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v0.1 of nla saturation

This commit is contained in:
Nikolaj Bjorner 2025-09-26 23:05:02 +03:00
parent 6adb234673
commit ef27e38d5f
12 changed files with 461 additions and 175 deletions

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@ -1,5 +0,0 @@
BasedOnStyle: Google
IndentWidth: 4
ColumnLimit: 0
NamespaceIndentation: All
BreakBeforeBraces: Attach

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@ -24,6 +24,7 @@ z3_add_component(lp
monomial_bounds.cpp
nex_creator.cpp
nla_basics_lemmas.cpp
nla_coi.cpp
nla_common.cpp
nla_core.cpp
nla_divisions.cpp

78
src/math/lp/nla_coi.cpp Normal file
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@ -0,0 +1,78 @@
#include "math/lp/nla_core.h"
#include "math/lp/nla_coi.h"
namespace nla {
void coi::init() {
indexed_uint_set visited;
unsigned_vector todo;
vector<occurs> var2occurs;
m_term_set.reset();
m_mon_set.reset();
m_constraint_set.reset();
auto& lra = c.lra_solver();
for (auto ci : lra.constraints().indices()) {
auto const& c = lra.constraints()[ci];
if (c.is_auxiliary())
continue;
for (auto const& [coeff, v] : c.coeffs()) {
var2occurs.reserve(v + 1);
var2occurs[v].constraints.push_back(ci);
}
}
for (auto const& m : c.emons()) {
for (auto v : m.vars()) {
var2occurs.reserve(v + 1);
var2occurs[v].monics.push_back(m.var());
}
}
for (const auto *t : lra.terms() ) {
for (auto const iv : *t) {
auto v = iv.j();
var2occurs.reserve(v + 1);
var2occurs[v].terms.push_back(t->j());
}
}
for (auto const& m : c.to_refine())
todo.push_back(m);
for (unsigned i = 0; i < todo.size(); ++i) {
auto v = todo[i];
if (visited.contains(v))
continue;
visited.insert(v);
var2occurs.reserve(v + 1);
for (auto ci : var2occurs[v].constraints) {
m_constraint_set.insert(ci);
auto const& c = lra.constraints()[ci];
for (auto const& [coeff, w] : c.coeffs())
todo.push_back(w);
}
for (auto w : var2occurs[v].monics)
todo.push_back(w);
for (auto ti : var2occurs[v].terms) {
for (auto iv : lra.get_term(ti))
todo.push_back(iv.j());
todo.push_back(ti);
}
if (lra.column_has_term(v)) {
m_term_set.insert(v);
for (auto kv : lra.get_term(v))
todo.push_back(kv.j());
}
if (c.is_monic_var(v)) {
m_mon_set.insert(v);
for (auto w : c.emons()[v])
todo.push_back(w);
}
}
}
}

29
src/math/lp/nla_coi.h Normal file
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@ -0,0 +1,29 @@
#pragma once
namespace nla {
class core;
class coi {
core& c;
indexed_uint_set m_mon_set, m_constraint_set;
indexed_uint_set m_term_set;
struct occurs {
unsigned_vector constraints;
unsigned_vector monics;
unsigned_vector terms;
};
public:
coi(core& c) : c(c) {}
void init();
indexed_uint_set const& mons() const { return m_mon_set; }
indexed_uint_set const& constraints() const { return m_constraint_set; }
indexed_uint_set& terms() { return m_term_set; }
};
}

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@ -1332,6 +1332,9 @@ lbool core::check() {
if (!m_lemmas.empty() || !m_literals.empty() || m_check_feasible)
return l_false;
}
if (false && no_effect())
ret = m_mul_saturate.saturate();
if (no_effect() && should_run_bounded_nlsat())
ret = bounded_nlsat();
@ -1348,8 +1351,7 @@ lbool core::check() {
if (no_effect())
m_order.order_lemma();
if (false && no_effect())
ret = m_mul_saturate.saturate();
if (no_effect()) {
unsigned num_calls = lp_settings().stats().m_nla_calls;

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@ -70,7 +70,7 @@ class core {
lbool bounded_nlsat();
var_eqs<emonics> m_evars;
lp::lar_solver& lra;
reslimit& m_reslim;
smt_params_helper m_params;
@ -127,6 +127,9 @@ public:
// constructor
