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remove nex grobner
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
2334ed5b66
commit
496a8c17aa
7 changed files with 3 additions and 996 deletions
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@ -1,746 +0,0 @@
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/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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<name>
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Abstract:
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<abstract>
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Author:
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Nikolaj Bjorner (nbjorner)
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Lev Nachmanson (levnach)
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Revision History:
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--*/
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#include "math/lp/nla_grobner.h"
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#include "math/lp/nla_core.h"
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#include "math/lp/factorization_factory_imp.h"
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using namespace nla;
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grobner::grobner(core *c, intervals *s)
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: common(c, s),
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m_gc(m_nex_creator, c->m_reslim) {
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std::function<void (lp::explanation const& e, std::ostream & out)> de;
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de = [this](lp::explanation const& e, std::ostream& out) { m_core->print_explanation(e, out); };
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grobner_core::params p;
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p.m_expr_size_limit = c->m_nla_settings.grobner_expr_size_limit();
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p.m_grobner_eqs_threshold = c->m_nla_settings.grobner_eqs_threshold();
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m_gc = de;
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m_gc = p;
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}
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void grobner::grobner_lemmas() {
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c().lp_settings().stats().m_grobner_calls++;
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m_reported = 0;
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TRACE("grobner", tout << "before:\n"; display(tout););
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m_gc.compute_basis_loop();
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for (grobner_core::equation* e : m_gc.equations()) {
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check_eq(e);
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}
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TRACE("grobner", tout << "after:\n"; display(tout););
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}
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void grobner::check_eq(grobner_core::equation* target) {
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if (m_intervals->check_nex(target->expr(), target->dep())) {
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TRACE("grobner", tout << "created a lemma for "; m_gc.display_equation(tout, *target) << "\n";
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tout << "vars = \n";
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for (lpvar j : get_vars_of_expr(target->expr())) {
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c().print_var(j, tout);
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}
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tout << "\ntarget->expr() val = " << get_nex_val(target->expr(), [this](unsigned j) { return c().val(j); }) << "\n";);
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c().lp_settings().stats().m_grobner_conflicts++;
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}
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}
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void grobner::add_row(const vector<lp::row_cell<rational>> & row) {
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TRACE("grobner", tout << "adding row to gb\n"; c().m_lar_solver.print_row(row, tout) << '\n';
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for (auto p : row) c().print_var(p.var(), tout) << "\n"; );
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nex_creator::sum_factory sf(m_nex_creator);
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u_dependency* dep = create_sum_from_row(row, m_nex_creator, sf, &m_gc.dep());
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nex* e = m_nex_creator.simplify(sf.mk());
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TRACE("grobner", tout << "e = " << *e << "\n";);
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m_gc.assert_eq_0(e, dep);
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}
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/// -------------------------------
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/// grobner_core
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/***
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The main algorithm maintains two sets (S, A),
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where S is m_to_superpose, and A is m_to_simplify.
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Initially S is empty and A contains the initial equations.
