Hmmm. I think you need to supply more information.
The Gaussian elimination algorithm in my brain wants to know some things
before knowing how to proceed:
Say the matrix is m x n, and you want to stop at the kth row.
1) Suppose I'm clearing the leading entry in the first row. Do I clear the
*whole column* or just rows 1 through (m-k)?
(proper elimination would require you to work on the whole column, even
though you don't want to finish the matrix. Is this why partitions won't
work for you?)
2) Suppose the only leading entry of the first column is in some row p > k.
Do you skip it? If you perform the elimination, do you shift row p into
the first k rows?
3) Say you throw away rows k+1 to m. Do you discard any of the columns?
3) Depending on where you go with questions like this, I wonder if you
really want elimination. For example, suppose the data are not random; you
want, say, k solutions for sure, and you have some definition for those k
solutions. Do you need to solve explicitly? Can you begin with two
vectors and append new rows until you have *k* solutions?
It seems to me that there are many ways to do this; hard to see how a
built-in function could be defined.
I'm making that up, of course.
{Don't hesitate to let me know if my questions are misplaced. Or if you
want to talk further}.
On Tuesday, June 12, 2012 2:59:10 PM UTC-7, Thomas Klotz wrote:
>
> I was wondering if anyone knows a way for sage to perform gaussian
> elimination on a matrix, but only up to the nth row and will stop at that
> point.
>
> I realize that I could just split up the matrix and perform the algorithm
> on that part of it, and just re-join it to the rest of the matrix, but I
> was wondering if there is some built-in function for this.
>
> Thanks,
> Tom
>
>
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