  Let $R_\Delta (f_1,\ldots,f_{n+1})$ be the {\it $\Delta$-resultant} (see
below) of $(n+1)$-tuple of Laurent polynomials. We provide an algorithm for
computing $R_\Delta$ assuming that an $n$-tuple $(f_2,\dots,f_{n+1})$ is {\it
developed} (see sec.6). We provide a relation between the product of $f_1$ over
roots of $f_2=\dots=f_{n+1}=0$ in $(\mathbb C^*)^n$ and the product of $f_2$
over roots of $f_1=f_3=\dots=f_{n+1}=0$ in $(\mathbb C^*)^n$ assuming that the
$n$-tuple $(f_1f_2,f_3,\ldots,f_{n+1})$ is developed. If all $n$-tuples
contained in $(f_1,\dots,f_{n+1})$ are developed we provide a signed version of
Poisson formula for $R_\Delta$. In our proofs we use a topological arguments
and topological version of the Parshin reciprocity laws.
