X-Received: by 10.224.45.74 with SMTP id d10mr18524168qaf.2.1422905914022; Mon, 02 Feb 2015 11:38:34 -0800 (PST) X-Received: by 10.50.142.36 with SMTP id rt4mr176288igb.2.1422905913922; Mon, 02 Feb 2015 11:38:33 -0800 (PST) Path: news.cambrium.nl!textnews.cambrium.nl!feeder3.cambriumusenet.nl!feed.tweaknews.nl!195.208.113.2.MISMATCH!goblin2!goblin.stu.neva.ru!newsfeed.xs4all.nl!newsfeed4.news.xs4all.nl!xs4all!newspeer1.nac.net!border2.nntp.dca1.giganews.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!bm13no5411307qab.0!news-out.google.com!qk8ni19963igc.0!nntp.google.com!hl2no7935649igb.0!postnews.google.com!glegroupsg2000goo.googlegroups.com!not-for-mail Newsgroups: comp.databases.theory Date: Mon, 2 Feb 2015 11:38:33 -0800 (PST) In-Reply-To: Complaints-To: groups-abuse@google.com Injection-Info: glegroupsg2000goo.googlegroups.com; posting-host=2601:9:100:600:808c:1aa9:1630:bac8; posting-account=PBsn8woAAADaWofLEAjNrE17YVrUmBlm NNTP-Posting-Host: 2601:9:100:600:808c:1aa9:1630:bac8 References: <61044dae-51c9-43d4-87f9-1e12e0e3b15e@googlegroups.com> <2807ea7c-a50e-4a67-8357-2ccd0bdc9e57@googlegroups.com> <6cc9b130-6adc-494f-905a-b43a343416c5@googlegroups.com> User-Agent: G2/1.0 MIME-Version: 1.0 Message-ID: <2d4ab7db-da83-4f84-8cb1-17b831773c16@googlegroups.com> Subject: Re: Why are [Database] Mathematicians Crippled ? From: Tegiri Nenashi Injection-Date: Mon, 02 Feb 2015 19:38:33 +0000 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Lines: 62 Xref: news.cambrium.nl On Monday, February 2, 2015 at 9:45:02 AM UTC-8, Norbert_Paul wrote: > > .... How do you represent polynomials in > > database? >=20 > CREATE TABLE Polynomials( > id INTEGER NOT NULL PRIMARY KEY > ); >=20 > CREATE TABLE Monomials( > id INTEGER NOT NULL > degree INTEGER NOT NULL, > coefficient 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? Ne= xt some queries like finding product of the two polynomials is relatively e= asy, but how about "give me all systems which roots are zero dimensional va= rieties"? =20 =20 > > ... 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 que= ry of > > matrix inverse is not expressible with standard relational operations. >=20 > 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 jo= in > (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 m= atrix of transitive closure is the following matrix inverse M^* =3D 1 + M + M^2 +... =3D (1-M)^(-1) =20 However, I don't consider transitive closure as a part of relational algebr= a. It is something that belongs to algebra of binary relations, which as be= en 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 clos= ure operator is not total in relational algebra). =20 > > ... Many CS researchers venture to do bold things, here is the > > example: > > > > http://arxiv.org/abs/1208.6416 >=20 > 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 pede= strian level.