core(lp::lar_solver& s, params_ref const& p, reslimit&);
const auto& monics_with_changed_bounds() const { return m_monics_with_changed_bounds; }
lp::lar_solver& lra_solver() { return lra; }
indexed_uint_set const& to_refine() const { return m_to_refine; }
void insert_to_refine(lpvar j);
void erase_from_to_refine(lpvar j);

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@ -19,13 +19,13 @@
--*/
#include "math/lp/nla_core.h"
#include "math/lp/nla_coi.h"
#include "math/lp/nla_mul_saturate.h"
namespace nla {
mul_saturate::mul_saturate(core* core) :
common(core) {}
mul_saturate::mul_saturate(core* core) : common(core), m_coi(*core) {}
lbool mul_saturate::saturate() {
lp::explanation ex;
@ -39,26 +39,81 @@ namespace nla {
void mul_saturate::init_solver() {
local_solver = alloc(lp::lar_solver);
m_vars2mon.reset();
m_mon2vars.reset();
m_values.reset();
m_coi.init();
init_vars();
}
void mul_saturate::init_vars() {
auto const& lra = c().lra_solver();
auto sz = lra.number_of_vars();
for (unsigned v = 0; v < sz; ++v) {
unsigned w;
if (m_coi.mons().contains(v))
init_monomial(v);
else
m_values.push_back(c().val(v));
if (m_coi.terms().contains(v)) {
auto const& t = lra.get_term(v);
// Assumption: variables in coefficients are always declared before term variable.
SASSERT(all_of(t, [&](auto p) { return p.j() < v; }));
w = local_solver->add_term(t.coeffs_as_vector(), v);
}
else
w = local_solver->add_var(v, lra.var_is_int(v));
VERIFY(w == v);
if (lra.column_has_lower_bound(v)) {
auto lo_dep = lra.get_column_lower_bound_witness(v);
auto lo_bound = lra.get_lower_bound(v);
auto k = lo_bound.y > 0 ? lp::lconstraint_kind::GT : lp::lconstraint_kind::GE;
auto ci = local_solver->add_var_bound(v, k, lo_bound.x);
}
if (lra.column_has_upper_bound(v)) {
auto hi_dep = lra.get_column_upper_bound_witness(v);
auto hi_bound = lra.get_upper_bound(v);
auto k = hi_bound.y < 0 ? lp::lconstraint_kind::LT : lp::lconstraint_kind::LE;
auto ci = local_solver->add_var_bound(v, k, hi_bound.x);
m_ci2dep.setx(ci, hi_dep, nullptr);
}
}
}
void mul_saturate::init_monomial(unsigned mon_var) {
auto& mon = c().emons()[mon_var];
svector<lpvar> vars(mon.vars());
std::sort(vars.begin(), vars.end());
m_vars2mon.insert(vars, mon_var);
m_mon2vars.insert(mon_var, vars);
rational p(1);
for (auto v : vars)
p *= m_values[v];
m_values.push_back(p);
}
void mul_saturate::add_lemma(lp::explanation const& ex1) {
auto& lra = c().lra_solver();
lp::explanation ex2;
for (auto p : ex1) {
lp::constraint_index src_ci;
if (m_new_mul_constraints.find(p.ci(), src_ci))
ex2.add_pair(src_ci, mpq(1));
else
ex2.add_pair(p.ci(), p.coeff());
if (!m_new_mul_constraints.find(p.ci(), src_ci))
src_ci = p.ci();
auto dep = m_ci2dep.get(src_ci, nullptr);
local_solver->push_explanation(dep, ex2);
}
for (auto [v, sign, dep] : m_var_signs) {
if (!dep) {
verbose_stream() << "TODO explain non-implied bound\n";
continue;
}
local_solver->push_explanation(dep, ex2);
}
lemma_builder new_lemma(c(), "stellensatz");
new_lemma &= ex2;
for (auto [v, sign] : m_var_signs) {
if (sign)
new_lemma.explain_existing_upper_bound(v);
else
new_lemma.explain_existing_lower_bound(v);
}
IF_VERBOSE(1, verbose_stream() << "unsat \n" << new_lemma << "\n");
TRACE(arith, tout << "unsat\n" << new_lemma << "\n");
}
lbool mul_saturate::solve(lp::explanation& ex) {
@ -68,49 +123,74 @@ namespace nla {
lbool r = l_undef;
if (st == lp::lp_status::INFEASIBLE) {
local_solver->get_infeasibility_explanation(ex);
IF_VERBOSE(0, c().print_explanation(ex, verbose_stream()) << "\n";);
r = l_false;
}
if (st == lp::lp_status::OPTIMAL || st == lp::lp_status::FEASIBLE) {
// TODO: check model just in case it got lucky.
