  Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system
of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$ variables,
just in the same way as determinant does for a system of linear equations.
Because of this, resultants are important special functions of upcoming
non-linear physics and begin to play a role in various topics related to string
theory. Unfortunately, there is a lack of convenient formulas for resultants
when the number of variables is large. To cure this problem, we generalize the
well-known identity Log Det = Trace Log from determinants to resultants. The
generalized identity allows to obtain explicit polynomial formulas for
multidimensional resultants: for any number of variables, resultant is given by
a Schur polynomial. We also give several integral representations for
resultants, as well as a sum-over-paths representation.
