ADDING HEURISTIC KNOWLEDGE TO COMPUTER ALGEBRA SYSTEMS

PRESENT COMPUTER ALGEBRA SYSTEMS SIGNIFICANTLY REDUCE THE TIME SPENT SOLVING MATHEMATICAL PROBLEMS FROM THAT REQUIRED IN THE PREVIOUS PENCIL-AND-PAPER OR NUMERICAL APPROXIMATION TECHNIQUES. HOWEVER, THESE SYSTEMS ARE STILL UNNECESSARILY TEDIOUS AND TIME-CONSUMING FOR THE SOLUTION OF MANY IMPORTANT PROBLEMS. IN PHASE I OF THIS PROJECT, SYSTEMS COGNITION WILL DEMONSTRATE THE FEASIBILITY OF APPLYING NEW ARTIFICAL INTELLIGENCE TECHNOLOGY TO THE PROBLEMS OF COMPLEXEXPRESSION SIMPLIFICATION AND AUTOMATIC MATHEMATICAL PROBLEMSOLVING IN CASES WHERE COMPLETE DETERMINISTIC ALGORITHMS DO NOT EXIST. THIS WILL BE ACCOMPLISHED BY INTEGRATING TWO OF THE COMPANY'S PRODUCTS: SMP, A STATE-OF-THE-ART COMPUTER ALGEBRA SYSTEM ORIGINALLY DEVELOPED AT THE CALIFORNIA INSTITUTE OF TECHNOLOGY, AND FOCUS, A STATE-OF-THE-ART A.I. KNOWLEDGE REPRESENTATION AND INFERENCING SYSTEM DEVELOPED AND OWNED BY THE COMPANY. THE INTEGRATION OF DIVERSE TYPES OF KNOWLEDGE SUPPORTED BY THE FOCUS ARCHITECTURE IS EXACTLY WHAT IS NEEDED TO SENSITIVELY CONTROL THE SEARCH FOR THE DESIRED SIMPLIFIED FORMS OF COMPLEX MATHEMATIC EXPRESSIONS.