OpenEuphoria

Re: Dimension of sequences

• Posted by Igor Kachan <kinz at peterlink??u> Sep 24, 2007
• 668 views

Fernando Bauer wrote:
> 
> Igor Kachan wrote:
> > 
> > > > Here, in Russia, we use 2 words for these things:
> > > > "izmerenie" -- it is just single "dimension"
> > > > and
> > > > "razmernost'" --  it is common number of dimensions, "dimensionality".
> > > > So I'd prefer to say that any sequence has dimensionality 2,
> > > > and its dimensions are named as "length" and "depth".
> > > 
> > > This looks ok to me, except that the length is really a very special case.
> > > 
> > > > But this 2-dimensional sequence can describe and contain
> > > > multi-dimensional objects.
> > > > Anyway, in machine memory, it is just 1-dimensional *range* of
> > > > addresses.
> > > > 
> > > 
> > > Exactly. So the "length" of a general sequence would be the total number
> > > of
> > > nodes it holds. The current definition of length() is very adequate for
> > > linear
> > > trees - one root with length(s) children, the nature of which is not taken
> > > into
> > > account -. For general trees, however, it barely makes sense.
> >  
> > OK, let's see what is every atom in some complicated sequence.
> > I think, that every atom can be, so to say, one of the dimensions
> > or coordinates of some multi-dimensional object, described by that
> > given sequence.
> > So the common number of atoms of some given sequence is very
> > interesting thing - it gives us sometimes the number of
> > dimensions of the described object!
> 
> A possibility is with this type of structure: {A1,{A2,{A3,{...}}...}.
> Example: {1,{2,{3,{4}}}}

Ok, there may be many examples for different objects, I think.
The thing is that the author of the described object wants
to tell us how many parameters of his object can be
*considered as dimensions*.

> > We can name this parameter with some suitable word to
> > characterize, so to say, a volume of a sequence, or its
> > capacity or something.
> > It is not the sum of all lengths, it is number of atoms,
> > and a function for calculation of this number may be
> > very simple.
> }}}
<eucode>
> function NumberOfAtoms(object o)
> integer n
>    if atom(o) then return 1 end if
>    n = 0
>    for i=1 to length(o) do
>       n += NumberOfAtoms(o[i])
>    end for
>    return n
> end function
> <\eucode>
It works for me nicely, thanks!

Regards,
Igor Kachan
kinz at peterlink.ru