Exploitation of permutation symmetry to construct symmetric homotopies in PHCv2. If the polynomial system is invariant under permutations of its unknowns, then it suffices to compute the generators of the solution set. This is accomplished by the construction of a homotopy that has the same symmetric structure as the polynomial system. This library is organized in four parts : 1) permutations, symmetry groups and equivariant systems 2) symmetric linear-product start systems with drivers 3) symmetric integer and floating-point lifting 4) main driver, as called by phc -------------------------------------------------------------------------------- file name : short description -------------------------------------------------------------------------------- permutations : data abstraction for permutations permute_operations : permutations acting on vectors/polynomials symmetry_group : list of permutations with some operations symmetry_group_io : input/output of lists of permutations symbolic_symmetry_group_io : uses symbol table for input/output equivariant_polynomial_systems : (G,V,W)-symmetric polynomial systems drivers_for_symmetric_group_io : user-friendly input of symmetry groups ts_equpol : test (G,V,W)-symmetric polynomial systems -------------------------------------------------------------------------------- templates : auxiliary for symmetric start systems symmetric_set_structure : construct (G,V,W)-symmetric set structure linear_symmetric_reduction : reducing number of linear systems to solve orbits_of_solutions : extracting generators from solution list orbits_of_solutions_io : writing information about orbits drivers_for_orbits_of_solutions : report on orbit computations driver_for_symmetric_set_structure : driver for symmetric start systems ts_drivsss : calls the driver -------------------------------------------------------------------------------- permutations_of_faces : permute faces of polytopes faces_of_symmetric_polytopes : generating faces of polytopes generating_mixed_cells : extract generators in mixed subdivision symmetric_lifting_functions : lift orbits with same lifting symmetric_randomize : symmetric random choice of coefficients symmetric_polyhedral_continuation : polyhedral continuation w.r.t. symmetry symmetric_bkk_bound_solvers : black-box computations drivers_for_symmetric_lifting : menu-driver for symmetric lifting ------------------------------------------------------------------------------- mainsmvc : mixed-volume-computation, as called by phc -------------------------------------------------------------------------------- wc *adb counts 5780 lines of Ada code