Determinant tries to access the record entry "matrix" of a sparse matrix over an internal ring about homalg_project HOT 4 CLOSED

Comment by mohamed-barakat
Sunday Jul 27, 2014 at 11:38 GMT

Yes, this is right. For this I would like to have an REF (used by our RREF) which gradually computes the determinant of the transformation matrix. But back to your problem: Maybe you only need to decide if the determinant is zero or not, for this you can simply compute the rank ;)

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Comment by martin-leuner
Sunday Jul 27, 2014 at 12:19 GMT

So the problem is that Gauss's sparse matrices are missing an REF method? I'll look into this a bit.
I'm trying to recognize root lattices via their gram matrix, for this job the rank is not sufficient. :)

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Comment by mohamed-barakat
Sunday Jul 27, 2014 at 13:33 GMT

I now see that Simon implemented an REF (EchelonMat). So what you can do is to gradually compute the determinant of the transformation matrix in EchelonMatTransformation (each step contributes either nothing (i.e., 1), a sign (i.e., -1) or a unit). Then you can implement a method multiplying this determinant with the product of the diagonal elements of the result of EchelonMat.

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Comment by mohamed-barakat
Sunday Jul 27, 2014 at 13:34 GMT

And yes, for this you really need a determinant :)

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