[ruby-core:29790] [Feature #2772] Matrix: Calculating determinant using Bareiss algorithm [patch]

Issue #2772 has been updated by Marc-Andre Lafortune.

File newdet.patch added

I have worked on the determinant (and the rank) methods for Matrix.

Unless I hear arguments against it, the methods #determinant_e and #rank_e will be deprecated. I don't know where the algorithm comes from, but it checks to see if the elimination didn't succeed, i.e. the float calculation introduced some small rounding error and that error remains instead of 0 (a sort of noise). In that case, the noise is then used as a pivot, so many values get divided by a small noisy value that should have been 0. Seems like a bad idea to me, and my informal tests seem to confirm that this gives erroneous results more often than the straight gaussian elimination (and much more than the bareiss-gauss elimination).

I've attached the patch I have so far if anyone is interested.

Note: this patch fixes a bug with #rank causing many rectangular matrices to not have the right rank (e.g Matrix[[0,1],[0,1],[0,1]].rank returned 2, now returns 1)

Also, Matrix#singular? and #regular? will raise an error for non-square matrices.
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