mirror of
https://github.com/Z3Prover/z3
synced 2025-04-15 13:28:47 +00:00
875 lines
30 KiB
C++
875 lines
30 KiB
C++
/*++
|
|
Copyright (c) 2017 Microsoft Corporation
|
|
|
|
Module Name:
|
|
|
|
<name>
|
|
|
|
Abstract:
|
|
|
|
<abstract>
|
|
|
|
Author:
|
|
Nikolaj Bjorner (nbjorner)
|
|
Lev Nachmanson (levnach)
|
|
|
|
Revision History:
|
|
|
|
|
|
--*/
|
|
#include "math/lp/nla_grobner.h"
|
|
#include "math/lp/nla_core.h"
|
|
#include "math/lp/factorization_factory_imp.h"
|
|
namespace nla {
|
|
nla_grobner::nla_grobner(core *c, intervals *s)
|
|
: common(c, s),
|
|
m_nl_gb_exhausted(false),
|
|
m_dep_manager(m_val_manager, m_alloc),
|
|
m_changed_leading_term(false),
|
|
m_look_for_fixed_vars_in_rows(false)
|
|
{}
|
|
|
|
bool nla_grobner::internalize_gb_eq(equation* ) {
|
|
NOT_IMPLEMENTED_YET();
|
|
return false;
|
|
}
|
|
|
|
void nla_grobner::add_var_and_its_factors_to_q_and_collect_new_rows(lpvar j, std::queue<lpvar> & q) {
|
|
SASSERT(!c().active_var_set_contains(j) && !c().var_is_fixed(j));
|
|
TRACE("grobner", tout << "j = " << j << ", "; c().print_var(j, tout) << "\n";);
|
|
const auto& matrix = c().m_lar_solver.A_r();
|
|
c().insert_to_active_var_set(j);
|
|
const auto & core_slv = c().m_lar_solver.m_mpq_lar_core_solver;
|
|
for (auto & s : matrix.m_columns[j]) {
|
|
unsigned row = s.var();
|
|
if (m_rows.contains(row)) continue;
|
|
lpvar basic_in_row = core_slv.m_r_basis[row];
|
|
if (false && c().var_is_free(basic_in_row)) {
|
|
TRACE("grobner", tout << "ignore the row " << row << " with the free basic var\n";);
|
|
continue; // mimic the behavior of the legacy solver
|
|
}
|
|
m_rows.insert(row);
|
|
for (auto& rc : matrix.m_rows[row]) {
|
|
if (c().active_var_set_contains(rc.var()) || c().var_is_fixed(rc.var()))
|
|
continue;
|
|
q.push(rc.var());
|
|
}
|
|
}
|
|
|
|
if (!c().is_monic_var(j))
|
|
return;
|
|
|
|
const monic& m = c().emons()[j];
|
|
for (auto fcn : factorization_factory_imp(m, c())) {
|
|
for (const factor& fc: fcn) {
|
|
lpvar j = var(fc);
|
|
if (!c().active_var_set_contains(j) && !c().var_is_fixed(j))
|
|
add_var_and_its_factors_to_q_and_collect_new_rows(j, q);
|
|
}
|
|
}
|
|
}
|
|
|
|
void nla_grobner::find_nl_cluster() {
|
|
prepare_rows_and_active_vars();
|
|
std::queue<lpvar> q;
|
|
for (lpvar j : c().m_to_refine) {
|
|
TRACE("grobner", c().print_monic(c().emons()[j], tout) << "\n";);
|
|
if (c().var_is_fixed(j)) {
|
|
TRACE("grobner", tout << "skip fixed var " << j << "\n";);
|
|
continue;
|
|
}
|
|
q.push(j);
|
|
}
|
|
|
|
while (!q.empty()) {
|
|
unsigned j = q.front();
|
|
q.pop();
|
|
if (c().active_var_set_contains(j))
|
|
continue;
|
|
add_var_and_its_factors_to_q_and_collect_new_rows(j, q);
|
|
}
|
|
set_active_vars_weights();
|
|
TRACE("grobner", display(tout););
|
|
}
|
|
|
|
void nla_grobner::prepare_rows_and_active_vars() {
|
|
m_rows.clear();
|
|
m_rows.resize(c().m_lar_solver.row_count());
|
|
c().clear_and_resize_active_var_set();
|
|
}
|
|
|
|
void nla_grobner::display_matrix(std::ostream & out) const {
|
|
const auto& matrix = c().m_lar_solver.A_r();
|
|
out << m_rows.size() << " rows" <<"\n";
|
