Update.

The versions of Fermat available for download were not able to use the best determinant algorithms for matrices with > 5000 rows. I've changed that now. Google "Lewis Fermat"

I experimented some more with examples like this. I created a random 10000 row square matrix with density 1.86. Using the best algorithm over GF(2), which turns out to be just Gaussian elimination for this example, the determinant (characteristic poly) is computed in 18 seconds using 18 megabytes, on a three-year old iMac. For larger densities, at some point the algorithm I mentioned above will be better.

Correction: Apologies for a mistake in the above: Gaussian elimination is effective only for densities < 1.01. However, the other method works well as far as I tied it, up to density 2.0, taking about 100 minutes and only about 68 meg of RAM.

Update.

The versions of Fermat available for download were not able to use the best determinant algorithms for matrices with > 5000 rows. I've changed that now. Google "Lewis Fermat"

I experimented some more with examples like this. I created a random 10000 row square matrix with density 1.86. Using the best algorithm over GF(2), which turns out to be just Gaussian elimination for this example, the determinant (characteristic poly) is computed in 18 seconds using 18 megabytes, on a three-year old iMac. For larger densities, at some point the algorithm I mentioned above will be better.

Correction: Apologies for a mistake in the above: Gaussian elimination is effective only for densities < 1.01. However, the other method works well as far as I tried it, up to density 2.0, taking about 100 minutes and only about 68 meg of RAM.

Update.

The versions of Fermat available for download were not able to use the best determinant algorithms for matrices with > 5000 rows. I've changed that now. Google "Lewis Fermat"

I experimented some more with examples like this. I created a random 10000 row square matrix with density 1.86. Using the best algorithm over GF(2), which turns out to be just Gaussian elimination for this example, the determinant (characteristic poly) is computed in 18 seconds using 18 megabytes, on a three-year old iMac. For larger densities, at some point the algorithm I mentioned above will be better.

Update.

The versions of Fermat available for download were not able to use the best determinant algorithms for matrices with > 5000 rows. I've changed that now. Google "Lewis Fermat"

I experimented some more with examples like this. I created a random 10000 row square matrix with density 1.86. Using the best algorithm over GF(2), which turns out to be just Gaussian elimination for this example, the determinant (characteristic poly) is computed in 18 seconds using 18 megabytes, on a three-year old iMac. For larger densities, at some point the algorithm I mentioned above will be better.

Correction: Apologies for a mistake in the above: Gaussian elimination is effective only for densities < 1.01. However, the other method works well as far as I tied it, up to density 2.0, taking about 100 minutes and only about 68 meg of RAM.