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add option to propagation quotients

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for equations x*y + z = 0,
with x, y, z integer, enforce that x divides z
It is (currently) enabled within Grobner completion
and applied partially to x a variable, z linear, and
only when |z| < |x|.
This commit is contained in:
Nikolaj Bjorner 2025-08-31 14:41:23 -07:00
parent 91b4873b79
commit e91e432496
10 changed files with 516 additions and 258 deletions
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170
src/math/lp/nla_grobner.cpp
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@ -11,6 +11,7 @@ Author:
--*/
#include "util/uint_set.h"
#include "params/smt_params_helper.hpp"
#include "math/lp/nla_core.h"
#include "math/lp/factorization_factory_imp.h"
#include "math/grobner/pdd_solver.h"
@ -27,6 +28,11 @@ namespace nla {
m_quota(m_core.params().arith_nl_gr_q())
{}
void grobner::updt_params(params_ref const& p) {
smt_params_helper ph(p);
m_config.m_propagate_quotients = ph.arith_nl_grobner_propagate_quotients();
}
lp::lp_settings& grobner::lp_settings() {
return c().lp_settings();
}
@ -72,6 +78,10 @@ namespace nla {
if (propagate_linear_equations())
return;
if (propagate_quotients())
return;
IF_VERBOSE(0, m_solver.display(verbose_stream() << "grobner\n"));
}
catch (...) {
@ -181,23 +191,12 @@ namespace nla {
// IF_VERBOSE(0, verbose_stream() << "factored " << q << " : " << vars << "\n");
term t;
rational lc(1);
auto ql = q;
while (!ql.is_val()) {
lc = lcm(lc, denominator(ql.hi().val()));
ql = ql.lo();
}
lc = lcm(denominator(ql.val()), lc);
auto [t, offset] = linear_to_term(q);
while (!q.is_val()) {
t.add_monomial(lc*q.hi().val(), q.var());
q = q.lo();
}
vector<ineq> ineqs;
for (auto v : vars)
ineqs.push_back(ineq(v, llc::EQ, rational::zero()));
ineqs.push_back(ineq(t, llc::EQ, -lc*q.val()));
ineqs.push_back(ineq(t, llc::EQ, -offset));
for (auto const& i : ineqs)
if (c().ineq_holds(i))
return false;
@ -210,6 +209,151 @@ namespace nla {
return true;
}
std::pair<lp::lar_term, rational> grobner::linear_to_term(dd::pdd q) {
SASSERT(q.is_linear());
rational lc(1);
auto ql = q;
lp::lar_term t;
while (!ql.is_val()) {
lc = lcm(lc, denominator(ql.hi().val()));
ql = ql.lo();
}
lc = lcm(denominator(ql.val()), lc);
while (!q.is_val()) {
t.add_monomial(lc * q.hi().val(), q.var());
q = q.lo();
}
rational offset = lc * q.val();
return {t, offset};
}
bool grobner::propagate_quotients() {
if (!m_config.m_propagate_quotients)
return false;
unsigned changed = 0;
for (auto eq : m_solver.equations())
if (propagate_quotients(*eq) && ++changed >= m_solver.number_of_conflicts_to_report())
return true;
return changed > 0;
}
// factor each nl var at a time.
// x*y + z = 0
// x = 0 => z = 0
// y = 0 => z = 0
// z = 0 => x = 0 or y = 0
// z > 0 & x > 0 => x <= z
// z < 0 & x > 0 => x <= -z
// z > 0 & x < 0 => -x <= z
// z < 0 & x < 0 => -x <= -z
bool grobner::propagate_quotients(dd::solver::equation const& eq) {
dd::pdd const& p = eq.poly();
if (p.is_linear())
return false;
if (p.is_val())
return false;
auto v = p.var();
if (!c().var_is_int(v))
return false;
for (auto v : p.free_vars())
if (!c().var_is_int(v))
return false;
tracked_uint_set nl_vars;
for (auto const& m : p) {
if (m.vars.size() == 1)
continue;
for (auto j : m.vars)
nl_vars.insert(j);
}
dd::pdd_eval eval;
eval.var2val() = [&](unsigned j) { return val(j); };
for (auto v : nl_vars) {
auto& m = p.manager();
dd::pdd lc(m), r(m);
p.factor(v, 1, lc, r);
if (!r.is_linear())
continue;
auto v_value = val(v);
auto r_value = eval(r);
auto lc_value = eval(lc);
if (r_value == 0) {
if (v_value == 0)
continue;
if (lc_value == 0)
continue;
if (!lc.is_linear())
continue;
auto [t, offset] = linear_to_term(lc);
auto [t2, offset2] = linear_to_term(r);
lemma_builder lemma(c(), "pdd-quotient");
add_dependencies(lemma, eq);
// v = 0 or lc = 0 or r != 0
lemma |= ineq(v, llc::EQ, rational::zero());
lemma |= ineq(t, llc::EQ, -offset);
lemma |= ineq(t2, llc::NE, -offset2);
return true;
}
// r_value != 0
if (v_value == 0) {
// v = 0 => r = 0
lemma_builder lemma(c(), "pdd-quotient");
add_dependencies(lemma, eq);
auto [t, offset] = linear_to_term(r);
lemma |= ineq(v, llc::NE, rational::zero());
lemma |= ineq(t, llc::EQ, -offset);
return true;
}
if (lc_value == 0) {
if (!lc.is_linear())
continue;
// lc = 0 => r = 0
lemma_builder lemma(c(), "pdd-quotient");
add_dependencies(lemma, eq);
auto [t, offset] = linear_to_term(lc);
auto [t2, offset2] = linear_to_term(r);
lemma |= ineq(t, llc::NE, -offset);
lemma |= ineq(t2, llc::EQ, -offset2);
return true;
}
if (divides(v_value, r_value))
continue;
if (abs(v_value) > abs(r_value)) {
// v*c + r = 0 & v > 0 => r >= v or -r >= v or r = 0
lemma_builder lemma(c(), "pdd-quotient");
auto [t, offset] = linear_to_term(r);
add_dependencies(lemma, eq);
if (v_value > 0) {
lemma |= ineq(v, llc::LE, rational::zero());
lemma |= ineq(t, llc::EQ, -offset);
t.add_monomial(rational(-1), v);
lemma |= ineq(t, llc::GE, -offset);
auto [t2, offset2] = linear_to_term(-r);
t2.add_monomial(rational(-1), v);
lemma |= ineq(t2, llc::GE, -offset2);
}
else {
// v*lc + r = 0 & v < 0 => r <= v or -r <= v or r = 0
lemma |= ineq(v, llc::GE, rational::zero());
lemma |= ineq(t, llc::EQ, -offset);
t.add_monomial(rational(-1), v);
lemma |= ineq(t, llc::LE, -offset);
auto [t2, offset2] = linear_to_term(-r);
t2.add_monomial(rational(-1), v);
lemma |= ineq(t2, llc::LE, -offset2);
}
return true;
}
// other division lemmas are possible.
// also extend to non-linear r, non-linear lc
}
return false;
}
void grobner::explain(dd::solver::equation const& eq, lp::explanation& exp) {
u_dependency_manager dm;
vector<unsigned, false> lv;