|
out << "the matrix\n";
|
|
|
|
for (const auto & r : matrix.m_rows) {
|
|
c().print_term(r, out) << std::endl;
|
|
}
|
|
}
|
|
std::ostream & nla_grobner::display(std::ostream & out) const {
|
|
display_equations(out, m_to_superpose, "m_to_superpose:");
|
|
display_equations(out, m_to_simplify, "m_to_simplify:");
|
|
return out;
|
|
}
|
|
|
|
|
|
common::ci_dependency* nla_grobner::dep_from_vector(svector<lp::constraint_index> & cs) {
|
|
ci_dependency * d = nullptr;
|
|
for (auto c : cs)
|
|
d = m_dep_manager.mk_join(d, m_dep_manager.mk_leaf(c));
|
|
return d;
|
|
}
|
|
|
|
void nla_grobner::add_row(unsigned i) {
|
|
const auto& row = c().m_lar_solver.A_r().m_rows[i];
|
|
TRACE("grobner", tout << "adding row to gb\n"; c().m_lar_solver.print_row(row, tout) << '\n';
|
|
for (auto p : row) {
|
|
c().print_var(p.var(), tout) << "\n";
|
|
}
|
|
);
|
|
nex_sum * ns = m_nex_creator.mk_sum();
|
|
create_sum_from_row(row, m_nex_creator, *ns, m_look_for_fixed_vars_in_rows);
|
|
nex* e = m_nex_creator.simplify(ns);
|
|
TRACE("grobner", tout << "e = " << *e << "\n";);
|
|
m_tmp_var_set.clear();
|
|
assert_eq_0(e, m_look_for_fixed_vars_in_rows? get_fixed_vars_dep_from_row(row, m_dep_manager) : nullptr);
|
|
}
|
|
|
|
void nla_grobner::simplify_equations_in_m_to_simplify() {
|
|
for (equation *eq : m_to_simplify) {
|
|
eq->expr() = m_nex_creator.simplify(eq->expr());
|
|
}
|
|
}
|
|
|
|
void nla_grobner::init() {
|
|
m_reported = 0;
|
|
m_conflict = false;
|
|
del_equations(0);
|
|
SASSERT(m_equations_to_delete.size() == 0);
|
|
m_to_superpose.reset();
|
|
m_to_simplify.reset();
|
|
|
|
find_nl_cluster();
|
|
c().clear_and_resize_active_var_set();
|
|
TRACE("grobner", tout << "m_rows.size() = " << m_rows.size() << "\n";);
|
|
for (unsigned i : m_rows) {
|
|
add_row(i);
|
|
}
|
|
simplify_equations_in_m_to_simplify();
|
|
}
|
|
|
|
bool nla_grobner::is_trivial(equation* eq) const {
|
|
SASSERT(m_nex_creator.is_simplified(eq->expr()));
|
|
return eq->expr()->size() == 0;
|
|
}
|
|
|
|
bool nla_grobner::is_better_choice(equation * eq1, equation * eq2) {
|
|
if (!eq2)
|
|
return true;
|
|
if (is_trivial(eq1))
|
|
return true;
|
|
if (is_trivial(eq2))
|
|
return false;
|
|
return m_nex_creator.lt(eq2->expr(), eq1->expr());
|
|
}
|
|
|
|
void nla_grobner::del_equation(equation * eq) {
|
|
m_to_superpose.erase(eq);
|
|
m_to_simplify.erase(eq);
|
|
SASSERT(m_equations_to_delete[eq->m_bidx] == eq);
|
|
m_equations_to_delete[eq->m_bidx] = nullptr;
|
|
dealloc(eq);
|
|
}
|
|
|
|
nla_grobner::equation* nla_grobner::pick_next() {
|
|
equation * r = nullptr;
|
|
ptr_buffer<equation> to_delete;
|
|
for (equation * curr : m_to_simplify) {
|
|
if (is_trivial(curr))
|
|
to_delete.push_back(curr);
|
|
else if (is_better_choice(curr, r)) {
|
|
TRACE("grobner", tout << "preferring "; display_equation(tout, *curr););
|
|
r = curr;
|
|
}
|
|
}
|
|
for (equation * e : to_delete)
|
|
del_equation(e);
|
|
if (r)
|
|
m_to_simplify.erase(r);
|
|
TRACE("grobner", tout << "selected equation: "; if (!r) tout << "<null>\n"; else display_equation(tout, *r););
|
|
return r;
|
|
}
|
|
|
|
