mirror of
https://github.com/Z3Prover/z3
synced 2025-10-31 19:52:29 +00:00
add rewrite for mod over negation, refine axioms for grobner quotients
This commit is contained in:
Nikolaj Bjorner
parent
e2235d81d3
commit
a382ddbd8a
4 changed files with 95 additions and 66 deletions
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@ -54,6 +54,7 @@ namespace nla {
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if (m_delay > 0) {
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--m_delay;
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TRACE(grobner, tout << "delay " << m_delay << "\n");
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return;
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}
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@ -71,20 +72,20 @@ namespace nla {
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if (is_conflicting())
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return;
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if (propagate_eqs())
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return;
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if (propagate_factorization())
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return;
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if (propagate_linear_equations())
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return;
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if (propagate_quotients())
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return;
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if (propagate_gcd_test())
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return;
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if (propagate_eqs())
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return;
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if (propagate_factorization())
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return;
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if (propagate_linear_equations())
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return;
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}
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catch (...) {
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@ -147,9 +148,10 @@ namespace nla {
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ineq new_eq(v, llc::EQ, rational::zero());
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if (c().ineq_holds(new_eq))
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return false;
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lemma_builder lemma(c(), "pdd-eq");
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lemma_builder lemma(c(), "grobner-eq");
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add_dependencies(lemma, eq);
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lemma |= new_eq;
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TRACE(grobner, lemma.display(tout););
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return true;
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}
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if (p.is_offset()) {
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@ -164,9 +166,10 @@ namespace nla {
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ineq new_eq(term(a, v), llc::EQ, b);
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if (c().ineq_holds(new_eq))
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return false;
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lemma_builder lemma(c(), "pdd-eq");
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lemma_builder lemma(c(), "grobner-eq");
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add_dependencies(lemma, eq);
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lemma |= new_eq;
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TRACE(grobner, lemma.display(tout););
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return true;
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}
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@ -196,7 +199,7 @@ namespace nla {
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if (c().ineq_holds(i))
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return false;
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lemma_builder lemma(c(), "pdd-factored");
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lemma_builder lemma(c(), "grobner-factored");
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add_dependencies(lemma, eq);
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for (auto const& i : ineqs)
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lemma |= i;
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@ -277,6 +280,8 @@ namespace nla {
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};
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for (auto [x, k] : m_powers) {
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SASSERT(k > 1);
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if (k > 4) // cut off at larger exponents.
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continue;
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bool gcd_fail = true;
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dd::pdd kx = m.mk_var(x) * m.mk_val(k);
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for (unsigned r = 0; gcd_fail && r < k; r++) {
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@ -286,7 +291,7 @@ namespace nla {
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gcd_fail = false;
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}
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if (gcd_fail) {
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lemma_builder lemma(c(), "pdd-power");
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lemma_builder lemma(c(), "grobner-gcd-test");
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add_dependencies(lemma, eq);
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return true;
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}
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@ -329,6 +334,7 @@ namespace nla {
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eval.var2val() = [&](unsigned j) { return val(j); };
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if (eval(p) == 0)
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return false;
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TRACE(grobner, tout << "propagate_quotients " << p << "\n");
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tracked_uint_set nl_vars;
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rational d(1);
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for (auto const& m : p) {
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@ -339,6 +345,7 @@ namespace nla {
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nl_vars.insert(j);
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}
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bool found_lemma = false;
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for (auto v : nl_vars) {
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auto& m = p.manager();
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dd::pdd lc(m), r(m);
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@ -364,70 +371,87 @@ namespace nla {
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continue;
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auto [t, offset] = linear_to_term(lc);
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auto [t2, offset2] = linear_to_term(r);
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lemma_builder lemma(c(), "pdd-quotient");
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lemma_builder lemma(c(), "grobner-quotient");
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add_dependencies(lemma, eq);
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// v = 0 or lc = 0 or r != 0
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lemma |= ineq(v, llc::EQ, rational::zero());
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lemma |= ineq(t, llc::EQ, -offset);
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lemma |= ineq(t2, llc::NE, -offset2);
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return true;
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TRACE(grobner, lemma.display(tout << "quotient1\n"));
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found_lemma = true;
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continue;
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}
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// r_value != 0
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if (v_value == 0) {
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// v = 0 => r = 0
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lemma_builder lemma(c(), "pdd-quotient");
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lemma_builder lemma(c(), "grobner-quotient");
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add_dependencies(lemma, eq);
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auto [t, offset] = linear_to_term(r);
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lemma |= ineq(v, llc::NE, rational::zero());
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lemma |= ineq(t, llc::EQ, -offset);
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return true;
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TRACE(grobner, lemma.display(tout << "quotient2\n"));
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found_lemma = true;
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continue;
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}
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if (lc_value == 0) {
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if (!lc.is_linear())
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continue;
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// lc = 0 => r = 0
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lemma_builder lemma(c(), "pdd-quotient");
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lemma_builder lemma(c(), "grobner-quotient");
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add_dependencies(lemma, eq);
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auto [t, offset] = linear_to_term(lc);