IF_VERBOSE(1, verbose_stream() << "saturation is LP feasible, maybe it is a model of the NLA problem\n");
}
IF_VERBOSE(0, local_solver->display(verbose_stream()); c().display(verbose_stream()));
IF_VERBOSE(0, display(verbose_stream()));
return r;
}
// record new monomials that are created and recursively down-saturate with respect to these.
// this is a simplistic pass
void mul_saturate::add_multiply_constraints() {
m_new_mul_constraints.reset();
m_seen_vars.reset();
m_var_signs.reset();
for (auto j : c().m_to_refine) {
for (auto con_id : local_solver->constraints().indices()) {
unsigned num_vars = c().emon(j).vars().size();
for (unsigned i = 0; i < num_vars; ++i) {
auto v = c().emon(j).vars()[i];
for (auto [coeff, u] : local_solver->constraints()[con_id].coeffs())
m_to_refine.reset();
vector<svector<lp::constraint_index>> var2cs;
for (auto ci : local_solver->constraints().indices()) {
auto const& con = local_solver->constraints()[ci];
for (auto [coeff, v] : con.coeffs()) {
if (v >= var2cs.size())
var2cs.resize(v + 1);
var2cs[v].push_back(ci);
}
// insert monomials to be refined
insert_monomials_from_constraint(ci);
}
for (unsigned it = 0; it < m_to_refine.size(); ++it) {
auto j = m_to_refine[it];
verbose_stream() << "refining " << j << " := " << m_mon2vars[j] << "\n";
auto vars = m_mon2vars[j];
for (auto v : vars) {
if (v >= var2cs.size())
continue;
auto cs = var2cs[v];
for (auto ci : cs) {
for (auto [coeff, u] : local_solver->constraints()[ci].coeffs()) {
if (u == v)
add_multiply_constraint(con_id, j, v);
add_multiply_constraint(ci, j, v);
}
}
}
}
IF_VERBOSE(0,
c().lra_solver().display(verbose_stream() << "original\n");
c().display(verbose_stream());
display(verbose_stream() << "saturated\n"));
}
// multiply by remaining vars
void mul_saturate::add_multiply_constraint(lp::constraint_index old_ci, lp::lpvar mi, lpvar x) {
lp::lar_base_constraint const& con = local_solver->constraints()[old_ci];
auto &lra = c().lra_solver();
auto const& lhs = con.coeffs();
auto const& rhs = con.rhs();
auto k = con.kind();
auto k = con.kind();
if (k == lp::lconstraint_kind::NE || k == lp::lconstraint_kind::EQ)
return; // not supported
auto sign = false;
svector<lpvar> vars;
bool first = true;
for (auto v : c().emon(mi).vars()) {
if (v != x || !first)
vars.push_back(v);
if (v != x || !first)
vars.push_back(v);
else
first = false;
}
@ -118,64 +198,186 @@ namespace nla {
for (auto v : vars) {
if (m_seen_vars.contains(v))
continue;
m_seen_vars.insert(v);
// retrieve bounds of v
// if v has non-negative lower bound add as positive
// if v has non-positive upper bound add as negative
// otherwise, fail
if (local_solver->column_has_lower_bound(v) && !local_solver->get_lower_bound(v).is_neg()) {
m_var_signs.push_back({v, false});
m_seen_vars.insert(v);
// if v has positive lower bound add as positive
// if v has negative upper bound add as negative
// otherwise, soft-fail (for now unsound)
// proper signs of variables from old tableau should be extracted using lra_solver()
// instead of local_solver.
