Homotopies, scaling and reduction in PHCv2.4.87

The Creators in the package Homotopy allow more accessibility constants for
the Cheater's homotopy.  A multiprecision version of the homotopy package
was needed for the new release 2.1.  A multiprecision version of the
scaling routines is under development.

This library is organized in three parts:
1) Homotopy with homogenization 
2) Scaling and reduction of polynomial systems.
3) Encapsulation of convolution circuits.

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

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file name                          : short description
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standard_embed_polynomials         : embed standard polynomial in larger space
standard_embed_laurentials         : embed standard Laurent polynomial
dobldobl_embed_polynomials         : embed dobldobl polynomial in larger space
dobldobl_embed_laurentials         : embed dobldobl Laurent polynomial
quaddobl_embed_polynomials         : embed quaddobl polynomial in larger space
quaddobl_embed_laurentials         : embed quaddobl Laurent polynomial
multprec_embed_polynomials         : embed multprec polynomial in larger space
homogenization                     : making polynomials homogeneous
projective_transformations         : transform polynomials and solutions
affine_transformations             : transform systems into affine coordinates
standard_homotopy                  : homotopy for standard polynomial systems
standard_laurent_homotopy          : homotopy for standard Laurent systems
dobldobl_homotopy                  : homotopy for systems of double doubles
dobldobl_laurent_homotopy          : homotopy for dobldobl Laurent systems
tripdobl_homotopy                  : homotopy for systems of triple doubles
quaddobl_homotopy                  : homotopy for systems of quad doubles
quaddobl_laurent_homotopy          : homotopy for quaddobl Laurent systems
ts_qdhom                           : compares eval & diff for dd & qd
pentdobl_homotopy                  : homotopy for systems of penta doubles
octodobl_homotopy                  : homotopy for systems of octo doubles
decadobl_homotopy                  : homotopy for systems of deca doubles
hexadobl_homotopy                  : homotopy for systems of hexa doubles
test_standard_laur_homotopy        : tests standard Laurent homotopy
test_standard_poly_homotopy        : tests standard polynomial homotopy
test_dobldobl_poly_homotopy        : tests dobldobl polynomial homotopy
test_tripdobl_poly_homotopy        : tests tripdobl polynomial homotopy
test_quaddobl_poly_homotopy        : tests quaddobl polynomial homotopy
test_pentdobl_poly_homotopy        : tests pentdobl polynomial homotopy
test_octodobl_poly_homotopy        : tests octodobl polynomial homotopy
test_decadobl_poly_homotopy        : tests decadobl polynomial homotopy
test_hexadobl_poly_homotopy        : tests hexadobl polynomial homotopy
ts_homotopy                        : runs tests on homotopies
multprec_homotopy                  : homotopy for multiprecision numbers
drivers_for_homotopy_creation      : menu-driven homotopy construction
standard_stable_homotopies         : for solutions with zero components
dobldobl_stable_homotopies         : version for double doubles
quaddobl_stable_homotopies         : version for quad doubles
standard_coefficient_homotopy      : coefficient-parameter homotopy
dobldobl_coefficient_homotopy      : double double coeff-parameter homotopy
tripdobl_coefficient_homotopy      : triple double coeff-parameter homotopy
quaddobl_coefficient_homotopy      : quad double coeff-parameter homotopy
pentdobl_coefficient_homotopy      : penta double coeff-parameter homotopy
octodobl_coefficient_homotopy      : octo double coeff-parameter homotopy
decadobl_coefficient_homotopy      : deca double coeff-parameter homotopy
hexadobl_coefficient_homotopy      : hexa double coeff-parameter homotopy
test_standard_coeff_homotopy       : tests standard coefficient homotopies
test_dobldobl_coeff_homotopy       : tests dobldobl coefficient homotopies
test_tripdobl_coeff_homotopy       : tests tripdobl coefficient homotopies
test_quaddobl_coeff_homotopy       : tests quaddobl coefficient homotopies
test_pentdobl_coeff_homotopy       : tests pentdobl coefficient homotopies
test_octodobl_coeff_homotopy       : tests octodobl coefficient homotopies
test_decadobl_coeff_homotopy       : tests decadobl coefficient homotopies
test_hexadobl_coeff_homotopy       : tests hexadobl coefficient homotopies
ts_evalhomt                        : main test on coefficient homotopies
hyperplane_solution_scaling        : scale a solution and a hyperplane
ts_scalplane                       : test on scaling last hyperplane
multi_projective_transformations   : transform to m-homogeneous coordinates
ts_multproj                        : test on multi-homogenization
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standard_scaling                   : scaling standard systems and solutions
dobldobl_scaling                   : scaling systems in double double precision
quaddobl_scaling                   : scaling systems in quad double precision
multprec_scaling                   : scaling multprec systems
ts_scal                            : simple test program
scaling_methods                    : equation and variable scaling methods
ts_mainscal                        : calls main scaling procedures
main_scaling                       : defines phc -s
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reduction_of_polynomials           : S-polynomials and R-polynomials
standard_linear_reduction          : utilities for double precision reduction
dobldobl_linear_reduction          : utilities for dobldobl precision reduction
quaddobl_linear_reduction          : utilities for quaddobl precision reduction
reduction_of_polynomial_systems    : linear and nonlinear reduction
reduction_of_nonsquare_systems     : transform overconstrained into square
main_reduction                     : main procedures to reduce systems
ts_reduce                          : calls a main reduction procedure
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standard_linear_poly_solvers       : solve linear polynomial systems
ts_linsol                          : test on the linear poly solvers
polynomial_drops                   : drop a variable from polynomials
ts_poldrop                         : interactive test on dropping
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random_conditioned_homotopies      : homotopy with middle conditioned system
varbprec_homotopy                  : variable precision homotopy
ts_vmphom                          : test variable precision homotopies
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artificial_parameter_homotopy_io   : prompts for artificial-parameter htpy
ts_homcnv                          : test convolution circuits for homotopies
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wrapped_solution_vectors           : xt = x+t <-> solution representations
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