Example 5.4 (An application from physics)

• Download Example5_4.zip and extract the files in an empty directory.
• At the command line, run:
  bertini input.sliceC
  cp witness_data witness_data_copy
  Note: if the output shows fewer than 8 components, then repeat this step and/or use stricter configuration settings.
• At the command line, run:
  bertini input.sliceW
  cp finite_solutions finite_solutions_copy
  cp finite_solutions member_points
  cp finite_solutions witness_points_fiber
• At the command line, run:
  cp witness_data_copy witness_data
  bertini input.membership
  cp incidence_matrix incidence_matrix_copy
• In Matlab, run:
  incidence_matrix_to_files
• At the command line, run:
  bertini input.eval fiber_points.1; mv function image_points.1
  ...
  bertini input.eval fiber_points.8; mv function image_points.8
• At the command line, run:
  cp witness_data_copy witness_data
  bertini input.sampleC
  When prompted, answer with:
  1, 0, 5000, 0, fiber_sample.1
  Repeat 7 more times, answering the prompts with:
  1, 1, 5000, 0, fiber_sample.2
  ...
  1, 7, 5000, 0, fiber_sample.8
  Note: In this step, it may be possible to get accurate results with fewer sample points (e.g. 1000), but here we sample 5000 for better numerical stability.
• At the command line, run:
  bertini input.eval fiber_sample.1; mv function image_sample.1
  ...
  bertini input.eval fiber_sample.8; mv function image_sample.8
• In Matlab, run:
  testacm
  When prompted, answer with:
  image_points.1, image_sample.1, 5
  Repeat 7 more times, answering the prompts with:
  image_points.2, image_sample.2, 5
  ...
  image_points.8, image_sample.8, 5