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https://github.com/Z3Prover/z3
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extend monomial bounds to handle powers
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
73fa5995d4
commit
b43ed70874
4 changed files with 151 additions and 99 deletions
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@ -11,53 +11,56 @@
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namespace nla {
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struct tangent_imp {
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point m_a;
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point m_b;
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point m_xy;
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rational m_correct_v;
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class tangent_imp {
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point m_a;
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point m_b;
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point m_xy;
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rational m_correct_v;
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// "below" means that the incorrect value is less than the correct one, that is m_v < m_correct_v
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bool m_below;
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rational m_v; // the monomial value
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lpvar m_j; // the monic variable
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const monic& m_m;
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bool m_below;
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rational m_v; // the monomial value
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lpvar m_j; // the monic variable
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const monic& m_m;
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const factor& m_x;
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const factor& m_y;
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lpvar m_jx;
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lpvar m_jy;
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tangents& m_tang;
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bool m_is_mon;
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lpvar m_jx;
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lpvar m_jy;
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tangents& m_tang;
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bool m_is_mon;
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public:
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tangent_imp(point xy,
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const rational& v,
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lpvar j, // the monic variable
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const monic& m,
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const factorization& f,
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tangents& tang) : m_xy(xy),
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m_correct_v(xy.x * xy.y),
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m_below(v < m_correct_v),
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m_v(v),
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m_j(tang.var(m)),
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m_j(m.var()),
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m_m(m),
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m_x(f[0]),
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m_y(f[1]),
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m_jx(tang.var(m_x)),
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m_jy(tang.var(m_y)),
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m_jx(m_x.var()),
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m_jy(m_y.var()),
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m_tang(tang),
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m_is_mon(f.is_mon()) {
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SASSERT(f.size() == 2);
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}
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core & c() { return m_tang.c(); }
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void tangent_lemma_on_bf() {
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get_tang_points();
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TRACE("nla_solver", tout << "tang domain = "; print_tangent_domain(tout) << std::endl;);
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generate_two_tang_lines();
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generate_tang_plane(m_a);
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generate_tang_plane(m_b);
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void operator()() {
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get_points();
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TRACE("nla_solver", print_tangent_domain(tout << "tang domain = ") << std::endl;);
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generate_line1();
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generate_line2();
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generate_plane(m_a);
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generate_plane(m_b);
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}
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private:
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core & c() { return m_tang.c(); }
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void explain(new_lemma& lemma) {
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if (!m_is_mon) {
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lemma &= m_m;
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@ -66,7 +69,7 @@ struct tangent_imp {
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}
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}
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void generate_tang_plane(const point & pl) {
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void generate_plane(const point & pl) {
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new_lemma lemma(c(), "generate tangent plane");
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c().negate_relation(lemma, m_jx, m_x.rat_sign()*pl.x);
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c().negate_relation(lemma, m_jy, m_y.rat_sign()*pl.y);
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@ -86,24 +89,24 @@ struct tangent_imp {
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lemma |= ineq(t, m_below? llc::GT : llc::LT, - pl.x*pl.y);
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explain(lemma);
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}
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void generate_two_tang_lines() {
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{
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new_lemma lemma(c(), "two tangent planes 1");
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// Should be v = val(m_x)*val(m_y), and val(factor) = factor.rat_sign()*var(factor.var())
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lemma |= ineq(m_jx, llc::NE, c().val(m_jx));
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lemma |= ineq(lp::lar_term(m_j, - m_y.rat_sign() * m_xy.x, m_jy), llc::EQ, 0);
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explain(lemma);
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}
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{
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new_lemma lemma(c(), "two tangent planes 2");
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lemma |= ineq(m_jy, llc::NE, c().val(m_jy));
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lemma |= ineq(lp::lar_term(m_j, - m_x.rat_sign() * m_xy.y, m_jx), llc::EQ, 0);
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explain(lemma);
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}
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void generate_line1() {
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new_lemma lemma(c(), "tangent line 1");
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// Should be v = val(m_x)*val(m_y), and val(factor) = factor.rat_sign()*var(factor.var())
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lemma |= ineq(m_jx, llc::NE, c().val(m_jx));
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lemma |= ineq(lp::lar_term(m_j, - m_y.rat_sign() * m_xy.x, m_jy), llc::EQ, 0);