nla_grobner::equation* nla_grobner::simplify_using_to_superpose(equation* eq) {
|
|
bool result = false;
|
|
bool simplified;
|
|
TRACE("grobner", tout << "simplifying: "; display_equation(tout, *eq); tout << "using equalities of m_to_superpose of size " << m_to_superpose.size() << "\n";);
|
|
do {
|
|
simplified = false;
|
|
for (equation * p : m_to_superpose) {
|
|
if (simplify_source_target(p, eq)) {
|
|
result = true;
|
|
simplified = true;
|
|
}
|
|
if (canceled()) {
|
|
return nullptr;
|
|
}
|
|
if (eq->expr()->is_scalar())
|
|
break;
|
|
}
|
|
if (eq->expr()->is_scalar())
|
|
break;
|
|
}
|
|
while (simplified);
|
|
if (result && eq->expr()->is_scalar()) {
|
|
TRACE("grobner",);
|
|
}
|
|
|
|
TRACE("grobner", tout << "simplification result: "; display_equation(tout, *eq););
|
|
return result ? eq : nullptr;
|
|
}
|
|
|
|
const nex* nla_grobner::get_highest_monomial(const nex* e) const {
|
|
switch (e->type()) {
|
|
case expr_type::MUL:
|
|
return to_mul(e);
|
|
case expr_type::SUM:
|
|
return *(to_sum(e)->begin());
|
|
case expr_type::VAR:
|
|
return e;
|
|
default:
|
|
TRACE("grobner", tout << *e << "\n";);
|
|
return nullptr;
|
|
}
|
|
}
|
|
// source 3f + k + l = 0, so f = (-k - l)/3
|
|
// target 2fg + 3fp + e = 0
|
|
// target is replaced by 2(-k/3 - l/3)g + 3(-k/3 - l/3)p + e = -2/3kg -2/3lg - kp -lp + e
|
|
bool nla_grobner::simplify_target_monomials(equation * source, equation * target) {
|
|
auto * high_mon = get_highest_monomial(source->expr());
|
|
if (high_mon == nullptr)
|
|
return false;
|
|
SASSERT(high_mon->all_factors_are_elementary());
|
|
TRACE("grobner", tout << "source = "; display_equation(tout, *source) << "target = "; display_equation(tout, *target) << "high_mon = " << *high_mon << "\n";);
|
|
|
|
nex * te = target->expr();
|
|
nex_sum * targ_sum;
|
|
if (te->is_sum()) {
|
|
targ_sum = to_sum(te);
|
|
} else if (te->is_mul()) {
|
|
targ_sum = m_nex_creator.mk_sum(te);
|
|
} else {
|
|
TRACE("grobner", tout << "return false\n";);
|
|
return false;
|
|
}
|
|
|
|
return simplify_target_monomials_sum(source, target, targ_sum, high_mon);
|
|
}
|
|
|
|
unsigned nla_grobner::find_divisible(nex_sum* targ_sum,
|
|
const nex* high_mon) const {
|
|
for (unsigned j = 0; j < targ_sum->size(); j++) {
|
|
auto t = (*targ_sum)[j];
|
|
if (divide_ignore_coeffs_check_only(t, high_mon)) {
|
|
TRACE("grobner", tout << "yes div: " << *t << " / " << *high_mon << "\n";);
|
|
return j;
|
|
}
|
|
}
|
|
TRACE("grobner", tout << "no div: " << *targ_sum << " / " << *high_mon << "\n";);
|
|
return -1;
|
|
}
|
|
|
|
|
|
bool nla_grobner::simplify_target_monomials_sum(equation * source,
|
|
equation * target, nex_sum* targ_sum,
|
|
const nex* high_mon) {
|
|
unsigned j = find_divisible(targ_sum, high_mon);
|
|
if (j + 1 == 0)
|
|
return false;
|
|
m_changed_leading_term = (j == 0);
|
|
unsigned targ_orig_size = targ_sum->size();
|
|
for (; j < targ_orig_size; j++) {
|
|
simplify_target_monomials_sum_j(source, target, targ_sum, high_mon, j);
|
|
}
|
|
TRACE("grobner_d", tout << "targ_sum = " << *targ_sum << "\n";);
|
|
target->expr() = m_nex_creator.simplify(targ_sum);
