A general CDC formulation for specializing the cell exclusion algorithms of finding all zeros of vector functions

Let ℱ be the family of analytic compositions of analytic mappings and their absolute values. A novel inequality on the range of the mappings in ℱ is proved, which is then used to yield a universal CDC (cell discarded condition) formulation for the system of equations F(x) = 0 with F in ℱ. With this CDC formulation, the cell exclusion algorithm developed in [1] is generalized. It is shown that the algorithm generalized can not only be applied assuredly to locate all the zeros of any functions F in ℱ, but it can do so much more efficiently and conveniently than the original algorithms as well.