So do you want "row echelon" form but are worried about cost of
zeroing elements above diagonal? Or do you want to preserve
information in upper part?
Well, my matrix actually comes from polynomial coefficients of several
polynomials. I want them to be of different degree eventually and want
to record how these different-degree polynomials came from the original
ones. Roughly speaking I want the "representation" of the new in terms
of the old as "small" as possible. Any tail-reduction would add a new
term to the representation, so I would like to avoid this.
You probably should look at LU decomposition ('LUDecomp' in
package LUDecomposition).
I've meanwhile found fractionFreeGauss! in MatrixLinearAlgebraFunctions.
That seems to do what I want. It even looks as if it divides out factors
that were multiplied in a previous step (the "exquo b" part) here.
https://github.com/fricas/fricas/blob/master/src/algebra/matfuns.spad#L623
https://github.com/fricas/fricas/blob/master/src/algebra/matfuns.spad#L628
The only thing I do not yet understand is what the ans thing does?
Why would I have to negate the last row in case of odd row swaps?
Ralf
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