Mixed-volume computation & polyhedral continuation by dynamic lifting in PHCv2. The aim of dynamic lifting is to control the heights of the lifting values, to obtain a stable evaluation of the polyhedral homotopy. When all supports are equal, then the mixed volume is reduced to an ordinary volume, which is computed by a regular triangulation. 1. Dynamic construction of regular triangulations : 2. The Cayley trick 3. Dynamic construction of mixed subdivision 4. The drivers and black-box computation -------------------------------------------------------------------------------- file name : short description -------------------------------------------------------------------------------- simplices : simplices of integer polytopes simplices_io : input/output of simplices triangulations : triangulations of integer polytopes triangulations_io : input/output of triangulations global_dynamic_triangulation : global aspects of dynamic lifting dynamic_lifting_functions : dynamic lifting functions dynamic_triangulations : construction of placing triangulation ts_dyntri : test on the construction of a triangulation -------------------------------------------------------------------------------- cayley_embedding : embeds tuple in one support cayley_trick : computing mixed subdivisions minkowski_polynomials : volume polynomials driver_for_minkowski_polynomials : driver to the volume polynomials ts_drivmink : calls the driver for volume polynomials -------------------------------------------------------------------------------- common_faces_of_polytope : computation of neighboring faces enumerate_faces_of_polytope : extract faces of a triangulation face_structures : management of faces of triangulations frequency_graph : computes occurencies of points in supports initial_mixed_cell : finds an initial mixed cell flatten_mixed_subdivisions : flattening of mixed subdivisions unfolding_subdivisions : re-lifting flattened parts of subdivisions triangulations_and_subdivisions : convert triangulations <> subdivisions dynamic_mixed_subdivisions : dynamic lifting in the mixed case dynamic_polyhedral_continuation : incremental polyhedral continuation -------------------------------------------------------------------------------- drivers_for_dynamic_lifting : menu-driver for dynamic lifting ts_drivdynl : calls the menu-driver black_mixed_volume_computations : black-box polyhedral methods babldmvc : calls the black-box mixed-volume computation -------------------------------------------------------------------------------- The Cayley trick is an efficient way to construct all cells in a mixed subdivision with the corresponding Minkowksi polynomial. wc *adb counts 7493 lines of Ada code