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Re: Bags vs. Sets

From: vc <boston103_at_hotmail.com>
Date: 28 Jun 2006 13:47:04 -0700
Message-ID: <1151527624.746783.308150@j72g2000cwa.googlegroups.com>

vadimtro_at_gmail.com wrote:
> vc wrote:
> > vadimtro_at_gmail.com wrote:
> > Consider a relation
> > >
> > > {(x=1,y=1),(x=2,y=1)}
> > >
> > > This set can be considered as a set of roots of some system of
> > > polynomial equations. Can we write those equations explicitly? Sure:
> > >
> > > (x-1)*(x-2)=0
> > > (y-1)=0
> > >
> >
> > That does not look right. Take different values for 'y'.
>
> OK, let's add a tuple {(x=2,y=2)} so that the relation becomes

No, let's just consider {(1,2), (3,4)}. You'd see that there would be 4 defining equations instead if just two as was in the case of {(1,1), (2,1)}. My point is that you want to explain to those interested how you recover polynoms from the variety and what computational complexity it would entail, not just say "Can we write those equations explicitly? Sure".

[...]
> > While there are some similarities, not surprizingly, between ideal
> > operations and RA, it's unclear what advantage if any the
> > variety/ideal lingo may have.
>
> I hope to extend relational algebra with introduction of clean bags
> semantics and aggregation.
>
> > For example, what field did you have
> > in mind when you talked about polynomials ?
>
> C ? This matter doesn't seem important to me.

Then, how do you intend to handle non-numeric domains like strings of characters, or user defined finite domains ?

> In the relational
> applications ideals are manufactured from 0-dimensional varieties, not
> the other way around. Therefore, we don't need fancy algebraic
> properties, like demanding the field to be algebraically closed.
Received on Wed Jun 28 2006 - 15:47:04 CDT

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