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Each step proceeds as follows:
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- pick a in A, and remove a from A
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- simplify a using S
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- simplify S using a
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- for s in S:
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b = superpose(a, s)
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add b to A
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- add a to S
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- simplify A using a
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*/
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void grobner::init() {
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m_gc.reset();
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}
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bool grobner_core::compute_basis_loop() {
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while (!done()) {
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if (compute_basis_step()) {
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TRACE("grobner", tout << "progress in compute_basis_step\n";);
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return true;
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}
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TRACE("grobner", tout << "continue compute_basis_loop\n";);
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}
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TRACE("grobner", tout << "return false from compute_basis_loop\n";);
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TRACE("grobner_stats", print_stats(tout););
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return false;
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}
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// return true iff cannot pick_next()
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bool grobner_core::compute_basis_step() {
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equation* eq = pick_next();
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if (!eq) {
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TRACE("grobner", tout << "cannot pick an equation\n";);
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return true;
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}
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m_stats.m_compute_steps++;
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simplify_eq_by_using_to_superpose(*eq);
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if (equation_is_too_complex(eq)) {
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return false;
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}
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if (!simplify_to_superpose_with_eq(eq)) {
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return false;
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}
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TRACE("grobner", tout << "eq = "; display_equation(tout, *eq););
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superpose(eq);
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if (equation_is_too_complex(eq)) {
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TRACE("grobner", display_equation(tout, *eq) << " is too complex: deleting it\n;";);
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del_equation(eq);
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return false;
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}
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insert_to_superpose(eq);
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simplify_m_to_simplify(eq);
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TRACE("grobner", tout << "end of iteration:\n"; display(tout););
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return false;
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}
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grobner_core::equation* grobner_core::pick_next() {
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equation* r = nullptr;
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ptr_buffer<equation> to_delete;
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for (equation* curr : m_to_simplify) {
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if (is_trivial(curr))
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to_delete.push_back(curr);
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else if (is_simpler(curr, r)) {
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TRACE("grobner", tout << "preferring " << *(curr->expr()) << "\n";);;
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r = curr;
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}
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}
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for (equation* e : to_delete)
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del_equation(e);
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if (r)
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m_to_simplify.erase(r);
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TRACE("grobner", tout << "selected equation: "; if (!r) tout << "<null>\n"; else tout << *r->expr() << "\n";);
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return r;
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}
