Mixed-volume computation & polyhedral continuation by dynamic lifting in PHCv2.
The aim of dynamic lifting is to control the heights of the lifting values,
to obtain a stable evaluation of the polyhedral homotopy.
When all supports are equal, then the mixed volume is reduced to an
ordinary volume, which is computed by a regular triangulation.
1. Dynamic construction of regular triangulations :
2. The Cayley trick
3. Dynamic construction of mixed subdivision
4. The drivers and black-box computation
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file name : short description
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simplices : simplices of integer polytopes
simplices_io : input/output of simplices
triangulations : triangulations of integer polytopes
triangulations_io : input/output of triangulations
global_dynamic_triangulation : global aspects of dynamic lifting
dynamic_lifting_functions : dynamic lifting functions
dynamic_triangulations : construction of placing triangulation
ts_dyntri : test on the construction of a triangulation
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cayley_embedding : embeds tuple in one support
cayley_trick : computing mixed subdivisions
minkowski_polynomials : volume polynomials
driver_for_minkowski_polynomials : driver to the volume polynomials
ts_drivmink : calls the driver for volume polynomials
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common_faces_of_polytope : computation of neighboring faces
enumerate_faces_of_polytope : extract faces of a triangulation
face_structures : management of faces of triangulations
frequency_graph : computes occurencies of points in supports
initial_mixed_cell : finds an initial mixed cell
flatten_mixed_subdivisions : flattening of mixed subdivisions
unfolding_subdivisions : re-lifting flattened parts of subdivisions
triangulations_and_subdivisions : convert triangulations <> subdivisions
dynamic_mixed_subdivisions : dynamic lifting in the mixed case
dynamic_polyhedral_continuation : incremental polyhedral continuation
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drivers_for_dynamic_lifting : menu-driver for dynamic lifting
ts_drivdynl : calls the menu-driver
black_mixed_volume_computations : black-box polyhedral methods
babldmvc : calls the black-box mixed-volume computation
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The Cayley trick is an efficient way to construct all cells in a mixed
subdivision with the corresponding Minkowksi polynomial.
wc *adb counts 7493 lines of Ada code