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I am looking for an algorithm which presents a given polynomial in many variables (given as a sum of monomials) in a form with the smallest number of multiplications of variables. For example $x_1^2x_3+x_1x_2+x_1x_3x_4 \to x_1(x_2+x_3(x_1+x_4)).$

Of course, one could consider some "dumb" approach testing all possibilities, but I am curious if there is a faster one. I need to do it for over 100,000 of polynomials in over 40 variables each.

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    How big do the degrees get?2012-08-04
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    degrees of polynomials are around 202012-08-04

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