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2021-01-07 17:40:14 +0200 asked a question How to express boolean polynomials by special form

If I have boolean polynomials like

x_1 * x_2 + x_1*x_3* x_5 + x_3 + x_7*x_2

then given a variable x_1, how can I represent it as

x_1 * (x_2 + x_3*x_5) + (x_3 + x_7*x_2)

using Sage?

In general, I want to find a way to represent a form of a * x_1 + c, where a is the linear combination of multiples of x_1 and c is the rest polynomial.