|
|
target->dep() = m_dep_manager.mk_join(source->dep(), target->dep());
|
|
TRACE("grobner_d", tout << "target = "; display_equation(tout, *target););
|
|
return true;
|
|
}
|
|
|
|
nex_mul* nla_grobner::divide_ignore_coeffs(nex* ej, const nex* h) {
|
|
TRACE("grobner", tout << "ej = " << *ej << " , h = " << *h << "\n";);
|
|
if (!divide_ignore_coeffs_check_only(ej, h))
|
|
return nullptr;
|
|
return divide_ignore_coeffs_perform(ej, h);
|
|
}
|
|
|
|
bool nla_grobner::divide_ignore_coeffs_check_only_nex_mul(nex_mul* t , const nex* h) const {
|
|
TRACE("grobner", tout << "t = " << *t << ", h=" << *h << "\n";);
|
|
SASSERT(m_nex_creator.is_simplified(t) && m_nex_creator.is_simplified(h));
|
|
unsigned j = 0; // points to t
|
|
for(unsigned k = 0; k < h->number_of_child_powers(); k++) {
|
|
lpvar h_var = to_var(h->get_child_exp(k))->var();
|
|
bool p_swallowed = false;
|
|
for (; j < t->size() && !p_swallowed; j++) {
|
|
auto &tp = (*t)[j];
|
|
if (to_var(tp.e())->var() == h_var) {
|
|
if (tp.pow() >= static_cast<int>(h->get_child_pow(k))) {
|
|
p_swallowed = true;
|
|
}
|
|
}
|
|
}
|
|
if (!p_swallowed) {
|
|
TRACE("grobner", tout << "no div " << *t << " / " << *h << "\n";);
|
|
return false;
|
|
}
|
|
}
|
|
TRACE("grobner", tout << "division " << *t << " / " << *h << "\n";);
|
|
return true;
|
|
|
|
}
|
|
|
|
// return true if h divides t
|
|
bool nla_grobner::divide_ignore_coeffs_check_only(nex* n , const nex* h) const {
|
|
if (n->is_mul())
|
|
return divide_ignore_coeffs_check_only_nex_mul(to_mul(n), h);
|
|
if (!n->is_var())
|
|
return false;
|
|
|
|
const nex_var * v = to_var(n);
|
|
if (h->is_var()) {
|
|
return v->var() == to_var(h)->var();
|
|
}
|
|
|
|
if (h->is_mul() || h->is_var()) {
|
|
if (h->number_of_child_powers() > 1)
|
|
return false;
|
|
if (h->get_child_pow(0) != 1)
|
|
return false;
|
|
const nex* e = h->get_child_exp(0);
|
|
return e->is_var() && to_var(e)->var() == v->var();
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
nex_mul * nla_grobner::divide_ignore_coeffs_perform_nex_mul(nex_mul* t, const nex* h) {
|
|
nex_mul * r = m_nex_creator.mk_mul();
|
|
unsigned j = 0; // points to t
|
|
for(unsigned k = 0; k < h->number_of_child_powers(); k++) {
|
|
lpvar h_var = to_var(h->get_child_exp(k))->var();
|
|
for (; j < t->size(); j++) {
|
|
auto &tp = (*t)[j];
|
|
if (to_var(tp.e())->var() == h_var) {
|
|
int h_pow = h->get_child_pow(k);
|
|
SASSERT(tp.pow() >= h_pow);
|
|
j++;
|
|
if (tp.pow() > h_pow)
|
|
r->add_child_in_power(tp.e(), tp.pow() - h_pow);
|
|
break;
|
|
} else {
|
|
r->add_child_in_power(tp);
|
|
}
|
|
}
|
|
}
|
|
TRACE("grobner", tout << "r = " << *r << " = " << *t << " / " << *h << "\n";);
|
|
return r;
|
|
}
|
|
|
|
// perform the division t / h, but ignores the coefficients
|
|
// h does not change
|
|
nex_mul * nla_grobner::divide_ignore_coeffs_perform(nex* e, const nex* h) {
|
|
if (e->is_mul())
|
|
return divide_ignore_coeffs_perform_nex_mul(to_mul(e), h);
|
|
SASSERT(e->is_var());
|
|
return m_nex_creator.mk_mul(); // return the empty nex_mul
|
|
}
|
|
|
|
// if targ_sum->children()[j] = c*high_mon*p,
|
|
