Re: Strange Det function behavior.

*To*: mathgroup at smc.vnet.net*Subject*: [mg65463] Re: Strange Det function behavior.*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Mon, 3 Apr 2006 06:59:28 -0400 (EDT)*Organization*: Universitaet Hannover*References*: <e0o513$1to$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Alexander schrieb: > Dear MathGroup! > > Suppose we have defined the following function: > > f[x_Integer] := Det[ Table[ Random[]*t + i/j, {i, x}, {j, x} ] ]; > > Now try to make a table for different values of argument (matrix > dimension): > > Table[f[i], {i, 12}] // TableForm > > It takes a considerable time on my Celeron 1700 with Mathematica 5.2 > under WinXP to make such a table. > > Once we made this table we see very strange bihavior, all results > before x=12 dimension are polynoms, > but starting from x=12 result become very big and very > strange, and in fact it's not even a polynom. > > I spend several hours try to understand why system acts so strange, and > finally came to idea that the answer is in numbers representation and > inner > system algorithms used to evaluate Det function. > > It would be very interesting to see explanations of this result. > > Thanks for your answers! Perhaps the determinant is calculated using some transformations to standard triangular form. The determainant then is a product of determinant of matrices some of which are given in inverse form. So in effect you get the determinant as a rational expression in the variable "t". To proceed further you have to invert a matrix or to find the common factors in the polynomials. -- Roland Franzius