Abstract: Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.

Abstract: Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.

Abstract: Improvements to optimal interval operators are developed for interval expression evaluation using arithmetic and real power operators applied to complex and hypercomplex number systems. A method for determining efficacy of numeric precision, incorporating minor changes to interval operators, provides detection of insufficient numeric evaluation precision.

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.

Abstract: Based on the root-product polynomial form, this method compresses essential information of a polynomial by transforming polynomials into a form which eliminates cancellation error, when evaluating polynomials, of one unknown, for real, complex, and quaternion, which are implemented with floating point numbers. Additional filtering methods simplify evaluation, including the elimination of extremely small and large root factors, which can cause out-of-range errors. The usual setup problem for root-product forms, that of needing potentially unlimited root precision and floating point range, is largely eliminated for real polynomials, and greatly mitigated for complex and quaternion, and other hypercomplex polynomials.

Abstract: Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.

Abstract: Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations

Abstract: Improvements to optimal interval operators are developed for interval expression evaluation using arithmetic and real power operators applied to complex and hypercomplex number systems. A method for determining efficacy of numeric precision, incorporating minor changes to interval operators, provides detection of insufficient numeric evaluation precision.

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations

Abstract: A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.

Abstract: Improvements to optimal interval operators are developed for interval expression evaluation using arithmetic and real power operators applied to complex and hypercomplex number systems. A method for determining efficacy of numeric precision, incorporating minor changes to interval operators, provides detection of insufficient numeric evaluation precision.