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void grobner_core::simplify_eq_by_using_to_superpose(equation& eq) {
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bool simplified;
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TRACE("grobner", tout << "simplifying: "; display_equation(tout, eq); tout << "using equalities of m_to_superpose of size " << m_to_superpose.size() << "\n";);
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do {
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simplified = false;
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for (equation* p : m_to_superpose) {
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if (simplify_source_target(*p, eq)) {
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simplified = true;
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}
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if (canceled() || eq.expr()->is_scalar()) {
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break;
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}
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}
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} while (simplified && !eq.expr()->is_scalar());
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TRACE("grobner",
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if (simplified) { tout << "simplification result: "; display_equation(tout, eq); }
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else { tout << "no simplification\n"; });
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}
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concat<grobner_core::equation_set, grobner_core::equation_set, grobner_core::equation*> grobner_core::equations() {
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return concat<grobner_core::equation_set, grobner_core::equation_set, grobner_core::equation*>(m_to_superpose, m_to_simplify);
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}
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void grobner_core::reset() {
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del_equations(0);
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m_nex_creator.pop(0);
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SASSERT(m_equations_to_delete.empty());
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m_to_superpose.reset();
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m_to_simplify.reset();
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m_stats.reset();
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}
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// Return true if the equation is of the form 0 = 0.
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bool grobner_core::is_trivial(equation* eq) const {
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return eq->expr()->is_scalar() && eq->expr()->to_scalar().value().is_zero();
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}
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// returns true if eq1 is simpler than eq2
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bool grobner_core::is_simpler(equation * eq1, equation * eq2) {
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if (!eq2)
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return true;
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if (is_trivial(eq1))
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return true;
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if (is_trivial(eq2))
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return false;
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return m_nex_creator.gt(eq2->expr(), eq1->expr());
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}
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void grobner_core::del_equation(equation * eq) {
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m_to_superpose.erase(eq);
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m_to_simplify.erase(eq);
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SASSERT(m_equations_to_delete[eq->m_bidx] == eq);
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m_equations_to_delete[eq->m_bidx] = nullptr;
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dealloc(eq);
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}
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const nex* grobner_core::get_highest_monomial(const nex* e) const {
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switch (e->type()) {
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case expr_type::MUL:
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return e;
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case expr_type::SUM:
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return e->to_sum()[0];
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case expr_type::VAR:
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return e;
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default:
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TRACE("grobner", tout << *e << "\n";);
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return nullptr;
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}
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}
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// source 3f + k + l = 0, so f = (-k - l)/3
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// target 2fg + 3fp + e = 0
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// target is replaced by 2(-k/3 - l/3)g + 3(-k/3 - l/3)p + e = -2/3kg -2/3lg - kp -lp + e