// and b*high_mon + e = 0, so high_mon = -e/b
|
|
// then targ_sum->children()[j] = - (c/b) * e*p
|
|
|
|
void nla_grobner::simplify_target_monomials_sum_j(equation * source, equation *target, nex_sum* targ_sum, const nex* high_mon, unsigned j) {
|
|
nex * ej = (*targ_sum)[j];
|
|
TRACE("grobner_d", tout << "high_mon = " << *high_mon << ", ej = " << *ej << "\n";);
|
|
nex_mul * ej_over_high_mon = divide_ignore_coeffs(ej, high_mon);
|
|
if (ej_over_high_mon == nullptr) {
|
|
TRACE("grobner_d", tout << "no div\n";);
|
|
return;
|
|
}
|
|
TRACE("grobner_d", tout << "ej_over_high_mon = " << *ej_over_high_mon << "\n";);
|
|
rational c = ej->is_mul()? to_mul(ej)->coeff() : rational(1);
|
|
TRACE("grobner_d", tout << "c = " << c << "\n";);
|
|
|
|
nex_sum * ej_sum = m_nex_creator.mk_sum();
|
|
(*targ_sum)[j] = ej_sum;
|
|
add_mul_skip_first(ej_sum ,-c/high_mon->coeff(), source->expr(), ej_over_high_mon);
|
|
TRACE("grobner_d", tout << "targ_sum = " << *targ_sum << "\n";);
|
|
}
|
|
|
|
// return true iff simplified
|
|
bool nla_grobner::simplify_source_target(equation * source, equation * target) {
|
|
TRACE("grobner", tout << "simplifying: "; display_equation(tout, *target); tout << "using: "; display_equation(tout, *source););
|
|
TRACE("grobner_d", tout << "simplifying: " << *(target->expr()) << " using " << *(source->expr()) << "\n";);
|
|
SASSERT(m_nex_creator.is_simplified(source->expr()));
|
|
SASSERT(m_nex_creator.is_simplified(target->expr()));
|
|
if (target->expr()->is_scalar()) {
|
|
TRACE("grobner_d", tout << "no simplification\n";);
|
|
return false;
|
|
}
|
|
if (source->get_num_monomials() == 0) {
|
|
TRACE("grobner_d", tout << "no simplification\n";);
|
|
return false;
|
|
}
|
|
m_stats.m_simplify++;
|
|
bool result = false;
|
|
do {
|
|
if (simplify_target_monomials(source, target)) {
|
|
TRACE("grobner", tout << "simplified target = ";display_equation(tout, *target) << "\n";);
|
|
result = true;
|
|
} else {
|
|
break;
|
|
}
|
|
} while (!canceled());
|
|
TRACE("grobner", tout << "result: " << result << "\n"; if (result) display_equation(tout, *target););
|
|
if (result) {
|
|
target->dep() = m_dep_manager.mk_join(target->dep(), source->dep());
|
|
TRACE("grobner_d", tout << "simplified to " << *(target->expr()) << "\n";);
|
|
return true;
|
|
}
|
|
TRACE("grobner_d", tout << "no simplification\n";);
|
|
return false;
|
|
}
|
|
|
|
void nla_grobner::process_simplified_target(equation* target, ptr_buffer<equation>& to_remove) {
|
|
if (is_trivial(target)) {
|
|
to_remove.push_back(target);
|
|
} else if (m_changed_leading_term) {
|
|
insert_to_simplify(target);
|
|
to_remove.push_back(target);
|
|
}
|
|
}
|
|
|
|
void nla_grobner::check_eq(equation* target) {
|
|
if(m_intervals->check_nex(target->expr(), target->dep())) {
|
|
TRACE("grobner", tout << "created a lemma for "; display_equation(tout, *target) << "\n";
|
|
tout << "vars = \n";
|
|
for (lpvar j : get_vars_of_expr(target->expr())) {
|
|
c().print_var(j, tout);
|
|
}
|
|
tout << "\ntarget->expr() val = " << get_nex_val(target->expr(), [this](unsigned j) { return c().val(j); }) << "\n";);
