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I'm working on finding solutions to a, not so very nice, system of equations. They are all polynomials of degree $4$ with $5$ parameters and all terms are of even order. I'll post the code on request, it's not that I don't want to post it, but it is rather lengthy and I thought I'd spare you the sight of it.

I did solve a similar system of equations last week using Reduce but then I had three equations and three unknowns. It took the computer some time to solve the system, like $30$ minutes or such. Though it seems that the same procedure is now failing to produce a solution. I use the following code:

Reduce[equation1==1/4 && equation2==1/4 && equation3==1/4 && equation4==1/4,{x1, x2, x3, x4}, Reals]

I know that the system to be solvable.

I understand that solving this system should take considerably more time. That's why I'm now wondering whether this problem could be parallelised in some way. I've read that reduce it isn't possible to parallelise Reduce, but perhaps there are some other means of parallelise the procedure? Or, well, is there means of making it run faster in general, of course?

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