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bool grobner_core::simplify_target_monomials(equation const& source, equation& target) {
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nex const* high_mon = get_highest_monomial(source.expr());
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if (high_mon == nullptr)
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return false;
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SASSERT(high_mon->all_factors_are_elementary());
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TRACE("grobner_d", tout << "source = "; display_equation(tout, source) << "target = "; display_equation(tout, target) << "high_mon = " << *high_mon << "\n";);
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nex * te = target.m_expr;
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nex_sum * targ_sum;
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if (te->is_sum()) {
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targ_sum = to_sum(te);
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} else if (te->is_mul()) {
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targ_sum = m_nex_creator.mk_sum(te);
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} else {
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TRACE("grobner_d", tout << "return false\n";);
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return false;
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}
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return simplify_target_monomials_sum(source, target, *targ_sum, *high_mon);
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}
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unsigned grobner_core::find_divisible(nex_sum const& targ_sum, const nex& high_mon) const {
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unsigned j = 0;
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for (auto t : targ_sum) {
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if (divide_ignore_coeffs_check_only(*t, high_mon)) {
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TRACE("grobner_d", tout << "yes div: " << *t << " / " << high_mon << "\n";);
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return j;
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}
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++j;
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}
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TRACE("grobner_d", tout << "no div: " << targ_sum << " / " << high_mon << "\n";);
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return -1;
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}
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bool grobner_core::simplify_target_monomials_sum(equation const& source,
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equation& target, nex_sum& targ_sum,
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const nex& high_mon) {
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unsigned j = find_divisible(targ_sum, high_mon);
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if (j + 1 == 0)
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return false;
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m_changed_leading_term = (j == 0);
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unsigned targ_orig_size = targ_sum.size();
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simplify_target_monomials_sum_j(source, target, targ_sum, high_mon, j, false); // false to avoid divisibility test
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for (j++; j < targ_orig_size; j++) {
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simplify_target_monomials_sum_j(source, target, targ_sum, high_mon, j, true);
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}
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TRACE("grobner_d", tout << "targ_sum = " << targ_sum << "\n";);
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target.m_expr = m_nex_creator.simplify(&targ_sum);
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target.m_dep = m_dep_manager.mk_join(source.dep(), target.dep());
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TRACE("grobner_d", tout << "target = "; display_equation(tout, target););
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return true;
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}
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bool grobner_core::divide_ignore_coeffs_check_only_nex_mul(nex_mul const& t, const nex& h) const {
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TRACE("grobner_d", tout << "t = " << t << ", h=" << h << "\n";);
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SASSERT(m_nex_creator.is_simplified(t) && m_nex_creator.is_simplified(h));
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unsigned j = 0; // points to t
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for(unsigned k = 0; k < h.number_of_child_powers(); k++) {
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lpvar h_var = h.get_child_exp(k)->to_var().var();
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bool p_swallowed = false;
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for (; j < t.size() && !p_swallowed; j++) {
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const nex_pow& tp = t[j];
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if (tp.e()->to_var().var() == h_var) {
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if (tp.pow() >= h.get_child_pow(k)) {
