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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2025-12-19 12:37:22 -10:00
parent e1db01a5b2
commit 9ee90b26bf
1 changed files with 48 additions and 30 deletions
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78
src/nlsat/levelwise.cpp
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@ -48,12 +48,10 @@ namespace nlsat {
// todo: consider to key polynomials in a set by using m_pm.eq // todo: consider to key polynomials in a set by using m_pm.eq
struct property { struct property {
prop_enum m_prop_tag; prop_enum m_prop_tag;
polynomial_ref m_poly; poly* m_poly = nullptr;
unsigned m_root_index = -1; // index of the root function, if applicable; -1 means unspecified unsigned m_root_index = static_cast<unsigned>(-1); // index of the root function, if applicable; -1 means unspecified
property(prop_enum pr, polynomial_ref const & pp, int si = -1) : m_prop_tag(pr), m_poly(pp), m_root_index(si) {} property(prop_enum pr, poly* pp, int si = -1) : m_prop_tag(pr), m_poly(pp), m_root_index(si) {}
property(prop_enum pr, polynomial_ref const & pp, polynomial::manager& pm) : m_prop_tag(pr), m_poly(pp), m_root_index(-1) {} property(prop_enum pr, polynomial::manager&) : m_prop_tag(pr), m_poly(nullptr), m_root_index(static_cast<unsigned>(-1)) {}
// have to pass polynomial::manager& to create a polynomial_ref even with a null object
property(prop_enum pr, polynomial::manager& pm) : m_prop_tag(pr), m_poly(polynomial_ref(pm)), m_root_index(-1) {}
}; };
struct compare_prop_tags { struct compare_prop_tags {
@ -236,7 +234,7 @@ namespace nlsat {
explicit level_t(unsigned lvl) { val = lvl; } explicit level_t(unsigned lvl) { val = lvl; }
}; };
bool find_in_Q(polynomial_ref & f, unsigned level) { bool find_in_Q(polynomial_ref const & f, unsigned level) {
if (level >= m_Q.size()) if (level >= m_Q.size())
return false; return false;
poly* fp = f.get(); poly* fp = f.get();
@ -244,7 +242,7 @@ namespace nlsat {
return false; return false;
unsigned const fid = m_pm.id(fp); unsigned const fid = m_pm.id(fp);
for (auto const& pr : m_Q[level]) { for (auto const& pr : m_Q[level]) {
poly* qp = pr.m_poly.get(); poly* qp = pr.m_poly;
if (qp && m_pm.id(qp) == fid) if (qp && m_pm.id(qp) == fid)
return true; return true;
} }
@ -484,12 +482,11 @@ namespace nlsat {
for (auto const& q : m_Q[m_level]) { for (auto const& q : m_Q[m_level]) {
if (q.m_prop_tag != prop_enum::sgn_inv) if (q.m_prop_tag != prop_enum::sgn_inv)
continue; continue;
polynomial_ref p(m_pm); polynomial_ref p(q.m_poly, m_pm);
p = q.m_poly;
SASSERT(max_var(p) == m_level); SASSERT(max_var(p) == m_level);
scoped_anum_vector roots(m_am); scoped_anum_vector roots(m_am);
m_am.isolate_roots(polynomial_ref(p, m_pm), undef_var_assignment(sample(), m_level), roots); m_am.isolate_roots(p, undef_var_assignment(sample(), m_level), roots);
unsigned num_roots = roots.size(); unsigned num_roots = roots.size();