// TODO is to also add case where lower or upper bound is zero and then the sign
// of the inequality is relaxed if it is strict.
if (lra.number_of_vars() > v && lra.column_has_lower_bound(v) && lra.get_lower_bound(v).is_pos()) {
m_var_signs.push_back({v, false, lra.get_column_lower_bound_witness(v)});
}
else if (local_solver->column_has_upper_bound(v) && !local_solver->get_upper_bound(v).is_pos()) {
m_var_signs.push_back({v, true});
m_seen_vars.insert(v);
else if (lra.number_of_vars() > v && lra.column_has_upper_bound(v) && lra.get_upper_bound(v).is_neg()) {
m_var_signs.push_back({v, true, lra.get_column_upper_bound_witness(v)});
sign = !sign;
}
else
return;
}
lp::lar_term new_lhs;
rational new_rhs(rhs);
for (auto [coeff, v] : lhs) {
#if 0
vars.push_back(v);
lpvar new_monic_var = c().m_add_monomial(vars);
auto const& new_m = c().emons()[new_monic_var];
verbose_stream() << vars << " v " << new_m.var() << " coeff " << coeff << "\n";
new_lhs.add_monomial(coeff, new_m.var());
vars.pop_back();
#endif
}
if (rhs != 0) {
if (vars.size() == 1) {
new_lhs.add_monomial(-rhs, vars[0]);
verbose_stream() << "rhs mul " << -rhs << " * j" << vars[0] << "\n";
}
else if (m_values[v].is_neg()) {
m_var_signs.push_back({v, true, nullptr});
sign = !sign;
}
else if (m_values[v].is_pos()) {
m_var_signs.push_back({v, false, nullptr});
}
else {
#if 0
lpvar new_monic_var = c().m_add_monomial(vars);
auto const& new_m = c().emons()[new_monic_var];
verbose_stream() << vars << " v " << new_m.var() << " coeff " << coeff << "\n";
new_lhs.add_monomial(-rhs, new_m.var());
verbose_stream() << "rhs mul " << -rhs << " * j" << new_m.var() << "\n";
#endif
IF_VERBOSE(0, verbose_stream() << "not separated from 0\n");
return;
}
}
lp::lar_term new_lhs;
rational new_rhs(rhs), term_value(0);
for (auto const & [coeff, v] : lhs) {
unsigned old_sz = vars.size();
if (m_mon2vars.contains(v))
vars.append(m_mon2vars[v]);
else
vars.push_back(v);
lpvar new_monic_var = add_monomial(vars);
new_lhs.add_monomial(coeff, new_monic_var);
term_value += coeff * m_values[new_monic_var];
vars.shrink(old_sz);
}
if (rhs != 0) {
lpvar new_monic_var = add_monomial(vars);
new_lhs.add_monomial(-rhs, new_monic_var);
term_value -= rhs * m_values[new_monic_var];
new_rhs = 0;
}
if (sign) {
switch (k) {
case lp::lconstraint_kind::LE: k = lp::lconstraint_kind::GE; break;
case lp::lconstraint_kind::LT: k = lp::lconstraint_kind::GT; break;
case lp::lconstraint_kind::GE: k = lp::lconstraint_kind::LE; break;
case lp::lconstraint_kind::GT: k = lp::lconstraint_kind::LT; break;
default: break;
case lp::lconstraint_kind::LE:
k = lp::lconstraint_kind::GE;
break;
case lp::lconstraint_kind::LT:
k = lp::lconstraint_kind::GT;
break;
case lp::lconstraint_kind::GE:
k = lp::lconstraint_kind::LE;
break;
case lp::lconstraint_kind::GT:
k = lp::lconstraint_kind::LT;
break;
default:
break;
}
}
c().display_constraint(verbose_stream(), old_ci) << " -> ";
c().display_constraint(verbose_stream(), new_lhs, k, new_rhs) << "\n";
// TODO:
// auto new_ci = lra.m_add_constraint(new_lhs, k, new_rhs);
// m_new_mul_constraints.insert(new_ci, old_ci);
}