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p_swallowed = true;
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}
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}
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}
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if (!p_swallowed) {
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TRACE("grobner_d", tout << "no div " << t << " / " << h << "\n";);
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return false;
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}
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}
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TRACE("grobner_d", tout << "division " << t << " / " << h << "\n";);
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return true;
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}
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// return true if h divides n
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bool grobner_core::divide_ignore_coeffs_check_only(nex const& n , const nex& h) const {
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if (n.is_mul())
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return divide_ignore_coeffs_check_only_nex_mul(n.to_mul(), h);
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if (!n.is_var())
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return false;
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const nex_var& v = n.to_var();
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if (h.is_var()) {
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return v.var() == h.to_var().var();
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}
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if (h.is_mul()) {
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if (h.number_of_child_powers() > 1)
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return false;
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if (h.get_child_pow(0) != 1)
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return false;
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const nex* e = h.get_child_exp(0);
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return e->is_var() && e->to_var().var() == v.var();
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}
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return false;
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}
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nex_mul * grobner_core::divide_ignore_coeffs_perform_nex_mul(nex_mul const& t, const nex& h) {
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m_nex_creator.m_mk_mul.reset();
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unsigned j = 0; // j points to t and k runs over h
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for(unsigned k = 0; k < h.number_of_child_powers(); k++) {
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lpvar h_var = to_var(h.get_child_exp(k))->var();
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for (; j < t.size(); j++) {
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auto const &tp = t[j];
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if (tp.e()->to_var().var() == h_var) {
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unsigned h_pow = h.get_child_pow(k);
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SASSERT(tp.pow() >= h_pow);
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j++;
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if (tp.pow() > h_pow) {
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m_nex_creator.m_mk_mul *= nex_pow(tp.e(), tp.pow() - h_pow);
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}
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break;
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} else {
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m_nex_creator.m_mk_mul *= tp;
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}
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}
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}
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for (; j < t.size(); j++) {
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m_nex_creator.m_mk_mul *= t[j];
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}
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nex_mul* r = m_nex_creator.m_mk_mul.mk();
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TRACE("grobner", tout << "r = " << *r << " = " << t << " / " << h << "\n";);
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TRACE("grobner_d", tout << "r = " << *r << " = " << t << " / " << h << "\n";);
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return r;
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}
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// perform the division t / h, but ignores the coefficients
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// h does not change
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nex_mul * grobner_core::divide_ignore_coeffs_perform(nex* e, const nex& h) {
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if (e->is_mul())
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return divide_ignore_coeffs_perform_nex_mul(e->to_mul(), h);
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SASSERT(e->is_var());
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return m_nex_creator.mk_mul(); // return the empty nex_mul
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}