|
|
register_report();
|
|
}
|
|
}
|
|
|
|
bool nla_grobner::simplify_to_superpose_with_eq(equation* eq) {
|
|
TRACE("grobner_d", tout << "eq->exp " << *(eq->expr()) << "\n";);
|
|
|
|
ptr_buffer<equation> to_insert;
|
|
ptr_buffer<equation> to_remove;
|
|
ptr_buffer<equation> to_delete;
|
|
equation_set::iterator it = m_to_superpose.begin();
|
|
equation_set::iterator end = m_to_superpose.end();
|
|
for (; it != end && !canceled() && !done(); ++it) {
|
|
equation * target = *it;
|
|
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))
|
|
to_delete.push_back(target);
|
|
else
|
|
SASSERT(m_nex_creator.is_simplified(target->expr()));
|
|
}
|
|
for (equation* eq : to_insert)
|
|
insert_to_superpose(eq);
|
|
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 nla_grobner::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))
|
|
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 nla_grobner::add_mul_skip_first(nex_sum* r, const rational& beta, nex *e, nex_mul* c) {
|
|
if (e->is_sum()) {
|
|
nex_sum *es = to_sum(e);
|
|
for (unsigned j = 1; j < es->size(); j++) {
|
|
r->add_child(m_nex_creator.mk_mul(beta, (*es)[j], c));
|
|
}
|
|
TRACE("grobner", tout << "r = " << *r << "\n";);
|
|
} else {
|
|
TRACE("grobner", tout << "e = " << *e << "\n";);
|
|
}
|
|
}
|
|
|
|
|
|
// let e1: alpha*ab+q=0, and e2: beta*ac+e=0, then beta*qc - alpha*eb = 0
|
|
nex * nla_grobner::expr_superpose(nex* e1, nex* e2, const nex* ab, const nex* ac, nex_mul* b, nex_mul* c) {
|
|
TRACE("grobner", tout << "e1 = " << *e1 << "\ne2 = " << *e2 <<"\n";);
|
|
nex_sum * r = m_nex_creator.mk_sum();
|
|
rational alpha = - ab->coeff();
|
|
TRACE("grobner", tout << "e2 *= " << alpha << "*(" << *b << ")\n";);
|
|
add_mul_skip_first(r, alpha, e2, b);
|
|
rational beta = ac->coeff();
|
|
TRACE("grobner", tout << "e1 *= " << beta << "*(" << *c << ")\n";);
|
|
add_mul_skip_first(r, beta, e1, c);
|
|
nex * ret = m_nex_creator.simplify(r);
|
|
TRACE("grobner", tout << "e1 = " << *e1 << "\ne2 = " << *e2 <<"\nsuperpose = " << *ret << "\n";);
|
|
if (ret->is_scalar()) {
|
|
TRACE("grobner",);
|
|
}
|
|
return ret;
|
|
}
|
|
// let eq1: ab+q=0, and eq2: ac+e=0, then qc - eb = 0
|
|
void nla_grobner::superpose(equation * eq1, equation * eq2) {
|
|
TRACE("grobner", 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, *c;
|
|
TRACE("grobner", 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", tout << "there is no non-trivial common divider, no superposing\n";);
|
|
return;
|
|
}
|
|
equation* eq = alloc(equation);
|
|
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.lt(eq->expr(), eq1->expr()) || m_nex_creator.lt(eq->expr(), eq2->expr())) {
|
|
TRACE("grobner", display_equation(tout, *eq) << " is too complex: deleting it\n;";);
|
|
del_equation(eq);
|
|
} else {
|
|
insert_to_simplify(eq);
|
|
}
|
|
|
|
}
|
|
|
|
void nla_grobner::register_report() {
|
|
m_reported++;
|
|
if (c().current_lemma().expl().size() == 0)
|
|
m_conflict = true;
|
|
}
|
|
// 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 nla_grobner::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;
|
|
