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Re: Smith Normal Form Algorithm

  • To: mathgroup at
  • Subject: [mg2680] Re: Smith Normal Form Algorithm
  • From: crstover at (CRStover)
  • Date: Tue, 5 Dec 1995 02:26:51 -0500
  • Organization: America Online, Inc. (1-800-827-6364)

Dear Mr. Chung,

WRI's ftp archive, (mathsource at, also accessible
via the Web), contains two independent implementations of the Smith normal
form algorithm that I know of. One is part of the LatticeTheory.m package,
which I think is found under "applications/mathematics/pure" as 0204-556.
The other is filed under "enhancements/linear algebra" as 0207-470.

Both of these packages use a conceptually straightforward algorithm that
is prone to spectacular numerical blowup,
especially when asked to provide det 1 integer matrices that will
transform the original matrix to the Smith form. (Note: the transformation
matrices are far from unique, contrary to the implication in
LatticeTheory.m.) If this blowup becomes a problem for you, I can send you
a package I have written that diagonalizes integer matrices (most of the
work of finding the Smith form) in a way that controls the blowup and
frequently produces much smaller transformation matrices.


Chris Stover
crstover at

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