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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Symmetry/READ_ME, Revision 1.1

1.1     ! maekawa     1: Exploitation of permutation symmetry to construct symmetric homotopies in PHCv2.
        !             2:
        !             3: If the polynomial system is invariant under permutations of its unknowns,
        !             4: then it suffices to compute the generators of the solution set.
        !             5: This is accomplished by the construction of a homotopy that has the
        !             6: same symmetric structure as the polynomial system.
        !             7:
        !             8: This library is organized in four parts :
        !             9: 1) permutations, symmetry groups and equivariant systems
        !            10: 2) symmetric linear-product start systems with drivers
        !            11: 3) symmetric integer and floating-point lifting
        !            12: 4) main driver, as called by phc
        !            13:
        !            14: --------------------------------------------------------------------------------
        !            15: file name                          : short description
        !            16: --------------------------------------------------------------------------------
        !            17: permutations                       : data abstraction for permutations
        !            18: permute_operations                 : permutations acting on vectors/polynomials
        !            19: symmetry_group                     : list of permutations with some operations
        !            20: symmetry_group_io                  : input/output of lists of permutations
        !            21: symbolic_symmetry_group_io         : uses symbol table for input/output
        !            22: equivariant_polynomial_systems     : (G,V,W)-symmetric polynomial systems
        !            23: drivers_for_symmetric_group_io     : user-friendly input of symmetry groups
        !            24: ts_equpol                          : test (G,V,W)-symmetric polynomial systems
        !            25: --------------------------------------------------------------------------------
        !            26: templates                          : auxiliary for symmetric start systems
        !            27: symmetric_set_structure            : construct (G,V,W)-symmetric set structure
        !            28: linear_symmetric_reduction         : reducing number of linear systems to solve
        !            29: orbits_of_solutions                : extracting generators from solution list
        !            30: orbits_of_solutions_io             : writing information about orbits
        !            31: drivers_for_orbits_of_solutions    : report on orbit computations
        !            32: driver_for_symmetric_set_structure : driver for symmetric start systems
        !            33: ts_drivsss                         : calls the driver
        !            34: --------------------------------------------------------------------------------
        !            35: permutations_of_faces              : permute faces of polytopes
        !            36: faces_of_symmetric_polytopes       : generating faces of polytopes
        !            37: generating_mixed_cells             : extract generators in mixed subdivision
        !            38: symmetric_lifting_functions        : lift orbits with same lifting
        !            39: symmetric_randomize                : symmetric random choice of coefficients
        !            40: symmetric_polyhedral_continuation  : polyhedral continuation w.r.t. symmetry
        !            41: symmetric_bkk_bound_solvers        : black-box computations
        !            42: drivers_for_symmetric_lifting      : menu-driver for symmetric lifting
        !            43: -------------------------------------------------------------------------------
        !            44: mainsmvc                           : mixed-volume-computation, as called by phc
        !            45: --------------------------------------------------------------------------------
        !            46:
        !            47: wc *adb counts 5780 lines of Ada code