THE RESULTANT OF DEVELOPED SYSTEMS OF LAURENT POLYNOMIALS

Let R-Delta (f(1), ... ,f(n+1)) be the Delta-resultant (defined in the paper) of (n + 1)-tuple of Laurent polynomials. We provide an algorithm for computing R-Delta assuming that an n-tuple (f(2), ... , f(n+1)) is developed. We provide a relation between the product of f(1) over roots of f(2) = ... = f(n+1) = 0 in (C*)(n) and the product of f(2) over roots of f(1) = f(3) = ... = f(n+1) = 0 in (C*)(n) assuming that the n-tuple (f(1)f(2), f(3), ... , f(n+1)) is developed. If all n-tuples contained in (f(1), ... , f(n+1)) are developed we provide a signed version of Poisson formula for R-Delta. In our proofs we use topological arguments and topological version of the Parshin reciprocity laws.