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Forum index » Science and Technology » Math » Symbolic
Efficient Determinant Computation over Z/p
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Robert H. Lewis
science forum beginner


Joined: 22 Jul 2005
Posts: 9

PostPosted: Sat Jul 01, 2006 5:11 pm    Post subject: Efficient Determinant Computation over Z/p Reply with quote
Hi,

Given a fairly large square matrix (say rows = n >= 300) over Z/p what is the best way to compute its determinant?

So, the entries are in the finite field F(p) = Z/p. The matrix may be sparse or dense.

Is there any method better than Gaussian elimination, which is O(n^3), under any reasonable assumptions?

Robert H. Lewis
Fordham University
New York
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Chip Eastham
science forum Guru


Joined: 01 May 2005
Posts: 412

PostPosted: Tue Jul 11, 2006 12:52 pm    Post subject: Re: Efficient Determinant Computation over Z/p Reply with quote
Robert H. Lewis wrote:

Quote:
Given a fairly large square matrix (say rows = n >= 300) over Z/p
what is the best way to compute its determinant?

So, the entries are in the finite field F(p) = Z/p. The matrix may
be sparse or dense.

Is there any method better than Gaussian elimination, which is
O(n^3), under any reasonable assumptions?

None that I know of, unless you count assumptions about a
special structure, e.g. Toeplitz matrices or similar, for which
an O(n^2) algorithm is possible.

Sorry!

regards, chip
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avidad
science forum beginner


Joined: 21 Jul 2005
Posts: 6

PostPosted: Thu Jul 13, 2006 9:09 pm    Post subject: Re: Efficient Determinant Computation over Z/p Reply with quote
Chip Eastham wrote:
Quote:
Robert H. Lewis wrote:


Given a fairly large square matrix (say rows = n >= 300) over Z/p
what is the best way to compute its determinant?

So, the entries are in the finite field F(p) = Z/p. The matrix may
be sparse or dense.

Is there any method better than Gaussian elimination, which is
O(n^3), under any reasonable assumptions?


None that I know of, unless you count assumptions about a
special structure, e.g. Toeplitz matrices or similar, for which
an O(n^2) algorithm is possible.

Sorry!

regards, chip

If the matrix is space (or structured as Toeplitz Hankel or low

deplacement rank) yes, look for a method based on matrix-vector product.
Look the web page of Jean-Guillaume Dumas for efficient determinant
computation over finite field.
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Google
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