TRACE(lws, ::nlsat::display(tout << "p:", m_solver, p) << ","; TRACE(lws, ::nlsat::display(tout << "p:", m_solver, p) << ",";
@ -516,6 +513,14 @@ namespace nlsat {
TRACE(lws_norm, tout << "normalized p:" << p << "\n";); TRACE(lws_norm, tout << "normalized p:" << p << "\n";);
} }
void normalize(poly*& p) {
if (!p)
return;
polynomial_ref pref(p, m_pm);
normalize(pref);
p = pref.get();
}
bool same_polynomial_up_to_constant(poly* a, poly* b) { bool same_polynomial_up_to_constant(poly* a, poly* b) {
if (a == b || m_pm.id(a) == m_pm.id(b)) if (a == b || m_pm.id(a) == m_pm.id(b))
return true; return true;
@ -568,13 +573,13 @@ namespace nlsat {
void add_to_Q_if_new(property pr, unsigned level) { void add_to_Q_if_new(property pr, unsigned level) {
if (pr.m_poly) if (pr.m_poly)
normalize(pr.m_poly); normalize(pr.m_poly);
SASSERT(pr.m_prop_tag != ord_inv || (pr.m_poly && !is_zero(pr.m_poly))); SASSERT(pr.m_prop_tag != ord_inv || (pr.m_poly && !m_pm.is_zero(pr.m_poly)));
for (auto const & q : m_Q[level]) { for (auto const & q : m_Q[level]) {
if (q.m_prop_tag != pr.m_prop_tag) continue; if (q.m_prop_tag != pr.m_prop_tag) continue;
if (q.m_root_index != pr.m_root_index) continue; if (q.m_root_index != pr.m_root_index) continue;
if ((q.m_poly && !pr.m_poly) || (!q.m_poly && pr.m_poly)) continue; if ((q.m_poly && !pr.m_poly) || (!q.m_poly && pr.m_poly)) continue;
if (!q.m_poly && !pr.m_poly) return; if (!q.m_poly && !pr.m_poly) return;
if (m_pm.id(q.m_poly.get()) != m_pm.id(pr.m_poly.get())) continue; if (m_pm.id(q.m_poly) != m_pm.id(pr.m_poly)) continue;
TRACE(lws, display(tout << "matched q:", q) << std::endl;); TRACE(lws, display(tout << "matched q:", q) << std::endl;);
return; return;
} }
@ -598,9 +603,9 @@ namespace nlsat {
// handle ord_inv(discriminant_{x_{i+1}}(p)) for an_del pre-processing // handle ord_inv(discriminant_{x_{i+1}}(p)) for an_del pre-processing
void add_ord_inv_discriminant_for(const property& p) { void add_ord_inv_discriminant_for(const property& p) {
unsigned x = max_var(p.m_poly); unsigned x = max_var(p.m_poly);
if (degree(p.m_poly, x) < 2) return; if (m_pm.degree(p.m_poly, x) < 2) return;
polynomial::polynomial_ref disc(m_pm); polynomial::polynomial_ref disc(m_pm);
disc = psc_discriminant(p.m_poly, x); disc = psc_discriminant(polynomial_ref(p.m_poly, m_pm), x);
TRACE(lws, display(tout << "p:", p) << "\n"; ::nlsat::display(tout << "discriminant by x" << max_var(p.m_poly)<< ": ", m_solver, disc) << "\n";); TRACE(lws, display(tout << "p:", p) << "\n"; ::nlsat::display(tout << "discriminant by x" << max_var(p.m_poly)<< ": ", m_solver, disc) << "\n";);
if (!is_const(disc)) { if (!is_const(disc)) {
for_each_distinct_factor(disc, [&](polynomial::polynomial_ref f) { for_each_distinct_factor(disc, [&](polynomial::polynomial_ref f) {
@ -613,7 +618,7 @@ namespace nlsat {
// handle sgn_inv(leading_coefficient_{x_{i+1}}(p)) for an_del pre-processing // handle sgn_inv(leading_coefficient_{x_{i+1}}(p)) for an_del pre-processing
void add_sgn_inv_leading_coeff_for(const property& p) { void add_sgn_inv_leading_coeff_for(const property& p) {