b = m_nex_creator.mk_mul(); c = m_nex_creator.mk_mul();
|
|
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.lt(m, n)) {
|
|
b->add_child_in_power(const_cast<nex*>(m), ab->get_child_pow(i));
|
|
if (++i == ab_size)
|
|
break;
|
|
} else if (m_nex_creator.lt(n, m)) {
|
|
c->add_child_in_power(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) {
|
|
b->add_child_in_power(const_cast<nex*>(m), b_pow - c_pow);
|
|
} else if (c_pow > b_pow) {
|
|
c->add_child_in_power(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) {
|
|
b->add_child_in_power(const_cast<nex*>(ab->get_child_exp(i)), ab->get_child_pow(i));
|
|
i++;
|
|
}
|
|
while (j != ac_size) {
|
|
c->add_child_in_power(const_cast<nex*>(ac->get_child_exp(j)), ac->get_child_pow(j));
|
|
j++;
|
|
}
|
|
TRACE("nla_grobner", tout << "b=" << *b << ", c=" <<*c << "\n";);
|
|
return true;
|
|
}
|
|
// Finds out if ab and bc have a non-trivial common divider
|
|
bool nla_grobner::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(ab));
|
|
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.lt(m , n)) {
|
|
i++;
|
|
if (i == ab->number_of_child_powers())
|
|
return false;
|
|
} else if (m_nex_creator.lt(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 nla_grobner::superpose(equation * eq) {
|
|
for (equation * target : m_to_superpose) {
|
|
superpose(eq, target);
|
|
}
|
|
}
|
|
|
|
// return true iff cannot pick_next()
|
|
bool nla_grobner::compute_basis_step() {
|
|
equation * eq = pick_next();
|
|
if (!eq) {
|
|
TRACE("grobner", tout << "cannot pick an equation\n";);
|
|
return true;
|
|
}
|
|
m_stats.m_num_processed++;
|
|
equation * new_eq = simplify_using_to_superpose(eq);
|
|
if (new_eq != nullptr && eq != new_eq) {
|
|
// equation was updated using non destructive updates
|
|
eq = new_eq;
|
|
}
|
|
if (canceled()) return false;
|
|
if (!simplify_to_superpose_with_eq(eq))
|
|
return false;
|
|
TRACE("grobner", tout << "eq = "; display_equation(tout, *eq););
|
|
superpose(eq);
|
|
insert_to_superpose(eq);
|
|
simplify_m_to_simplify(eq);
|
|
TRACE("grobner", tout << "end of iteration:\n"; display(tout););
|
|
return false;
|
|
}
|
|
|
|
void nla_grobner::compute_basis(){
|
|
compute_basis_init();
|
|
if (m_rows.size() < 2) {
|
|
TRACE("nla_grobner", tout << "there are only " << m_rows.size() << " rows, exiting compute_basis()\n";);
|
|
return;
|
|
}
|
|
if (!compute_basis_loop()) {
|
|
TRACE("grobner", tout << "false from compute_basis_loop\n";);
|
|
set_gb_exhausted();
|
|
} else {
|
|
TRACE("grobner", display(tout););
|
|
for (equation* e : m_to_simplify) {
|
|
check_eq(e);
|
|
}
|
|
for (equation* e : m_to_superpose) {
|
|
check_eq(e);
|
|
}
|
|
}
|
|
}
|
|
void nla_grobner::compute_basis_init(){
|
|
c().lp_settings().stats().m_grobner_basis_computatins++;
|
|
}
|
|
|
|
bool nla_grobner::canceled() const {
|
|
return c().lp_settings().get_cancel_flag();
|
|
}
|
|
|
|
|
|
bool nla_grobner::done() const {
|
|
if (
|
|
num_of_equations() >= c().m_nla_settings.grobner_eqs_threshold()
|
|
||
|
|
canceled()
|
|
||
|
|
m_reported > 100000
|
|
||
|
|
m_conflict) {
|
|
TRACE("grobner",
|
|
tout << "done() is true because of ";
