Helloooooooo !!
> Cartesian product is a generic construction, so it should be clear that it
> is much slower than the super-optimized routines for prime finite fields.
It probably will never be as fast as those fields, but there is a waste of
time anyway.
> Do you need element-wise multiplication? If you are only interested in the
> Abelian group structure then there is AbelianGroup([2,3]). Maybe you want
> IntegerModRing(6).
Most of the code in sage.combinat.designs.database does.
For instance :
sage: %time _=designs.orthogonal_array(16,208)
CPU times: user 6.82 s, sys: 64 ms, total: 6.88 s
Wall time: 6.79 s
sage: %prun -s cumulative _=designs.orthogonal_array(16,208)
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.008 0.008 11.477 11.477 <string>:1(<module>)
1 0.000 0.000 11.469 11.469
orthogonal_arrays.py:617(orthogonal_array)
1 0.000 0.000 11.455 11.455 database.py:2602(OA_16_208)
1 0.008 0.008 11.454 11.454
database.py:3266(_helper_function_when_n_is_prime_times_power_of_2)
1 1.068 1.068 11.268 11.268
orthogonal_arrays.py:1181(OA_from_quasi_difference_matrix)
656760 0.512 0.000 10.246 0.000
additive_magmas.py:392(__add__)
656760 1.181 0.000 8.105 0.000 additive_magmas.py:500(_add_)
1313520 2.468 0.000 4.880 0.000
sets_cat.py:1944(cartesian_factors)
659880 1.219 0.000 1.765 0.000
cartesian_product.py:179(_cartesian_product_of_elements)
656760 1.512 0.000 1.512 0.000
{sage.structure.sage_object.have_same_parent}
3940560 1.051 0.000 1.441 0.000 sets_cat.py:1965(<genexpr>)
Nathann
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