Re: Determinant Function (Final Version?)

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: Determinant Function (Final Version?)*From*: fateman at peoplesparc.berkeley.edu (Richard Fateman)*Date*: Sun, 19 Apr 92 20:26:59 PDT

There is a rather extensive literature on computing the determinant of a symbolic matrix. The generation of the determinant of a matrix where the i,j element is a unique symbol is a rather special case. What you'd like is a method that takes advantage of sparseness in a sparse matrix; that minimizes intermediate expression growth (esp. in the case that Det=0) ; that maintains factored forms if plausible; minimizes GCD computation if the elements are rational, etc. Rearranging the Mathematica computation does not affect the asymptotic running speed (O(n!) for an n x n). Taking advantage of special structure can sometimes do much better. Since the Mathematica book refuses to provide references to algorithms, people who want to know more will have to look elsewhere. Richard Fateman, UC Berkeley