A PRODUCT-DECOMPOSITION BOUND FOR BEZOUT NUMBERS

Most polynomial systems that arise in practice are not completely gene ral but have special structures. A common form is that each equation m ust be a sum of products, where each factor has an identifiable generi c type. A theorem is proven for such systems which offers a method for obtaining a tighter upper bound on the number of nonsingular solution s than is generally available. At the same time, this theorem provides an approach for solving such systems via polynomial continuation, whi ch results in less computational work. To illustrate the practical use fulness of these ideas, we show that a significant design-of-mechanism s problem can be solved with an order of magnitude less work than the published solution.