I am trying to use Maple 18 to do some computations with matrices over a ring of polynomials in one variable over the integers $\mathbb{Z}[x]$, or the corresponding field of fractions $\mathbb{Q}(x)$.

The matrices in question are of dimension approximately 5000 and are sparse. The algorithm requires at least as many matrix multiplications as the dimension of the space.

Doing some small examples, of dimension 674, with a laptop (i7-3520 M CPU @2.9GHz with 8GB of Ram) gave the following disappointing result:

time(LinearAlgebra[MatrixMatrixMultiply](A,A);

34.694

When a colleague with access to a Mathematica license performed an identical calculation using sparse matrices in Mathematica, we found that Mathematica performed the calcuation in fractions of a second.

In small dimensional examples, constructing the matrices over the field of fractions as sparse in Maple 18 resulted in a four fold decrease in the already disappointing performance of the LinearAlgebra package in Maple 18.

Is there any way to improve the computational performance of Maple 18 for symbolic linear algebra? Alternatively, is the performance of Maple 2015 for symbolic linear algebra noticably better than Maple 18?

Thanks in advance.

Dave