TRACE(lws, tout << "p:"; display(tout, p) << "\n";); TRACE(lws, tout << "p:"; display(tout, p) << "\n";);
poly * pp = p.m_poly.get(); poly * pp = p.m_poly;
unsigned lvl = max_var(p.m_poly); unsigned lvl = max_var(p.m_poly);
unsigned deg = m_pm.degree(pp, lvl); unsigned deg = m_pm.degree(pp, lvl);
polynomial_ref coeff(m_pm); polynomial_ref coeff(m_pm);
@ -679,18 +684,19 @@ namespace nlsat {
for (auto const& pr : m_Q[level]) { for (auto const& pr : m_Q[level]) {
if (pr.m_prop_tag != prop_enum::sgn_inv) if (pr.m_prop_tag != prop_enum::sgn_inv)
continue; continue;
poly* q = pr.m_poly.get(); poly* q = pr.m_poly;
if (q && m_pm.id(q) == pid) if (q && m_pm.id(q) == pid)
return true; return true;
} }
return false; return false;
} }
// If a polynomial has a coefficient which is a non-zero constant or a non-vanishisg coefficient for which sgn_inv has been asserted already then non_null holds // If a polynomial has a coefficient which is a non-zero constant or a non-vanishisg coefficient for which sgn_inv has been asserted already then non_null holds
bool has_non_null_coeff(const polynomial_ref& p) { bool has_non_null_coeff(poly* p) {
unsigned level = max_var(p); unsigned level = max_var(p);
unsigned deg = m_pm.degree(p, level); unsigned deg = m_pm.degree(p, level);
for (unsigned j = 0; j <= deg; ++j) { for (unsigned j = 0; j <= deg; ++j) {
polynomial_ref coeff(m_pm.coeff(p, level, j), m_pm); polynomial_ref coeff(m_pm);
coeff = m_pm.coeff(p, level, j);
TRACE(lws, tout << "coeff:" << coeff << "\n";); TRACE(lws, tout << "coeff:" << coeff << "\n";);
if (is_const(coeff) || (sign(coeff, sample(), m_am) && has_sgn_inv(coeff, max_var(coeff)))) if (is_const(coeff) || (sign(coeff, sample(), m_am) && has_sgn_inv(coeff, max_var(coeff))))
return true; return true;
@ -723,13 +729,13 @@ namespace nlsat {
return polynomial_ref(m_pm); return polynomial_ref(m_pm);
polynomial_ref d(m_pm); polynomial_ref d(m_pm);
d = derivative(p.m_poly, level); d = m_pm.derivative(p.m_poly, level);
if (!m_cache.contains_chain(p.m_poly.get(), d.get(), level)) if (!m_cache.contains_chain(p.m_poly, d.get(), level))
return polynomial_ref(m_pm); return polynomial_ref(m_pm);
polynomial_ref_vector& chain = m_psc_tmp; polynomial_ref_vector& chain = m_psc_tmp;
chain.reset(); chain.reset();
m_cache.psc_chain(p.m_poly.get(), d.get(), level, chain); m_cache.psc_chain(p.m_poly, d.get(), level, chain);
polynomial_ref disc(m_pm); polynomial_ref disc(m_pm);
for (unsigned i = 0; i < chain.size(); ++i) { for (unsigned i = 0; i < chain.size(); ++i) {
disc = polynomial_ref(chain.get(i), m_pm); disc = polynomial_ref(chain.get(i), m_pm);
@ -748,7 +754,7 @@ namespace nlsat {
// TODO: use cached non-null properties // TODO: use cached non-null properties
void try_non_null_via_coeffs(const property& p) { void try_non_null_via_coeffs(const property& p) {
unsigned level = max_var(p.m_poly); unsigned level = max_var(p.m_poly);
poly* pp = p.m_poly.get(); poly* pp = p.m_poly;
