Increment-and-fix tracking of solution paths of polynomial homotopies in PHCv2. New in this release are the multi-precision root refiners and the usage of QR and Least Squares in the correctors at the end of the paths. This library of continuation routines is organized in three layers: 0. The basic data structures 1. Increment-and-Fix continuation 2. Driver routines Hierarchical organization : conpar_io : 0.0. Continuation_Parameters_io |-- conpar : 0.0.0. Continuation_Parameters |-- cont_data : 0.0.1. Continuation_Data process_io : 0.1. Process_io continue : 1.0. Increment_and_Fix_Continuation |-- pathtrac : 1.0.1. Path_Trackers |-- dispred : 1.0.2. Dispatch_Predictors |-----|-- predictors : 1.0.3. Predictors |-- correctors : 1.0.4. Correctors |-- dirpaths : 1.0.5. Directions_of_Solution_Paths |-- vlprsalg : 1.0.5.0. vLpRs_Algorithm |-- vlrpstab : 1.0.5.0.0. vLpRs_Tables rootrefi : 1.1. Root_Refiners drivwind : 2.0. Driver_for_Winding_Numbers |-- drivpoco : 2.0.0. Drivers_for_Polynomial_Continuation |-- drivpadi : 2.0.0.0. Drivers_for_Path_Directions -------------------------------------------------------------------------------- file name : short description -------------------------------------------------------------------------------- continuation_data : data structures for parameters/variables continuation_parameters : management of tuning of parameters continuation_parameters_io : interactive setting of parameters process_io : output during path tracking -------------------------------------------------------------------------------- predictors : increment t, predict solutions dispatch_predictors : selection of predictor correctors : Newton's method as corrector vlprs_tables : data management for extrapolation vlprs_algorithm : extrapolation algorithm directions_of_solution_paths : routines for polyhedral end game path_trackers : path following routines increment_and_fix_continuation : increment-and-fix continuation drivers_for_poly_continuation : menu-driver for polynomial continuation ts_poco : calls the polynomial continuation driver -------------------------------------------------------------------------------- standard_root_refiners : refining over standard complex numbers multprec_root_refiners : refining up to arbitrary precision ts_rootrefi : calls the root refiners -------------------------------------------------------------------------------- scanners_for_continuation : scans the continuation parameters black_polynomial_continuations : black-box polynomial continuation mainpoco : poco as called by the main program bablpoco : calls black-box polynomial continuation valipoco : validation of computed path directions postpoco : stand-alone routine for polyhedral end game -------------------------------------------------------------------------------- An important feature is that much of the routines in this library are independent of how polynomials are represented. The basic data structures allow the management of data that is generated during the path-following. Tuning of parameters is menu-driven. Increment-and-Fix continuation is typical for polynomial continuation, since paths do not turn back, when working over the complex numbers. There is a rich variety of predictors available. Increment-and-fix continuation with a polyhedral end game for the computation of the directions of the solution paths. wc *adb counts 8844 lines of Ada code