A Numerical Irreducible Decomposition with PHCv2.3.21

This directory is entirely new in release 2.1 and contains homotopies to
compute witness points on all positive dimensional solution components.
There are two approaches:
  1) using a sequence of homotopies starting at the top dimension;
  2) with diagonal homotopies we incrementally compute witness point sets.
The extrinsic/intrinsic approach to implement diagonal homotopies is
under development and is improved in release 2.2.

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file name                        : short description
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irreducible_decompositions       : data representation + primitives
irreducible_decompositions_io    : input-output facilities
filtered_points                  : structure to collect filtering data
witness_generate_and_classify    : creators of irreducible decomposition
ts_irdeco                        : test on witness generate and classify
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standard_affine_planes           : intrinsic <-> extrinsic affine planes
standard_affine_solutions        : intrinsic <-> extrinsic solutions
multihomogeneous_solutions       : representing multi-homogeneous solutions
extrinsic_diagonal_homotopies    : extrinsic version of diagonal homotopies 
extrinsic_diagonal_homotopies_io : tools to double symbol table
extrinsic_diagonal_solvers       : drivers for extrinsic diagonal homotopies
p_intrinsic_diagonal_continuation: premature intrinsic diagonal continuation
p_intrinsic_diagonal_homotopies  : premature intrinsic diagonal homotopies
p_intrinsic_diagonal_solvers     : solving with intrinsic diagonal homotopies
ts_diahom                        : test on diagonal homotopies
diagonal_homotopy_continuation   : diagonal homotopies to intersect witsets
driver_to_intersect_varieties    : driver to intrinsic diagonal homotopies
ts_intdia                        : test to intersect varieties intrinsically
jumpstart_diagonal_homotopies    : jumpstart to intersect varieties
ts_jmpdia                        : jumpstarting diagonal homotopies
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maindeco                         : dispatcher calls decomposition (all dim)
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ts_dimred                          : test on dimension determination
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the remaining part is no longer actively maintained :
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standard_membership_tests          : membership for point in component or not
standard_breakup_components        : component interpolation in standard arith
multprec_membership_tests          : membership for point in component or not
multprec_breakup_components        : component interpolation in multprec arith
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drivers_to_breakup_components      : drivers to construct interpolators
ts_breakup                         : test on breaking up components
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standard_irreducible_decomp        : data structure for solution components
standard_irreducible_decomp_io     : output of hypersurfaces and components
multprec_irreducible_decomp        : data structure for solution components
multprec_irreducible_decomp_io     : output of hypersurfaces and components
homotopy_cascade_filter            : witness generate + classify
drivers_to_cascade_filtering       : drivers to cascade of homotopies 
ts_cascade                         : calls the cascade routine
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Positive dimensional components of solutions are represented in the
package Standard/Multprec_Irreducible_Decomp by means of a list of
generic points, projection operators, and interpolating hypersurfaces.
The cascade of homotopies runs from the top dimensional components
down to the isolated solutions.  The multi-precision facilities are
needed to deal with curves and surfaces of high degree.
