Computing multidimensional residues
Eduardo H. Cattani, Alicia Dickenstein, Bernd Sturmfels · Birkhäuser Basel eBooks · 1996
Given n polynomials in n variables with a finite number of complex roots, for any of their roots there is a local residue operator assigning a complex number to any polynomial. This is an algebraic, but generally not rational, function of the coefficients. On the other hand, the global residue, which is defined as the sum of the local residues over all roots, has invariance properties which guarantee its rational dependence on the coefficients [9], [27]. In this paper we present symbolic algorithms for evaluating that rational function.