Re: Why are [Database] Mathematicians Crippled ?

On Monday, February 2, 2015 at 9:45:02 AM UTC-8, Norbert_Paul wrote:
> > .... How do you represent polynomials in
> > database?
>
> CREATE TABLE Polynomials(
> id INTEGER NOT NULL PRIMARY KEY
> );
>
> CREATE TABLE Monomials(
> id INTEGER NOT NULL
> degree INTEGER NOT NULL,
> coefficient <YourFieldOfChoice> NOT NULL,
> PRIMARY KEY(id, degree),
> FOREIGN KEY(id) REFERENCES Polynomials(id)
> );

Fair enough. I meant systems of multivariate polynomials, but sure you can have

table UnivariateMonomials
table MonomialProducts
table Polynomials
table PolynomialSystems

My question is how useful this is; have you seen such beast in the wild? Next some queries like finding product of the two polynomials is relatively easy, but how about "give me all systems which roots are zero dimensional varieties"?  

> > ... One can even be impressed by matrix
> > multiplication query which is just relation's self-join followed by
> > aggregation with group by. However, the success is short-lived, and query of
> > matrix inverse is not expressible with standard relational operations.
>
> I'd bet it is. You might first want to compute the determinant. Then use that
> query to compute the matrix inverse. I suppose this requires recursive join
> (transitive closure) iff the matrix size is not limited.

Yes, transitive closure is required. It can also go the opposite way: given adjacency matrix of a graph, if we know it's inverse, then the adjacency matrix of transitive closure is the following matrix inverse

M^* = 1 + M + M^2 +... = (1-M)^(-1)  

However, I don't consider transitive closure as a part of relational algebra. It is something that belongs to algebra of binary relations, which as been married against its will. She is unhappy in her marriage because she is allowed to make love only on second day of each month (i.e. transitive closure operator is not total in relational algebra).

> > ... Many CS researchers venture to do bold things, here is the
> > example:
> >
> > http://arxiv.org/abs/1208.6416
>
> This looks interesting. I like tha categorial viewpoint of the paper.
> So it might be worth reading it.

That part is inaccessible to me. I wish somebody translated it to more pedestrian level. Received on Mon Feb 02 2015 - 20:38:33 CET