display_constraint(verbose_stream(), old_ci) << " -> ";
display_constraint(verbose_stream(), new_lhs.coeffs_as_vector(), k, new_rhs) << "\n";
auto ti = local_solver->add_term(new_lhs.coeffs_as_vector(), local_solver->number_of_vars());
auto new_ci = local_solver->add_var_bound(ti, k, new_rhs);
insert_monomials_from_constraint(new_ci);
m_values.push_back(term_value);
SASSERT(m_values.size() - 1 == ti);
m_new_mul_constraints.insert(new_ci, old_ci);
}
lpvar mul_saturate::add_monomial(svector<lpvar> const& vars) {
lpvar v;
if (vars.size() == 1)
return vars[0];
svector<lpvar> _vars(vars);
std::sort(_vars.begin(), _vars.end());
if (m_vars2mon.find(_vars, v))
return v;
v = add_var(is_int(vars));
m_vars2mon.insert(_vars, v);
m_mon2vars.insert(v, _vars);
rational p(1);
for (auto v : vars)
p *= m_values[v];
m_values.push_back(p);
SASSERT(m_values.size() - 1 == v);
return v;
}
bool mul_saturate::is_int(svector<lp::lpvar> const& vars) const {
auto const& lra = m_core.lra;
return all_of(vars, [&](lpvar v) { return lra.var_is_int(v); });
}
lpvar mul_saturate::add_var(bool is_int) {
auto v = local_solver->number_of_vars();
auto w = local_solver->add_var(v, is_int);
VERIFY(v == w);
return w;
}
void mul_saturate::insert_monomials_from_constraint(lp::constraint_index ci) {
if (constraint_is_true(ci))
return;
auto const& con = local_solver->constraints()[ci];
for (auto [coeff, v] : con.coeffs())
if (c().is_monic_var(v))
m_to_refine.insert(v);
}
bool mul_saturate::constraint_is_true(lp::constraint_index ci) {
auto const& con = local_solver->constraints()[ci];
auto lhs = -con.rhs();
for (auto const& [coeff, v] : con.coeffs())
lhs += coeff * m_values[v];
switch (con.kind()) {
case lp::lconstraint_kind::GT:
return lhs > 0;
case lp::lconstraint_kind::GE:
return lhs >= 0;
case lp::lconstraint_kind::LE:
return lhs <= 0;
case lp::lconstraint_kind::LT:
return lhs < 0;
case lp::lconstraint_kind::EQ:
return lhs == 0;
case lp::lconstraint_kind::NE:
return lhs != 0;
default:
UNREACHABLE();
return false;
}
}
std::ostream& mul_saturate::display(std::ostream& out) const {
local_solver->display(out);
for (auto const& [vars, v] : m_vars2mon) {
out << "j" << v << " := ";
display_product(out, vars);
out << "\n";
}
return out;
}
std::ostream& mul_saturate::display_product(std::ostream& out, svector<lpvar> const& vars) const {
bool first = true;
for (auto v : vars) {
if (first)
first = false;
else
out << " * ";
out << "j" << v;
}
return out;
}
std::ostream& mul_saturate::display_constraint(std::ostream& out, lp::constraint_index ci) const {
auto const& con = local_solver->constraints()[ci];
return display_constraint(out, con.coeffs(), con.kind(), con.rhs());
}
std::ostream& mul_saturate::display_constraint(std::ostream& out,
vector<std::pair<rational, lpvar>> const& lhs,
lp::lconstraint_kind k, rational const& rhs) const {
bool first = true;
for (auto [coeff, v] : lhs) {
c().display_coeff(out, first, coeff);
first = false;
if (m_mon2vars.contains(v))
display_product(out, m_mon2vars[v]);
else
out << "j" << v;
}
return out << " " << k << " " << rhs;
}
}

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@ -4,24 +4,65 @@
--*/
#pragma once
