Path: utzoo!mnetor!tmsoft!itcyyz!yrloc!hui
From: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Newsgroups: comp.lang.apl
Subject: Re: Determinant
Message-ID: <1991May22.125919.1759@yrloc.ipsa.reuter.COM>
Date: 22 May 91 12:59:19 GMT
References: <1991May19.053021.7840@yrloc.ipsa.reuter.COM> <1991May21.161641.18112@jato.jpl.nasa.gov>
Reply-To: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Organization: Iverson Software Inc.
Lines: 25

Sam Sirlin writes:

>This sounds interesting, but if I was given a matrix and told to take its
>determinant, I would use LU or SV decomposition if the matrix was above 
>about 6th order. Isn't the minor calculation ill conditioned? If so then
>isn't a built in determinant using minors missleading to naive programmers?

The system will recognize the ordinary determinant -/ . * as a special
case, and use an equivalent but O(n^3) algorithm to compute it.  Having a 
determinant operator encourages experimentation with generalized determinants.
For example:

   + / . *          permanent
   <./ . +          minimum cost in assignment problem
   +./ . *.         whether a Latin square is covered
   + / . *.         how many Latin squares are covered
   [   . (,&.>)     try it

All except the last are from K.E. Iverson, "Determinant-like Functions
Produced by the Dot Operator", Sharp APL Technical Notes 42, 1982 4 1.

-----------------------------------------------------------------
Roger Hui
Iverson Software Inc., 33 Major Street, Toronto, Ontario  M5S 2K9
(416) 925 6096