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MathGroup Archive 1992

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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





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