python - Constrained non-linear optimization - overdetermined system of polynomial equations -


i have system of 21 polynomial equations in total of 12 unknowns a, ..., l. each equation has general form v1*abc + v2*abd + ... + v64*jkl = x, v1, ..., v64 each either 0 or 1, i.e., each equation contains on left hand side sum of products of 3 different unknowns.

there set of constrains: a + b + c + d = 1, e + f + g + h = 1, i + j + k + l = 1. sum of xs (right hand sides) equal 1.

i have input vector of xs. there solver provide me values of a, ..., l yield vector of x's close possible original xs while adhering constrains ? i'm looking python implementation.

i looked in scipy.optimize i'm not able establish method preferable problem.


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