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// if targ_sum->children()[j] = c*high_mon*p,
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// and b*high_mon + e = 0, so high_mon = -e/b
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// then targ_sum->children()[j] = - (c/b) * e*p
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void grobner_core::simplify_target_monomials_sum_j(equation const& source, equation& target, nex_sum& targ_sum, const nex& high_mon, unsigned j, bool test_divisibility) {
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nex * ej = targ_sum[j];
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TRACE("grobner_d", tout << "high_mon = " << high_mon << ", ej = " << *ej << "\n";);
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if (test_divisibility && !divide_ignore_coeffs_check_only(*ej, high_mon)) {
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TRACE("grobner_d", tout << "no div\n";);
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return;
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}
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nex_mul * ej_over_high_mon = divide_ignore_coeffs_perform(ej, high_mon);
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TRACE("grobner_d", tout << "ej_over_high_mon = " << *ej_over_high_mon << "\n";);
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rational c = ej->is_mul() ? to_mul(ej)->coeff() : rational(1);
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TRACE("grobner_d", tout << "c = " << c << "\n";);
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nex_creator::sum_factory sf(m_nex_creator);
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add_mul_skip_first(sf ,-c/high_mon.coeff(), source.expr(), ej_over_high_mon);
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targ_sum[j] = sf.mk();
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TRACE("grobner_d", tout << "targ_sum = " << targ_sum << "\n";);
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}
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// return true iff simplified
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bool grobner_core::simplify_source_target(equation const& source, equation& target) {
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TRACE("grobner", tout << "simplifying: "; display_equation(tout, target); tout << "\nusing: "; display_equation(tout, source););
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TRACE("grobner_d", tout << "simplifying: " << *(target.expr()) << " using " << *(source.expr()) << "\n";);
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SASSERT(m_nex_creator.is_simplified(*source.expr()) && !equation_is_too_complex(&source));
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if (equation_is_too_complex(&target))
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return false;
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SASSERT(m_nex_creator.is_simplified(*target.expr()));
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if (target.expr()->is_scalar()) {
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TRACE("grobner_d", tout << "no simplification\n";);
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return false;
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}
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if (source.get_num_monomials() == 0) {
|
||||
TRACE("grobner_d", tout << "no simplification\n";);
|
||||
return false;
|
||||
}
|
||||
m_stats.m_simplified++;
|
||||
bool result = false;
|
||||
while (!canceled() && simplify_target_monomials(source, target)) {
|
||||
TRACE("grobner", tout << "simplified target = "; display_equation(tout, target) << "\n";);
|
||||
result = true;
|
||||
}
|
||||
if (result) {
|
||||
target.m_dep = m_dep_manager.mk_join(target.dep(), source.dep());
|
||||
update_stats_max_degree_and_size(&target);
|
||||
TRACE("grobner", tout << "simplified "; display_equation(tout, target) << "\n";);
|
||||
TRACE("grobner_d", tout << "simplified to " << *(target.expr()) << "\n";);
|
||||
return true;
|
||||
}
|
||||
TRACE("grobner_d", tout << "no simplification\n";);
|
||||
return false;
|
||||
}
|
||||
|
||||
void grobner_core::process_simplified_target(equation* target, ptr_buffer<equation>& to_remove) {
|
||||
if (is_trivial(target) || equation_is_too_complex(target)) {
|
||||
to_remove.push_back(target);
|
||||
} else if (m_changed_leading_term) {
|
||||
insert_to_simplify(target);
|
||||
to_remove.push_back(target);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
bool grobner_core::simplify_to_superpose_with_eq(equation* eq) {
|
||||
TRACE("grobner_d", tout << "eq->exp " << *(eq->expr()) << "\n";);
|
||||
SASSERT(!equation_is_too_complex(eq));
|
||||
ptr_buffer<equation> to_remove;
|
||||
ptr_buffer<equation> to_delete;
|
||||
for (equation * target : m_to_superpose) {
|
||||
if (canceled() || done())
|
||||
break;
|
||||
m_changed_leading_term = false;
|
||||
// if the leading term is simplified, then the equation has to be moved to m_to_simplify
|
||||
if (simplify_source_target(*eq, *target)) {
|
||||
process_simplified_target(target, to_remove);
|
||||
}
|
||||
if (is_trivial(target)||equation_is_too_complex(target)) {
|
||||
to_delete.push_back(target);
|
||||
}
|
||||
else {
|
||||
SASSERT(m_nex_creator.is_simplified(*target->expr()));
|
||||
}
|
||||
}
|
||||
|
||||
for (equation* eq : to_remove)
|
||||
m_to_superpose.erase(eq);
|
||||
for (equation* eq : to_delete)
|
||||
del_equation(eq);
|
||||
return !canceled();
|
||||
}
|
||||
|
||||
/*
|
||||
