Mixed-volume computation and polyhedral homotopies by implicit lifting in PHCv2. This directory contains software for the computation of mixed volumes, according to the recursive formula Bershtein used in his proof. Also the homotopy method of Bernshtein has been implemented. -------------------------------------------------------------------------------- file name : short description -------------------------------------------------------------------------------- power_lists : manipulating support sets of polynomials ts_powlis : test the power lists vertices : extracting vertices from supports drivers_for_vertex_points : drivers to the vertex extraction ts_drivpts : calls the driver to vertices -------------------------------------------------------------------------------- transformations : unimodular transformations on monomials transformations_io : input/output of unimodular transformations integer_vectors_utilities : utilities to manipulate integer vectors transforming_solutions : transformations on solution lists transforming_integer_vector_lists : transformations on lists of integer vectors transforming_laurent_systems : transformations on Laurent systems -------------------------------------------------------------------------------- trees_of_vectors : data structure to hold outer normals trees_of_vectors_io : input/output of trees of vectors lists_of_vectors_utilities : utilities to manipulate lists of vectors arrays_of_lists_utilities : utilities to manipulate arrays of lists volumes : compute volumes and mixed volumes ts_impvol : test on mixed-volume computation -------------------------------------------------------------------------------- binomial_system_solvers : solvers of systems of two monomials fewnomial_system_solvers : solvers of fewnomial systems durand_kerner : solve polynomial equation in one variable ts_binsolve : test binomial system solvers ts_fewnom : test fewnomial system solvers ts_durker : test polynomial equation solver mixed_homotopy_continuation : polyhedral continuation set_structures_and_volumes : combines product and polyhedral methods generic_position : test on genericity of system driver_for_polyhedral_continuation : set-up for continuation drivers_for_implicit_lifting : menu-driver for implicit lifting ts_drivimpl : calls the menu-driver for implicit lifting -------------------------------------------------------------------------------- This is the first implementation of polyhedral homotopy continuation. Everytime PHC is reorganized, I go through a deep pain struggling through packages as Volumes and Mixed_Homotopy_Continuation. There are far too many dynamic structures and pointers to make it efficient. About half of this library is needed in the other polyhedral methods. Vertices and fewnomial system solvers are fundamental and deserve a thorough reorganization. wc *adb counts 6658 lines of Ada code