Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?

"Steve Kass" <skass_at_drew.edu> wrote in message news:b3k8ks$kca$1_at_slb5.atl.mindspring.net... [snpi]
> I'm lost on who is countering whose argument here, but you have
> described one type that represents the 9 points on and at the
> center of the 2 x 2 square at the origin of Z x Z, and another type
> that represents 9 points on and at the center of a circle (I think you
> may have meant to allow -0.75PI, ..., 0.75PI, 1 PI), instead of twice
> these values).
>
> These certainly represent very different subsets of cartesian space,
> so what do you mean by saying these are equivalent? Once you stray
> from points of the cartesian form (N,0) and (0,N), I don't think you'll
> have much luck finding equivalent polar and cartesian representations.

I was attempting to counter my own argument. With a flawed example as you point out.
However if I fix the example, I think I do have equivalent polar and cartesian representations outside of (N,0) and (0,N).

To support these 9 points

( 0,  0)    =    (      0,  0)
( 1,  0)    =    (      0,  1)
( 1,  1)    =    ( 0.25PI,  1SQRT2)
( 0,  1)    =    (  0.5PI,  1)
(-1,  1)    =    ( 0.75PI,  1SQRT2)
(-1,  0)    =    (    -PI,  1)
(-1, -1)    =    (-0.75PI,  1SQRT2)
( 0, -1)    =    ( -0.5PI,  1)
( 1, -1)    =    (-0.25PI,  1SQRT2)

we could have a type such as

TYPE TINY_INT POSREP( {-1,0,1 } ); TYPE TINY_PI
POSREP( {-0.75 PI, -0.5 PI, -0.25 PI, 0, 0.25 PI, 0.5 PI, .75} ); TYPE TINY_R2 POSREP( { 0, 1SQRT2, 1 } ); TYPE TINY_POINT
POSREP POINT_XY (X TINY_INT, Y TINY_INT) POSREP POINT_RT (T TINY_PI, R TINY_R2

        CONSTRAINT
             IF R = 0 SQRT2 THEN T = 0
             IF T IN (0.5PI, 0, -PI, -0.5PI) THEN R = 1
             ELSE R = 1SQRT2
                );

I guess things get a little more involved when X or Y > 2, but I'm happy for the moment.

Regards
Paul Vernon
Business Intelligence, IBM Global Services Received on Thu Feb 27 2003 - 11:45:40 CET