Find all combinations of coefficients for an equality

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I have a mathematical problem, and I don't know how to solve it in python.

I have the following equality: P = ∑αi Pi

I know P and all Pi and I am looking for all αi combinations for the equality. Besides for all αi, 0 <= αi <= 1

If you can help, it would be very great! Thanks a lot.

I tried a brute force approach, but with a step of 0.05 for each coefficients, I am not very convinced by this method even if I increase the sampling rate and increase the tolerance of the result (I try to found the solution that is between [P-epsilon;P+epsilon] I am sure that some optimisation algorithms can suit my needs better. I use python as programming language.

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