A Numerical Irreducible Decomposition with PHCv2.4.87

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.
The binomial solver was added as an option to phc -c in release 2.3.70.

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

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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
standard_diagonal_polynomials    : polynomials in diagonal homotopies
dobldobl_diagonal_polynomials    : dd polynomials in diagonal homotopies
quaddobl_diagonal_polynomials    : qd polynomials in diagonal homotopies
standard_diagonal_solutions      : solutions in diagonal homotopies
dobldobl_diagonal_solutions      : dd solutions in diagonal homotopies
quaddobl_diagonal_solutions      : qd solutions in diagonal homotopies
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
ts_diahom                        : test on diagonal homotopies
extrinsic_diagonal_continuation  : track paths of extrinsic diagonal homotopies
intrinsic_diagonal_continuation  : track paths of intrinsic diagonal homotopies
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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add_and_remove_embedding         : adding and removing an embedding
main_decomposition               : defines phc -c
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ts_dimred                        : test on dimension determination
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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
square_and_embed_systems         : squaring and embedding systems
path_counts_table                : counts the paths with zero & nonzero slacks
standard_witness_solutions       : stores a numerical irreducible decomposition
dobldobl_witness_solutions       : double double version of witness solutions
quaddobl_witness_solutions       : quad double version of witness solutions
store_witness_solutions          : default callback procedures
write_witness_solutions          : output for testing purposes
ts_witsols                       : tests the witness solutions package
cascade_homotopy_steps           : run one step in a cascade homotopy
cascade_homotopies_io            : defines the writing of witness super sets
cascade_homotopies               : versions of cascade homotopies
cascade_membership_filters       : filter sequences of witness super sets
cascade_homotopy_filters         : run a cascade and filter junk
running_cascades                 : given top solutions, run cascades
embeddings_and_cascades          : embed system and launch cascade
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 multiprecision facilities are
needed to deal with curves and surfaces of high degree.