Use the given equation to simplify m_to_simplify equations
|
||||
*/
|
||||
void grobner_core::simplify_m_to_simplify(equation* eq) {
|
||||
TRACE("grobner_d", tout << "eq->exp " << *(eq->expr()) << "\n";);
|
||||
ptr_buffer<equation> to_delete;
|
||||
for (equation* target : m_to_simplify) {
|
||||
if (simplify_source_target(*eq, *target) && (is_trivial(target) || equation_is_too_complex(target)))
|
||||
to_delete.push_back(target);
|
||||
}
|
||||
for (equation* eq : to_delete)
|
||||
del_equation(eq);
|
||||
}
|
||||
|
||||
// if e is the sum then add to r all children of e multiplied by beta, except the first one
|
||||
// which corresponds to the highest monomial,
|
||||
// otherwise do nothing
|
||||
void grobner_core::add_mul_skip_first(nex_creator::sum_factory& sf, const rational& beta, nex const*e, nex_mul* c) {
|
||||
if (e->is_sum()) {
|
||||
nex_sum const & es = e->to_sum();
|
||||
for (unsigned j = 1; j < es.size(); j++) {
|
||||
sf += m_nex_creator.mk_mul(beta, es[j], c);
|
||||
}
|
||||
} else {
|
||||
TRACE("grobner_d", tout << "e = " << *e << "\n";);
|
||||
}
|
||||
}
|
||||
|
||||
// let e1: alpha*ab+q=0, and e2: beta*ac+e=0, then beta*qc - alpha*eb = 0
|
||||
nex * grobner_core::expr_superpose(nex const* e1, nex const* e2, const nex* ab, const nex* ac, nex_mul* b, nex_mul* c) {
|
||||
TRACE("grobner", tout << "e1 = " << *e1 << "\ne2 = " << *e2 <<"\n";);
|
||||
nex_creator::sum_factory sf(m_nex_creator);
|
||||
rational alpha = - ab->coeff();
|
||||
TRACE("grobner", tout << "e2 *= " << alpha << "*(" << *b << ")\n";);
|
||||
add_mul_skip_first(sf, alpha, e2, b);
|
||||
rational beta = ac->coeff();
|
||||
TRACE("grobner", tout << "e1 *= " << beta << "*(" << *c << ")\n";);
|
||||
add_mul_skip_first(sf, beta, e1, c);
|
||||
nex * ret = m_nex_creator.simplify(sf.mk());
|
||||
TRACE("grobner", tout << "e1 = " << *e1 << "\ne2 = " << *e2 <<"\nsuperpose = " << *ret << "\n";);
|
||||
CTRACE("grobner", ret->is_scalar(), tout << "\n";);
|
||||
return ret;
|
||||
}
|
||||
|
||||
// let eq1: ab+q=0, and eq2: ac+e=0, then qc - eb = 0
|
||||
void grobner_core::superpose(equation * eq1, equation * eq2) {
|
||||
TRACE("grobner_d", tout << "eq1="; display_equation(tout, *eq1) << "eq2="; display_equation(tout, *eq2););
|
||||
const nex * ab = get_highest_monomial(eq1->expr());
|
||||
const nex * ac = get_highest_monomial(eq2->expr());
|
||||
nex_mul *b = nullptr, *c = nullptr;
|
||||
TRACE("grobner_d", tout << "ab="; if(ab) { tout << *ab; } else { tout << "null"; };
|
||||
tout << " , " << " ac="; if(ac) { tout << *ac; } else { tout << "null"; }; tout << "\n";);
|
||||
if (!find_b_c(ab, ac, b, c)) {
|
||||
TRACE("grobner_d", tout << "there is no non-trivial common divider, no superposing\n";);
|
||||
return;
|
||||
}
|
||||
equation* eq = alloc(equation);
|
||||
TRACE("grobner_d", tout << "eq1="; display_equation(tout, *eq1) << "eq2="; display_equation(tout, *eq2););
|
||||
init_equation(eq, expr_superpose(eq1->expr(), eq2->expr(), ab, ac, b, c), m_dep_manager.mk_join(eq1->dep(), eq2->dep()));
|
||||
if (m_nex_creator.gt(eq->expr(), eq1->expr()) || m_nex_creator.gt(eq->expr(), eq2->expr()) ||
|
||||
equation_is_too_complex(eq)) {
|
||||
TRACE("grobner", display_equation(tout, *eq) << " is too complex: deleting it\n;";);
|
||||
del_equation(eq);
|
||||
} else {
|
||||
m_stats.m_superposed++;
|
||||
update_stats_max_degree_and_size(eq);
|
||||
insert_to_simplify(eq);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Let a be the greatest common divider of ab and bc,
|
||||
// then ab/a is stored in b, and ac/a is stored in c
|
||||
bool grobner_core::find_b_c(const nex* ab, const nex* ac, nex_mul*& b, nex_mul*& c) {
|
||||
if (!find_b_c_check_only(ab, ac))
|
||||
return false;
|
||||
nex_creator::mul_factory fb(m_nex_creator), fc(m_nex_creator);
|
||||
unsigned ab_size = ab->number_of_child_powers();
|
||||
unsigned ac_size = ac->number_of_child_powers();
|
||||
unsigned i = 0, j = 0;
|
||||
for (;;) {
|
||||
const nex* m = ab->get_child_exp(i);
|
||||
const nex* n = ac->get_child_exp(j);
|
||||
if (m_nex_creator.gt(m, n)) {
|
||||
fb *= nex_pow(const_cast<nex*>(m), ab->get_child_pow(i));
|
||||
if (++i == ab_size)
|
||||
break;
|
||||
} else if (m_nex_creator.gt(n, m)) {
|
||||
fc *= nex_pow(const_cast<nex*>(n), ac->get_child_pow(j));
|
||||
if (++j == ac_size)
|
||||
break;
|
||||
} else {
|
||||
unsigned b_pow = ab->get_child_pow(i);
|
||||
unsigned c_pow = ac->get_child_pow(j);
|
||||
if (b_pow > c_pow) {
|
||||
fb *= nex_pow(const_cast<nex*>(m), b_pow - c_pow);
|
||||
} else if (c_pow > b_pow) {
|
||||
fc *= nex_pow(const_cast<nex*>(n), c_pow - b_pow);
|
||||
} // otherwise the power are equal and no child added to either b or c
|
||||
i++; j++;
|
||||
|
||||
if (i == ab_size || j == ac_size) {
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
while (i != ab_size) {
|
||||
fb *= nex_pow(const_cast<nex*>(ab->get_child_exp(i)), ab->get_child_pow(i));
|
||||
i++;
|
||||
}
|
||||
while (j != ac_size) {
|
||||
fc *= nex_pow(const_cast<nex*>(ac->get_child_exp(j)), ac->get_child_pow(j));
|
||||
j++;
|
||||
}
|
||||
b = fb.mk();
|
||||
c = fc.mk();
|
||||
TRACE("nla_grobner", tout << "b=" << *b << ", c=" <<*c << "\n";);
|
||||
SASSERT(test_find_b_c(ab, ac, b, c));
|
||||
return true;
|
||||
}
|
||||
|
||||
// Finds out if ab and bc have a non-trivial common divider
|
||||
bool grobner_core::find_b_c_check_only(const nex* ab, const nex* ac) const {
|
||||
if (ab == nullptr || ac == nullptr)
|
||||
return false;
|
||||
SASSERT(m_nex_creator.is_simplified(*ab) && m_nex_creator.is_simplified(*ac));
