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add lc(p) and disc(p) for a rootless p in section case

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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2026-02-02 16:39:30 -10:00
parent a19db1f7a7
commit 4587ecec9c
3 changed files with 19 additions and 13 deletions
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25
src/nlsat/levelwise.cpp
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@ -1106,27 +1106,34 @@ namespace nlsat {
bool is_section() { return m_I[m_level].is_section();}
// Section case: only the section-defining polynomial needs disc and lc projections.
//
// Theory: For a section (sample on a root), sign-invariance of other polynomials
// is ensured by resultants with the section-defining polynomial. Their leading
// coefficients and discriminants are not needed because:
// - Resultant Res(p, q) being order-invariant ensures relative root ordering (Thm 2.2 in [1])
// - The section polynomial's delineability (via its disc/lc) anchors the cell
// Section case: the section-defining polynomial needs disc and lc projections.
// For polynomials WITH roots: resultants with section polynomial ensure root ordering.
// For polynomials WITHOUT roots: they need LC + disc to ensure they don't gain roots.
//
// Theory: For a section (sample on a root), sign-invariance of polynomials with roots
// is ensured by resultants with the section-defining polynomial (Thm 2.2 in [1]).
// But polynomials without roots need delineability (LC + disc) to stay root-free.
//
// [1] Nalbach et al., "Projective Delineability for Single Cell Construction", SC² 2025
void add_section_projections() {
poly* section_poly = m_I[m_level].l;
SASSERT(section_poly);
// Build set of polynomial indices that have roots at this level
std::set<unsigned> has_roots;
for (auto const& rf : m_rel.m_rfunc)
has_roots.insert(rf.ps_idx);
for (unsigned i = 0; i < m_level_ps.size(); ++i) {
polynomial_ref p(m_level_ps.get(i), m_pm);
polynomial_ref witness = m_witnesses[i];
if (m_level_ps.get(i) == section_poly)
add_projection_for_poly(p, m_level, witness, /*add_lc=*/true, /*add_disc=*/true);
add_projection_for_poly(p, m_level, witness, true, true); // section poly: full projection
else if (has_roots.find(i) == has_roots.end())
add_projection_for_poly(p, m_level, witness, true, true); // no roots: need LC+disc for delineability
else if (witness && !is_const(witness))
request_factorized(witness, inv_req::sign);
request_factorized(witness, inv_req::sign); // has roots: witness only
}
}

5
src/test/nlsat.cpp
View file

@ -2346,9 +2346,8 @@ static void tst_unsound_lws_ppblockterm() {
}
void tst_nlsat() {
// TODO: Fix z3-76w - ppblockterm test fails because counterexample is inside cell
// tst_unsound_lws_ppblockterm();
// std::cout << "------------------\n";
tst_unsound_lws_ppblockterm();
std::cout << "------------------\n";
tst_unsound_lws_n46();
std::cout << "------------------\n";
tst_unsound_lws_et4();