Re: x*x-1=0

In article <94jj6o$r5p$1_at_news.tue.nl>,   hidders_at_win.tue.nl (Jan Hidders) wrote:
> > > But things get, from an algebraic perspective, a little more
> > > complicated because the cartesian product does not commute as the
> > > join does.
>
> The relational cartesian product is defined as follows
>
> R1 CP R2 = { <m_1,...,m_k, n_1,...,n_l> |<m_1,...,m_k> in R1 and
> <n_1,...,n_l> in R2 }
>
> If you want to simulate R1 JOIN R2 then you have to write SEL[#i=#j]
 (R1
> CP R2) where #i and #j are the numbers of the fields upon which you
> want to join. If you join on more than one field than you add another
> selection. But the problem is that as you can tell by the definition
> the cartesian product does not commute, i.e., R1 CP R2 <> R2 CP R1.

It is the order of tuple components that makes CR incommutative. Then, applying SEL is not a remedy, because tuples still have their components ordered differently for SEL[...](R1 CP R2) and SEL[...](R2 CP R1). If CR is uncommutative, then JOIN should be as well, right?

I disagree that CP = MULTIPLY, and, in general, that order of columns matters. This is why I wanted some congruences on tuples.

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http://www.deja.com/ Received on Tue Jan 23 2001 - 20:58:01 CET