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explain(lemma);
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}
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void generate_line2() {
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new_lemma lemma(c(), "tangent line 2");
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lemma |= ineq(m_jy, llc::NE, c().val(m_jy));
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lemma |= ineq(lp::lar_term(m_j, - m_x.rat_sign() * m_xy.y, m_jx), llc::EQ, 0);
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explain(lemma);
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}
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// Get two planes tangent to surface z = xy, one at point a, and another at point b, creating a cut
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void get_initial_tang_points() {
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void get_initial_points() {
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const rational& x = m_xy.x;
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const rational& y = m_xy.y;
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bool all_ints = m_v.is_int() && x.is_int() && y.is_int();
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@ -130,7 +133,7 @@ struct tangent_imp {
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}
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}
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void push_tang_point(point & a) {
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void push_point(point & a) {
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SASSERT(plane_is_correct_cut(a));
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int steps = 10;
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point del = a - m_xy;
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@ -139,7 +142,7 @@ struct tangent_imp {
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point na = m_xy + del;
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TRACE("nla_solver_tp", tout << "del = " << del << std::endl;);
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if (!plane_is_correct_cut(na)) {
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TRACE("nla_solver_tp", tout << "exit";tout << std::endl;);
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TRACE("nla_solver_tp", tout << "exit\n";);
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return;
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}
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a = na;
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@ -147,25 +150,24 @@ struct tangent_imp {
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}
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rational tang_plane(const point& a) const {
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return a.x * m_xy.y + a.y * m_xy.x - a.x * a.y;
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return a.x * m_xy.y + a.y * m_xy.x - a.x * a.y;
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}
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void get_tang_points() {
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get_initial_tang_points();
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void get_points() {
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get_initial_points();
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TRACE("nla_solver", tout << "xy = " << m_xy << ", correct val = " << m_correct_v;
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tout << "\ntang points:"; print_tangent_domain(tout);tout << std::endl;);
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push_tang_point(m_a);
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TRACE("nla_solver", tout << "pushed a = " << m_a << std::endl;);
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push_tang_point(m_b);
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TRACE("nla_solver", tout << "pushed b = " << m_b << std::endl;);
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print_tangent_domain(tout << "\ntang points:") << std::endl;);
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push_point(m_a);
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push_point(m_b);
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TRACE("nla_solver",
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tout << "tang_plane(a) = " << tang_plane(m_a) << " , val = " << m_v << ", tang_plane(b) = " << tang_plane(m_b) << " , val = " << std::endl;);
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tout << "pushed a = " << m_a << std::endl
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<< "pushed b = " << m_b << std::endl
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<< "tang_plane(a) = " << tang_plane(m_a) << " , val = " << m_a << ", "
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<< "tang_plane(b) = " << tang_plane(m_b) << " , val = " << m_b << std::endl;);
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}
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std::ostream& print_tangent_domain(std::ostream& out) {
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out << "(" << m_a << ", " << m_b << ")";
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return out;
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return out << "(" << m_a << ", " << m_b << ")";
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}
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bool plane_is_correct_cut(const point& plane) const {
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@ -173,7 +175,7 @@ struct tangent_imp {
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tout << "tang_plane() = " << tang_plane(plane) << ", v = " << m_v << ", correct_v = " << m_correct_v << "\n";);
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SASSERT((m_below && m_v < m_correct_v) ||
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((!m_below) && m_v > m_correct_v));
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rational sign = m_below? rational(1) : rational(-1);
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rational sign = rational(m_below ? 1 : -1);
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rational px = tang_plane(plane);
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return ((m_correct_v - px)*sign).is_pos() && !((px - m_v)*sign).is_neg();
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}
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@ -182,21 +184,12 @@ struct tangent_imp {
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tangents::tangents(core * c) : common(c) {}
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void tangents::tangent_lemma() {
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if (!c().m_nla_settings.run_tangents()) {
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TRACE("nla_solver", tout << "not generating tangent lemmas\n";);
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return;
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}
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factorization bf(nullptr);
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const monic* m;
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if (c().find_bfc_to_refine(m, bf)) {
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unsigned j = m->var();
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tangent_imp i(point(val(bf[0]), val(bf[1])),
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c().val(j),
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j,
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*m,
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bf,
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*this);
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i.tangent_lemma_on_bf();
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const monic* m = nullptr;
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if (c().m_nla_settings.run_tangents() && c().find_bfc_to_refine(m, bf)) {
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lpvar j = m->var();
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tangent_imp tangent(point(val(bf[0]), val(bf[1])), c().val(j), *m, bf, *this);
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tangent();
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}
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}
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