Re: Why are [Database] Mathematicians Crippled ?

Tegiri Nenashi wrote:
> On Monday, February 2, 2015 at 9:45:02 AM UTC-8, Norbert_Paul wrote:
>>> .... How do you represent polynomials in database?
> My question is how useful this is;

No. Your question was as cited above.

> ..., but how about "give me all systems which roots are zero dimensional
> varieties"?

If this requires to find the root, you could stumble into undamental problems: en.wikipedia.org/wiki/Galois_theory#Solvable_groups_and_solution_by_radicals But maybe there is a way do decide "p has roots of dimension zero" without actually solving the polynomial p.

>> 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)

Is this supposed to be a proof that transotove closure is required? Then I don't get it.

> However, I don't consider transitive closure as a part of relational algebra.

This is more a personal opinion you have. I prefer to distinguish between "relational algebra with transitive closure" and "relational algebra without transitive closure".

See Page 527 (or Page 5)

   14.3 LIMITATIONS OF RELATIONAL ALGEBRA in

   http://web.cecs.pdx.edu/~maier/TheoryBook/MAIER/C14.pdf .

> 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).

How sad! Poor binary! But why are operaitons on binary relations not part of relational algebra?

given

   R(a,b) and S(b,c) .

Then

   R NATJOIN S
   PROJECT[a](R)
   SELECT[b=7](S)

look like Relational Algebra expressions to me.

>>> ... 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.

You must do this by yourself. Such papers are usually unaccessible to me, too, without effort. This kind of papers cannot be read like novels. It sometimes is hard work to understand the notions the authors use and follow their arguments. I then often have to familiarize with a subject matter that is new to me. Hence I used the word "might", because I cannot know in advance if I get any profit from working through (aka "reading") the paper. Received on Tue Feb 03 2015 - 19:10:17 CET