I have a set of polynomials which are generated from a truth table, an example is given in the following. Notice that a monomial is generated form each row, and the rule is that for each $0$ in the row you multiply an $x$ in the monomial and for each $1$, you multiply it's positional variable i.e. the header of that column.
| u | v | w | Monomial |
|---|---|---|---|
| 0 | 0 | 0 | $x^3$ |
| 0 | 0 | 1 | $x^2w$ |
| 0 | 1 | 0 | $x^2v$ |
| 0 | 1 | 1 | $xvw$ |
| 1 | 0 | 0 | $x^2u$ |
| 1 | 0 | 1 | $xuw$ |
| 1 | 1 | 0 | $xuv$ |
| 1 | 1 | 1 | $uvw$ |
$F(x,u,v,w) =x^3 + x^2w + x^2v + xvw + x^2u +xuw+ xuv + uvw $
My question is that is there a more copact representation for such polynomials ?
This particular function can be written as $$F(x,u,v,w)=(x+u)(x+v)(x+w)$$ This should work analogue in similar cases.