Implicit polynomials have proved themselves as having excellent representation power for complicated objects, and there is growing use of them in computer vision, graphics, and CAD. A must for every system that tries to recognize objects based on their representation by implicit polynomials are invariants, which are quantities assigned to polynomials that do not change under coordinate transformations. In the recognition system developed at the Laboratory for Engineering Man-Machine Studies in Brown University (LEMS), it became necessary to use invariants which are explicit and simple functions of the polynomial coefficients. A method to find such invariants is described and the new invariants presented. This work addresses only the problem of finding the invariants; their stability is studied in another paper. >