Implement weight-based dynamic selection of projection heuristics in
levelwise CAD. The weight function w(p, level) = deg(p, level) estimates
projection complexity, with w(res(a,b)) ≈ w(a) + w(b).
At each level, all three heuristics (biggest_cell, chain, lowest_degree)
are evaluated and the one with minimum estimated resultant weight is
selected. When fewer than 2 root functions exist, the default heuristic
is used since all produce equivalent results.
Add parameter nlsat.lws_dynamic_heuristic (default: true) to enable or
disable dynamic selection. When disabled, the static heuristic from
lws_sector_rel_mode/lws_section_rel_mode is used.
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
- Change m_todo from todo_set* to todo_set
- Initialize m_todo in constructor initializer list
- Use m_todo.reset() in single_cell_work instead of creating local todo_set
- Replace pointer access (m_todo->) with member access (m_todo.)
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Replace local variables and function parameters with member variables:
- m_level_ps: polynomials at current level (owned)
- m_level_tags: tags for each polynomial (owned)
- m_witnesses: non-zero coefficient witnesses
- m_poly_has_roots: which polynomials have roots
- m_todo: pointer to todo_set
Functions now use these member variables directly:
- extract_max_tagged() fills m_level_ps/m_level_tags and sets m_level
- process_level() and process_top_level() are now parameterless
- All helper functions use member variables instead of parameters
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Replace scattered local l_index/u_index parameters and m_partition_boundary
with two impl members:
- m_l_rf: position of lower bound in m_rel.m_rfunc
- m_u_rf: position of upper bound in m_rel.m_rfunc (UINT_MAX in section case)
This simplifies the code by:
- Removing parameter passing through multiple function calls
- Removing redundant m_partition_boundary from relation_E
- Making the partition state explicit in impl
Also clean up nlsat_explain.cpp to trust root_function_interval invariants:
- Section case: assert l and l_index are valid instead of defensive check
- Sector bounds: !l_inf()/!u_inf() implies valid polynomial and index
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Store the partition boundary (index of first root > sample) in
relation_E after sorting root functions. Use this cached value
in compute_omit_lc_sector_chain() and compute_omit_lc_section_chain()
instead of recomputing via algebraic number comparisons.
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Match SMT-RAT behavior: noDisc (discriminant omission for leaves
connected only to section polynomial) is only applied for
sectionHeuristic == 3 (lowest_degree), not for biggest_cell or chain.
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Add find_partition_boundary() helper to locate the boundary between
lower and upper root partitions in m_rfunc.
Implement compute_omit_lc_sector_chain() and compute_omit_lc_section_chain()
following SMT-RAT's OneCellCAD.h logic:
- Omit ldcf for extreme of lower chain (index 0) if it appears on upper side
- Omit ldcf for extreme of upper chain (last index) if it appears on lower side
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
