Exploitation of permutation symmetry for symmetric homotopies in PHCv2.4.85

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) the main procedures, as called by phc -m

Run "gprbuild symmetry.gpr" to make all test programs.
On windows, type "gprbuild symmetry.gpr -Xos=windows"
at the PowerShell prompt.
The "gprclean symmetry.gpr" removes all files created by gprbuild.

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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
ts_group                           : test on group operations
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
-------------------------------------------------------------------------------
mixed_volume_calculator            : defines phc -m
-------------------------------------------------------------------------------
