What i had in mind is something like this:

right now you can compute the primary decomposition of an ideal using

I.primary_decomposition(algorithm='sy') (default) or
I.primary_decomposition(algorithm='gtz')

what i propose is to keep this, and add some option like

I.primary_decomposition(algorithm='parallel')

that triggers two independent processes that compute the two previous
options. And once the first one gives an answer, the other is killed.

This could raise some problems in doctests, since the output could
differ if the different algorithsm give different answers (but all of
them correct), and it is posible that which is the fastest algorithm
deppends on the machine that runs them.

Even so, i think that in some cases the potential speed gain is a good
reason to go this way.

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