#include "math/lp/nla_coi.h"
namespace nla {
class core;
class lar_solver;
class lar_solver;
class mul_saturate : common {
struct var_sign {
lpvar v = lp::null_lpvar;
bool is_neg = false;
u_dependency* dep = nullptr;
};
coi m_coi;
// source of multiplication constraint
u_map<lp::constraint_index> m_new_mul_constraints;
svector<std::pair<lpvar, bool>> m_var_signs;
svector<var_sign> m_var_signs;
tracked_uint_set m_seen_vars;
indexed_uint_set m_to_refine;
scoped_ptr<lp::lar_solver> local_solver;
ptr_vector<u_dependency> m_ci2dep;
vector<rational> m_values;
struct eq {
bool operator()(unsigned_vector const& a, unsigned_vector const& b) const {
return a == b;
}
};
map<unsigned_vector, unsigned, svector_hash<unsigned_hash>, eq> m_vars2mon;
u_map<unsigned_vector> m_mon2vars;
// initialization
void init_solver();
void init_vars();
void init_monomial(unsigned mon_var);
bool constraint_is_true(lp::constraint_index ci);
void insert_monomials_from_constraint(lp::constraint_index ci);
// additional variables and monomials and constraints
lpvar add_monomial(svector<lp::lpvar> const& vars);
bool is_int(svector<lp::lpvar> const& vars) const;
lpvar add_var(bool is_int);
void add_multiply_constraints();
void add_multiply_constraint(lp::constraint_index con_id, lp::lpvar mi, lpvar x);
// solving
lbool solve(lp::explanation& ex);
void add_lemma(lp::explanation const& ex1);
// lemmas
void add_lemma(lp::explanation const& ex);
std::ostream& display(std::ostream& out) const;
std::ostream& display_product(std::ostream& out, svector<lpvar> const& vars) const;
std::ostream& display_constraint(std::ostream& out, lp::constraint_index ci) const;
std::ostream& display_constraint(std::ostream& out, vector<std::pair<rational, lpvar>> const& lhs,
lp::lconstraint_kind k, rational const& rhs) const;
public:
mul_saturate(core* core);
lbool saturate();
};

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@ -250,15 +250,17 @@ std::ostream& core::display_coeff(std::ostream& out, bool first, lp::mpq const&
if (first && p == 1)
return out;
if (first && p > 0)
out << p;
out << p << " * ";
else if (first && p == -1)
out << "-";
else if (first)
out << p << " * ";
else if (p == 1)
out << " + ";
else if (p > 0)
out << " + " << p << " * ";
else if (p == -1)
out << " - ";
else if (first)
out << p << " * ";
else
out << " - " << -p << " * ";
return out;

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@ -9,6 +9,7 @@
#include <fstream>
#include "math/lp/lar_solver.h"
#include "math/lp/nra_solver.h"
#include "math/lp/nla_coi.h"
#include "nlsat/nlsat_solver.h"
#include "math/polynomial/polynomial.h"
#include "math/polynomial/algebraic_numbers.h"
@ -29,107 +30,30 @@ struct solver::imp {
reslimit& m_limit;
params_ref m_params;
u_map<polynomial::var> m_lp2nl; // map from lar_solver variables to nlsat::solver variables
indexed_uint_set m_term_set;
scoped_ptr<nlsat::solver> m_nlsat;
scoped_ptr<scoped_anum_vector> m_values; // values provided by LRA solver
scoped_ptr<scoped_anum> m_tmp1, m_tmp2;
nla::coi m_coi;
nla::core& m_nla_core;
imp(lp::lar_solver& s, reslimit& lim, params_ref const& p, nla::core& nla_core):