unsigned deg = m_pm.degree(pp, level); unsigned deg = m_pm.degree(pp, level);
for (unsigned j = 0; j <= deg; ++j) { for (unsigned j = 0; j <= deg; ++j) {
polynomial_ref coeff(m_pm); polynomial_ref coeff(m_pm);
@ -800,20 +806,32 @@ namespace nlsat {
add_to_Q_if_new(property(pe, m_pm), level.val); add_to_Q_if_new(property(pe, m_pm), level.val);
} }
void mk_prop(prop_enum pe, polynomial_ref poly) { void mk_prop(prop_enum pe, poly* poly) {
add_to_Q_if_new(property(pe, poly), max_var(poly)); add_to_Q_if_new(property(pe, poly), max_var(poly));
} }
void mk_prop(prop_enum pe, polynomial_ref poly, level_t level) { void mk_prop(prop_enum pe, poly* poly, level_t level) {
add_to_Q_if_new(property(pe, poly), level.val); add_to_Q_if_new(property(pe, poly), level.val);
} }
void mk_prop(prop_enum pe, polynomial_ref const& poly) {
mk_prop(pe, poly.get());
}
void mk_prop(prop_enum pe, polynomial_ref const& poly, level_t level) {
mk_prop(pe, poly.get(), level);
}
bool precondition_on_sign_inv(const property& p) const {
return p.m_prop_tag == prop_enum::sgn_inv && p.m_poly != nullptr;
}
void apply_pre_sgn_inv(const property& p) { void apply_pre_sgn_inv(const property& p) {
SASSERT(is_square_free(p.m_poly)); SASSERT(is_square_free(p.m_poly));
scoped_anum_vector roots(m_am); scoped_anum_vector roots(m_am);
SASSERT(max_var(p.m_poly) == m_level); SASSERT(max_var(p.m_poly) == m_level);
m_am.isolate_roots(p.m_poly, undef_var_assignment(sample(), m_level), roots); m_am.isolate_roots(polynomial_ref(p.m_poly, m_pm), undef_var_assignment(sample(), m_level), roots);
if (roots.size() == 0) { if (roots.size() == 0) {
/* Rule 4.6. Let i ∈ N, R ⊆ Ri, s ∈ R_{i−1}, and realRoots(p(s, xi )) = ∅. /* Rule 4.6. Let i ∈ N, R ⊆ Ri, s ∈ R_{i−1}, and realRoots(p(s, xi )) = ∅.
sample(s)(R), an_del(p)(R) ⊢ sgn_inv(p)(R) */ sample(s)(R), an_del(p)(R) ⊢ sgn_inv(p)(R) */
@ -837,10 +855,10 @@ namespace nlsat {
mk_prop(prop_enum::repr, level_t(m_level - 1)); mk_prop(prop_enum::repr, level_t(m_level - 1));
} }
mk_prop(prop_enum::an_del, m_I[m_level].l); mk_prop(prop_enum::an_del, m_I[m_level].l);
if (I.l == p.m_poly.get()) { if (I.l.get() == p.m_poly) {
// nothing is added // nothing is added
} else { } else {
add_ord_inv_resultant(I.l, p.m_poly.get(), m_level); add_ord_inv_resultant(I.l.get(), p.m_poly, m_level);
} }
} else { } else {
/* /*
@ -873,7 +891,7 @@ namespace nlsat {
void apply_pre_ord_inv(const property& p) { void apply_pre_ord_inv(const property& p) {
SASSERT(p.m_prop_tag == prop_enum::ord_inv && is_square_free(p.m_poly)); SASSERT(p.m_prop_tag == prop_enum::ord_inv && is_square_free(p.m_poly));
unsigned level = max_var(p.m_poly); unsigned level = max_var(p.m_poly);
auto sign_on_sample = sign(p.m_poly, sample(), m_am); auto sign_on_sample = sign(polynomial_ref(p.m_poly, m_pm), sample(), m_am);
if (sign_on_sample) { if (sign_on_sample) {
mk_prop(prop_enum::sgn_inv, p.m_poly); mk_prop(prop_enum::sgn_inv, p.m_poly);
} else { // sign is zero } else { // sign is zero