On Wed, May 26, 2010 at 5:32 PM, VictorMiller <[email protected]> wrote:
> It's possible. Probably a better test would be to write a loop in
> Magma which would modify the matrix in each iteration (say by adding
> something to one location).
> This came about because one of my colleagues had a large search
> program written in Magma in which almost all the computation was done
> in calls to IsConsistent in the inner loop. Each call was with a
> different matrix A. I rewrote the program in Sage, and found, much to
> my chagrin, that it was about a factor of 30 slower. So in that
> program no caching could have helped.
>
> Victor
Remark: For your problem you can reduce checking inclusion to doing a
single matrix vector multiplication, and looking at the last entry of
the product.
sage: A = Matrix([[1,0,1,0],[1,1,0,1],[0,1,0,1],[1,1,0,0],[1,0,0,0]])
sage: b=vector([13,1,7,5,14])
sage: timeit('A.solve_right(b,check=False)')
125 loops, best of 3: 1.72 ms per loop
sage: At = A.transpose(); At
[1 1 0 1 1]
[0 1 1 1 0]
[1 0 0 0 0]
[0 1 1 0 0]
sage: E = At.echelon_form(); E
[ 1 0 0 0 0]
[ 0 1 0 0 1]
[ 0 0 1 0 -1]
[ 0 0 0 1 0]
sage: v = vector([13,1,7,5])
sage: v*E
(13, 1, 7, 5, -6)
sage: timeit('v*E')
625 loops, best of 3: 47 µs per loop
Rewriting your code to use that trick would speed it up by a factor of
36 in Sage (at least on my laptop). Maybe Magma uses an algorithm
like that internally?
William
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