lra(s),
m_limit(lim),
m_params(p),
m_coi(nla_core),
m_nla_core(nla_core) {}
bool need_check() {
return m_nla_core.m_to_refine.size() != 0;
}
indexed_uint_set m_mon_set, m_constraint_set;
struct occurs {
unsigned_vector constraints;
unsigned_vector monics;
unsigned_vector terms;
};
void init_cone_of_influence() {
indexed_uint_set visited;
unsigned_vector todo;
vector<occurs> var2occurs;
m_term_set.reset();
m_mon_set.reset();
m_constraint_set.reset();
for (auto ci : lra.constraints().indices()) {
auto const& c = lra.constraints()[ci];
if (c.is_auxiliary())
continue;
for (auto const& [coeff, v] : c.coeffs()) {
var2occurs.reserve(v + 1);
var2occurs[v].constraints.push_back(ci);
}
}
for (auto const& m : m_nla_core.emons()) {
for (auto v : m.vars()) {
var2occurs.reserve(v + 1);
var2occurs[v].monics.push_back(m.var());
}
}
for (const auto *t : lra.terms() ) {
for (auto const iv : *t) {
auto v = iv.j();
var2occurs.reserve(v + 1);
var2occurs[v].terms.push_back(t->j());
}
}
for (auto const& m : m_nla_core.m_to_refine)
todo.push_back(m);
for (unsigned i = 0; i < todo.size(); ++i) {
auto v = todo[i];
if (visited.contains(v))
continue;
visited.insert(v);
var2occurs.reserve(v + 1);
for (auto ci : var2occurs[v].constraints) {
m_constraint_set.insert(ci);
auto const& c = lra.constraints()[ci];
for (auto const& [coeff, w] : c.coeffs())
todo.push_back(w);
}
for (auto w : var2occurs[v].monics)
todo.push_back(w);
for (auto ti : var2occurs[v].terms) {
for (auto iv : lra.get_term(ti))
todo.push_back(iv.j());
todo.push_back(ti);
}
if (lra.column_has_term(v)) {
m_term_set.insert(v);
for (auto kv : lra.get_term(v))
todo.push_back(kv.j());
}
if (m_nla_core.is_monic_var(v)) {
m_mon_set.insert(v);
for (auto w : m_nla_core.emons()[v])
todo.push_back(w);
}
}
}
void reset() {
m_values = nullptr;
m_tmp1 = nullptr; m_tmp2 = nullptr;
m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
m_values = alloc(scoped_anum_vector, am());
m_term_set.reset();
m_lp2nl.reset();
}
@ -149,17 +73,17 @@ struct solver::imp {
reset();
vector<nlsat::assumption, false> core;
init_cone_of_influence();
m_coi.init();
// add linear inequalities from lra_solver
for (auto ci : m_constraint_set)
for (auto ci : m_coi.constraints())
add_constraint(ci);
// add polynomial definitions.
for (auto const& m : m_mon_set)
for (auto const& m : m_coi.mons())
add_monic_eq(m_nla_core.emons()[m]);
// add term definitions.
for (unsigned i : m_term_set)
for (unsigned i : m_coi.terms())
add_term(i);
TRACE(nra, m_nlsat->display(tout));
@ -370,7 +294,7 @@ struct solver::imp {
for (auto const& m : m_nla_core.emons())
if (any_of(m.vars(), [&](lp::lpvar v) { return m_lp2nl.contains(v); }))
add_monic_eq_bound(m);
for (unsigned i : m_term_set)
for (unsigned i : m_coi.terms())
add_term(i);
for (auto const& [v, w] : m_lp2nl) {
if (lra.column_has_lower_bound(v))
@ -554,8 +478,8 @@ struct solver::imp {
if (!m_lp2nl.find(v, r)) {
r = m_nlsat->mk_var(is_int(v));
m_lp2nl.insert(v, r);
if (!m_term_set.contains(v) && lra.column_has_term(v)) {
m_term_set.insert(v);
if (!m_coi.terms().contains(v) && lra.column_has_term(v)) {
m_coi.terms().insert(v);
}
}
return r;