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Question: large matrices and Rank mod p

Question:large matrices and Rank mod p

fschueller 0 Maple
modular sparse linearalgebra rank
September 10 2012
0

I'm trying to compute the rank of large, non-quadratic matrices modulo p=2,3,5 and 7.

For matrix-sizes of (approx.) 20000 x 20000 everything works fine with Rank(p,M) of LinearAlgebra[Modular].

But for (approx.) 40000 x 40000 even the parsing of the matrix is not finished after 5 days (for 20k x 20k this takes 1 or 2 hours) . The system I use has enough ram, so no swaping is involved.

 

First question: I expected the parsing to be O(n^2), why is this not the case?

 

Also the matrix contains mainly zeros, so I would like to use "storage=sparse", but then Rank(p,M) does not work. (I'm using Maple 11-13)

 

Second Question: does this work with maple 15 or 16?

 

TIA,

  Felix
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