>
> I do not know what to do with this new parameter
> of a sequence, with this new term, 'dimension'.
>
> Ok, say, dimension of some sequence is 2.
> So what?
Then you know that the sequence can be viewed as a matrix (a 2D array).
This is true if all non-rectangular sequences have a dimension different from
integer 2.
>
> But if I have some 2 components vector, I do know
> what to do with that vector.
If you know what to do with that vector then you know what to do with that
matrix too.
>
> > > > > Why do you need to know the 'dimension' of a sequence? I mean if you
> > > > > knew
> that</font></i>
> > > > > 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.
>
> Ok, I see, I do understand this other concept,
> but this concept itself is just some definition
> of some new term for some specific kind of sequences,
> so named rectangular sequences.
> But 'rectangular' sequence itself needs some
> definition now, and so on.
>
In the initial post I define "rectangular sequence" as:
A sequence generated by using iteratively the function repeat() beginning with
an atom".
> 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!
>
> 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..
> Euphoria itself is very simple language without complicated
> abstractions. But can describe any complicated objects
> using simple concept of sequence.
>
> > > But we must not confuse sequence itself and thing,
> > > which is described with that sequence.
>
> Well, back to above your question, I do not think that someone
> already knows how to define 'dimension of NRS' and so on and
> for what purpose.
Maybe this answer and others can be found in Tree theory which was more studied.
>
> Ok, try to define it yourself, why not?
> But remember please, Euphoria is simple thing, first of all.
>
> Good Luck!
Thank you!
>
> Regards,
> Igor Kachan
> kinz at peterlink.ru
Regards,
Fernando
|
Not Categorized, Please Help
|
|
