Subject: Help with very very slow determinant calcuation
From: Barton Willis
Date: Sun, 7 Aug 2011 12:34:21 -0500
-----Bernard Hurley <bernard at marcade.biz> wrote: -----
An n x n determinant of terms of the form x[1,1],..., x[1,n],
x[2,1]...., x[n,n] is the sum of n! terms each the product of n terms.
There is no getting away from that however you evaluate the determinant!
Whether or not Maxima can compute the determinat of a matrix with
symbolic entries in a reasonable time depends on the matrix:
(%i1) m : genmatrix(lambda([a,b], random(3) + random(3)*z),50,50)$
(%i2) m : matrixmap(rat,m)$
(%i3) (showtime : all, ratmx : true)$
(%i4) determinant(m)$
Evaluation took 13.3220 seconds (13.4630 elapsed)
Roughly, Avogadro constant < 50! < Eddington number.
--Barton