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These are replies submitted by Dave09


Thank you Roman for your response.

I tried doing some work with some sparse 4000 by 4000 matrices whose non-zero entries are either 1 or $x$, where $x$ is an indeterminate over the integers. In this case the output should also have been matrices with small degree monomial entries. After more than one week with no result, I terminated the calculation.

Maple currently seems to be far too slow for any real sized problem that involves algebraic manipulation of matrices with non-float, ie in this case rational or polynomial, entries.


Any chance that this issue can be addressed?



@Carl Love 

Thank you Carl for your response to my query.

In the 674 dimensional example, the maximal degree for the numerator and denominator entries p(x)/q(x) in the matrices over $Q(x)$ is 5. The maximum density of non-zero entries is approximately 0.8%.

If I change the basis so that the matrices are over Z[x], the maximum degree becomes 1.  Actually, the original problem involves either starting with a collection rational matrices over Q(x), which act on a vector space V over Q(x), and doing a lot of matrix multiplications and additions in order to construct a basis over the integers Z[x] for an integral subspace of V, or vice versa.

Here is the result of the 34 second calculation, run on a slightly older computer this time

memory used=4.58GiB, alloc change=-236.99MiB, cpu time=46.82s, real time=47.56s, gc time=22.09s

This time, I ran it on a slightly older and slower i7-2620 M CPU @2.70 GHZ, which probably accounts for the extra time.

The structure of the matrices varies a lot, depending on whether they are over $Q(x)$ or $Z[x]$.  However, in the multiplication computed above, all non-zero entries happen to be close to the diagonal.



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