From: msk@beta.hut.fi (Mikko S Kiviranta)
Subject: Integer Relation Detection (was: Cost of the Fast Multipole...)
Date: 15 Jun 2000 21:36:48 GMT
Newsgroups: sci.physics.research
Summary: [missing]

In article <8i4t0n$vtt$1@nntp.hut.fi> msk@beta.hut.fi (Mikko S Kiviranta) writes:
>  The top 10 algorithms were, by the way:
>
>- Integer relation detection
>- The Dantzig simplex method for LP
>- Krylov subspace iteration
>- The QR method for eigenvalues
>- Quicksort
>- The decompositional approach to matrix computation
>- FFT
>- Metropolis
>- The Fortran I compiler
>- The fast multipole algorithm

  The other 7 (except for the Fortran compiler)
belong to the standard toolbox of an average physicist
doing numerical work, I believe, but the Fast Multipole
and Integer Relation algorithms at least I hadn't heard of
before (they both appear to be quite recent developements).

  Especially utilization of the Integer Relation Detection 
algorithm, has (according to the CSE article) lead to
discovery of some pretty cool algebraic relations, like:

- The fact that the 3rd bifurcation point of the logistic
map is actually a root of a 12th degree polynomial with
simple integer constants, and a similar (but more 
complicated) result for the 4th bifurcation point.

- Discovery of a formula which allows fast calculation of
the n:th digit of Pi, without having to calculate the
preceeding digits.

- Discovery of a seven-letter alphabet, with four-letter
words that somehow represent (I don't understand this
stuff well enough) the finite part of certain 3-loop 
vacuum Feynmann diagrams in the QFT. There was a
reference to hep-th/9803091 in the CSE article.

  Considering the fact that the effective algorithm was
only discovered in -97, the Integer Relation Detection 
sounds like a very fruitful algorithm, well worthy for 
the 'top ten' title.

  (Just wanted to share what I find quite exciting a
developement)
 
  Best regards,
               Mikko