Re: x*x-1=0

 wrote:
> In article <949sjq$k1s$3_at_news.tue.nl>,
> hidders_at_win.tue.nl (Jan Hidders) wrote:
> > wrote:
> > > What the closest analog of
> > > x^2-1=0
> > > in relational algebra would be? Does
> > > A MULTIPLY B MULTIPLY C
> > > have any resemblance to power 2?
> >
> > Not really, it is more just like multiplication. A better kind of
> > candidate would be the powerset operation that you sometimes find in
> > some nested relational algebras.
>
> Thank you for the reference. Before doing my howework, though, a newbie
> question: Overall, are nested algebras a kind of generalization that
> pays of?

Yes, but mainly in the sense that it allows you to manipulate nested relations which can be a better description of your data. So the interest is mainly a practical one.

> Is it more elegant? Does it have less number of atomic
> operators?

No, it has more; at least nesting and unnesting. Sometimes also other operations such as the powerset or some kind of recursion/iteration mechanism.

> I, personally, have difficulties understanding simple
> relational model, could I hope to get some new insights from nested one?

No, things only get more complicated. But if I may ask, what is it that you find difficult about the flat relational model?

> [...] My question is about our abilities
> solving equations in Relational Algebra, whatever operation definitions
> are. (Although, Distributive, Commutative, and Associative laws would
> help:-). For example,
>
> x MULTIPLY A UNION B = DUM
>
> where A and B some table constants and x is rel var.

Aha, now I am beginning to see what you mean. But I am not sure what your question exactly is. If you look at the equation you gave

  x^2 - 1 = 0

then there is no problem. It is just an equation with two solutions. That can also happen in the relational algebra. But I suspect what you wanted to talk about was the equation

  x^2 + 1 = 0

which under the usual interpretation does not have a solution, but leads to interesting theories if you assume that it does. Let's see what happens. First, we try to translate this into rel. algebra:

  (X TIMES ({<1>} UNION {<2>})) UNION ({<3>} TIMES {<3>}) = {}

Notation:

  TIMES = the cartesian product (similar to multiplication)
  UNION = the union (similar to addition)
  {<x>} = singleton set with a unary tuple containing the number x

Assuming that this equation is solveable leads to the peculiar property that there will be sets that you can add a non-empty set to such that the result will be an empty. You might call them "negative sets" if you will. I doubt it they will turn out to be very useful concepts. :-)

-- 
  Jan Hidders

PS. Could you tell your newsreader/poster your real name please? The
    quotation of your lines now looks a bit funny. :-)