|
||||
unsigned i = 0, j = 0; // i points to ab, j points to ac
|
||||
for (;;) {
|
||||
const nex* m = ab->get_child_exp(i);
|
||||
const nex* n = ac->get_child_exp(j);
|
||||
if (m_nex_creator.gt(m , n)) {
|
||||
i++;
|
||||
if (i == ab->number_of_child_powers())
|
||||
return false;
|
||||
} else if (m_nex_creator.gt(n, m)) {
|
||||
j++;
|
||||
if (j == ac->number_of_child_powers())
|
||||
return false;
|
||||
} else {
|
||||
TRACE("grobner", tout << "found common " << *m << "\n";);
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
TRACE("grobner", tout << "not found common " << " in " << *ab << " and " << *ac << "\n";);
|
||||
return false;
|
||||
}
|
||||
|
||||
void grobner_core::superpose(equation * eq) {
|
||||
for (equation * target : m_to_superpose) {
|
||||
superpose(eq, target);
|
||||
}
|
||||
}
|
||||
|
||||
bool grobner_core::canceled() {
|
||||
return m_limit.get_cancel_flag();
|
||||
}
|
||||
|
||||
bool grobner_core::done() {
|
||||
return num_of_equations() >= m_params.m_grobner_eqs_threshold || canceled();
|
||||
}
|
||||
|
||||
void grobner_core::del_equations(unsigned old_size) {
|
||||
TRACE("grobner", );
|
||||
SASSERT(m_equations_to_delete.size() >= old_size);
|
||||
for (unsigned i = m_equations_to_delete.size(); i-- > old_size; ) {
|
||||
equation* eq = m_equations_to_delete[i];
|
||||
if (eq)
|
||||
del_equation(eq);
|
||||
}
|
||||
m_equations_to_delete.shrink(old_size);
|
||||
}
|
||||
|
||||
std::ostream& grobner_core::print_stats(std::ostream & out) const {
|
||||
return out << "stats:\nsteps = " << m_stats.m_compute_steps << "\nsimplified: " <<
|
||||
m_stats.m_simplified << "\nsuperposed: " <<
|
||||
m_stats.m_superposed << "\nexpr degree: " << m_stats.m_max_expr_degree <<
|
||||
"\nexpr size: " << m_stats.m_max_expr_size << "\n";
|
||||
}
|
||||
|
||||
void grobner_core::update_stats_max_degree_and_size(const equation *e) {
|
||||
if (m_stats.m_max_expr_size < e->expr()->size()) {
|
||||
TRACE("grobner_stats_d", tout << "expr size = " << e->expr()->size() << "\n";);
|
||||
TRACE("grobner_stats_d", display_equation(tout, *e););
|
||||
|
||||
m_stats.m_max_expr_size = e->expr()->size();
|
||||
}
|
||||
auto deg = e->expr()->get_degree();
|
||||
if (m_stats.m_max_expr_degree < deg) {
|
||||
TRACE("grobner_stats_d", tout << "expr degree = " << deg << "\n";);
|
||||
m_stats.m_max_expr_degree = deg;
|
||||
}
|
||||
}
|
||||
|
||||
void grobner_core::display_equations(std::ostream & out, equation_set const & v, char const * header) const {
|
||||
out << header << "\n";
|
||||
for (const equation* e : v)
|
||||
display_equation(out, *e);
|
||||
}
|
||||
|
||||
void grobner_core::display_equations_no_deps(std::ostream & out, equation_set const & v, char const * header) const {
|
||||
out << header << "\n";
|
||||
for (const equation* e : v)
|
||||
out << *(e->expr()) << "\n";
|
||||
}
|
||||
|
||||
std::ostream& grobner_core::display_equation(std::ostream & out, const equation & eq) const {
|
||||
out << "expr = " << *eq.expr() << "\n";
|
||||
return display_dependency(out, eq.dep());
|
||||
}
|
||||
|
||||
std::ostream& grobner_core::display(std::ostream& out) const {
|
||||
display_equations_no_deps(out, m_to_superpose, "m_to_superpose:");
|
||||
display_equations_no_deps(out, m_to_simplify, "m_to_simplify:");
|
||||
return out;
|
||||
}
|
||||
|
||||
void grobner_core::assert_eq_0(nex* e, u_dependency * dep) {
|
||||
if (e == nullptr || is_zero_scalar(e))
|
||||
return;
|
||||
equation * eq = alloc(equation);
|
||||
init_equation(eq, e, dep);
|
||||
TRACE("grobner",
|
||||
display_equation(tout, *eq);
|
||||
/*tout << "\nvars\n";
|
||||
for (unsigned j : get_vars_of_expr_with_opening_terms(e)) {
|
||||
c().print_var(j, tout << "(") << ")\n";
|
||||
} */);
|
||||
insert_to_simplify(eq);
|
||||
update_stats_max_degree_and_size(eq);
|
||||
}
|
||||
|
||||
void grobner_core::init_equation(equation* eq, nex*e, u_dependency * dep) {
|
||||
eq->m_bidx = m_equations_to_delete.size();
|
||||
eq->m_dep = dep;
|
||||
eq->m_expr = e;
|
||||
m_equations_to_delete.push_back(eq);
|
||||
SASSERT(m_equations_to_delete[eq->m_bidx] == eq);
|
||||
}
|
||||
|
||||
grobner_core::~grobner_core() {
|
||||
del_equations(0);
|
||||
}
|
||||
|
||||
std::ostream& grobner_core::display_dependency(std::ostream& out, u_dependency* dep) const {
|
||||
svector<lp::constraint_index> expl;
|
||||
m_dep_manager.linearize(dep, expl);
|
||||
lp::explanation e(expl);
|
||||
if (!expl.empty()) {
|
||||
out << "constraints\n";
|
||||
m_print_explanation(e, out);
|
||||
out << "\n";
|
||||
} else {
|
||||
out << "no deps\n";
|
||||
}
|
||||
return out;
|
||||
}
|
||||
|
||||
#ifdef Z3DEBUG
|
||||
bool grobner_core::test_find_b(const nex* ab, const nex_mul* b) {
|
||||
if (ab->is_var()) {
|
||||
return b->size() == 0 || (b->get_degree() == 1 && b->get_child_exp(0)->to_var().var() ==
|
||||
ab->to_var().var());
|
||||
}
|
||||
nex_mul& ab_clone = m_nex_creator.clone(ab)->to_mul();
|
||||
nex_mul * a= divide_ignore_coeffs_perform(&ab_clone, *b);
|
||||
ab_clone.m_coeff = rational(1);
|
||||
SASSERT(b->coeff().is_one());
|
||||
nex * m = m_nex_creator.mk_mul(a, m_nex_creator.clone(b));
|
||||
m = m_nex_creator.simplify(m);
|
||||
return m_nex_creator.equal(m, &ab_clone);
|
||||
}
|
||||
|
||||
bool grobner_core::test_find_b_c(const nex* ab, const nex* ac, const nex_mul* b, const nex_mul* c) {
|
||||
return test_find_b(ab, b) && test_find_b(ac, c);
|
||||
}
|
||||
|
||||
#endif
|
||||
Loading…
Add table
Add a link
Reference in a new issue