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auto [t2, offset2] = linear_to_term(r);
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lemma |= ineq(t, llc::NE, -offset);
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lemma |= ineq(t2, llc::EQ, -offset2);
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return true;
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TRACE(grobner, lemma.display(tout << "quotient3\n"));
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found_lemma = true;
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continue;
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}
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if (divides(v_value, r_value))
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continue;
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if (abs(v_value) > abs(r_value)) {
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// v*c + r = 0 & v > 0 => r >= v or -r >= v or r = 0
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lemma_builder lemma(c(), "pdd-quotient");
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lemma_builder lemma(c(), "grobner-quotient");
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auto [t, offset] = linear_to_term(r);
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add_dependencies(lemma, eq);
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if (v_value > 0) {
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lemma |= ineq(v, llc::LE, rational::zero());
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lemma |= ineq(t, llc::EQ, -offset);
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if (v_value > 0 && r_value > 0) {
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// v*c + t = 0 => v <= 0 or v <= t or t <= 0
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lemma |= ineq(v, llc::LE, rational::zero()); // v <= 0
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lemma |= ineq(t, llc::LE, -offset); // t <= 0
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t.add_monomial(rational(-1), v);
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lemma |= ineq(t, llc::GE, -offset);
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auto [t2, offset2] = linear_to_term(-r);
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t2.add_monomial(rational(-1), v);
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lemma |= ineq(t2, llc::GE, -offset2);
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lemma |= ineq(t, llc::GE, -offset); // t - v >= 0
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}
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else {
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// v*lc + r = 0 & v < 0 => r <= v or -r <= v or r = 0
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lemma |= ineq(v, llc::GE, rational::zero());
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lemma |= ineq(t, llc::EQ, -offset);
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else if (v_value > 0 && r_value < 0) {
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// v*c + t = 0 => v <= 0 or v <= -t or t >= 0
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lemma |= ineq(v, llc::LE, rational::zero()); // v <= 0
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lemma |= ineq(t, llc::GE, -offset); // t >= 0
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t.add_monomial(rational(1), v);
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lemma |= ineq(t, llc::LE, -offset); // t + v <= 0
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}
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else if (v_value < 0 && r_value > 0) {
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// v*c + t = 0 => v >= 0 or -v <= t or t <= 0
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lemma |= ineq(v, llc::GE, rational::zero()); // v >= 0
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lemma |= ineq(t, llc::LE, -offset); // t <= 0
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t.add_monomial(rational(1), v);
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lemma |= ineq(t, llc::GE, -offset); // t + v >= 0
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}
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else if (v_value < 0 && r_value < 0) {
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// v*c + t = 0 => v >= 0 or v >= t or t >= 0
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lemma |= ineq(v, llc::GE, rational::zero()); // v >= 0
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lemma |= ineq(t, llc::GE, -offset); // t >= 0
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t.add_monomial(rational(-1), v);
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lemma |= ineq(t, llc::LE, -offset);
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auto [t2, offset2] = linear_to_term(-r);
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t2.add_monomial(rational(-1), v);
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lemma |= ineq(t2, llc::LE, -offset2);
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lemma |= ineq(t, llc::LE, -offset); // t - v <= 0
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}
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return true;
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TRACE(grobner, lemma.display(tout << "quotient4\n"));
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found_lemma = true;
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continue;
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}
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// other division lemmas are possible.
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// also extend to non-linear r, non-linear lc
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}
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return false;
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CTRACE(grobner, !found_lemma, tout << "no lemmas found for " << p << "\n");
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return found_lemma;
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}
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void grobner::explain(dd::solver::equation const& eq, lp::explanation& exp) {
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@ -542,24 +566,11 @@ namespace nla {
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};
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scoped_dep_interval i(di), i_wd(di);
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evali.get_interval<dd::w_dep::without_deps>(e.poly(), i);
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if (!di.separated_from_zero(i)) {
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TRACE(grobner, m_solver.display(tout << "not separated from 0 ", e) << "\n";
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evali.get_interval_distributed<dd::w_dep::without_deps>(e.poly(), i);
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tout << "separated from 0: " << di.separated_from_zero(i) << "\n";
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for (auto j : e.poly().free_vars()) {
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scoped_dep_interval a(di);
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c().m_intervals.set_var_interval<dd::w_dep::without_deps>(j, a);
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c().m_intervals.display(tout << "j" << j << " ", a); tout << " ";
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}
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tout << "\n");
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if (add_horner_conflict(e))
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if (!di.separated_from_zero(i)) {
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if (add_horner_conflict(e)) {
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TRACE(grobner, m_solver.display(tout << "horner conflict ", e) << "\n");
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return true;
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#if 0
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if (add_nla_conflict(e))
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return true;
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#endif
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}
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return false;
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}
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evali.get_interval<dd::w_dep::with_deps>(e.poly(), i_wd);
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@ -572,10 +583,6 @@ namespace nla {
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return true;
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}
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else {
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#if 0
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if (add_nla_conflict(e))
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return true;
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#endif
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TRACE(grobner, m_solver.display(tout << "no conflict ", e) << "\n");
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return false;
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}
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@ -662,7 +669,7 @@ namespace nla {
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if (!lra.var_is_int(k))
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continue;
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// free integer columns are ignored unless m_add_all_eqs is set or we are doing gcd test.
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if (!m_add_all_eqs && !m_config.m_gcd_test)
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if (!m_add_all_eqs && !m_config.m_gcd_test && !m_config.m_propagate_quotients)
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continue;
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// a free integer column with integer coefficients can be assigned.
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if (!m_add_all_eqs && all_of(c().lra.get_row(row), [&](auto& ri) { return ri.coeff().is_int();}))
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