|
|
if (num_of_equations() >= c().m_nla_settings.grobner_eqs_threshold()) {
|
|
tout << "m_num_of_equations = " << num_of_equations() << "\n";
|
|
} else if (canceled()) {
|
|
tout << "canceled\n";
|
|
} else if (m_reported > 100000) {
|
|
tout << "m_reported = " << m_reported;
|
|
} else {
|
|
tout << "m_conflict = " << m_conflict;
|
|
}
|
|
tout << "\n";);
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
bool nla_grobner::compute_basis_loop(){
|
|
int i = 0;
|
|
while (!done()) {
|
|
if (compute_basis_step()) {
|
|
TRACE("grobner", tout << "progress in compute_basis_step\n";);
|
|
return true;
|
|
}
|
|
TRACE("grobner", tout << "continue compute_basis_loop i= " << ++i << "\n";);
|
|
}
|
|
TRACE("grobner", tout << "return false from compute_basis_loop i= " << i << "\n";);
|
|
return false;
|
|
}
|
|
|
|
void nla_grobner::set_gb_exhausted(){
|
|
m_nl_gb_exhausted = true;
|
|
}
|
|
|
|
void nla_grobner::update_statistics(){
|
|
/* todo : implement
|
|
m_stats.m_gb_simplify += gb.m_stats.m_simplify;
|
|
m_stats.m_gb_superpose += gb.m_stats.m_superpose;
|
|
m_stats.m_gb_num_to_superpose += gb.m_stats.m_num_to_superpose;
|
|
m_stats.m_gb_compute_basis++;*/
|
|
}
|
|
|
|
|
|
bool nla_grobner::push_calculation_forward(ptr_vector<equation>& eqs, unsigned & next_weight) {
|
|
return (!m_nl_gb_exhausted) &&
|
|
try_to_modify_eqs(eqs, next_weight);
|
|
}
|
|
|
|
bool nla_grobner::try_to_modify_eqs(ptr_vector<equation>& eqs, unsigned& next_weight) {
|
|
// NOT_IMPLEMENTED_YET();
|
|
return false;
|
|
}
|
|
|
|
|
|
void nla_grobner::grobner_lemmas() {
|
|
c().lp_settings().stats().m_grobner_calls++;
|
|
|
|
init();
|
|
|
|
ptr_vector<equation> eqs;
|
|
unsigned next_weight =
|
|
(unsigned)(var_weight::MAX_DEFAULT_WEIGHT) + 1; // next weight using during perturbation phase.
|
|
do {
|
|
TRACE("grobner", tout << "before:\n"; display(tout););
|
|
compute_basis();
|
|
update_statistics();
|
|
TRACE("grobner", tout << "after:\n"; display(tout););
|
|
// if (find_conflict(eqs))
|
|
// return;
|
|
}
|
|
while(push_calculation_forward(eqs, next_weight));
|
|
}
|
|
void nla_grobner:: del_equations(unsigned old_size) {
|
|
TRACE("grobner", );
|
|
SASSERT(m_equations_to_delete.size() >= old_size);
|
|
equation_vector::iterator it = m_equations_to_delete.begin();
|
|
equation_vector::iterator end = m_equations_to_delete.end();
|
|
it += old_size;
|
|
for (; it != end; ++it) {
|
|
equation * eq = *it;
|
|
if (eq)
|
|
del_equation(eq);
|
|
}
|
|
m_equations_to_delete.shrink(old_size);
|
|
}
|
|
|
|
void nla_grobner::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);
|
|
}
|
|
|
|
std::ostream& nla_grobner::display_equation(std::ostream & out, const equation & eq) const {
|
|
out << "expr = " << *eq.expr() << "\n";
|
|
display_dependency(out, eq.dep());
|
|
return out;
|
|
}
|
|
std::unordered_set<lpvar> nla_grobner::get_vars_of_expr_with_opening_terms(const nex *e ) {
|
|
auto ret = get_vars_of_expr(e);
|
|
auto & ls = c().m_lar_solver;
|
|
do {
|
|
svector<lpvar> added;
|
|
for (lpvar j : ret) {
|
|
if (ls.column_corresponds_to_term(j)) {
|
|
const auto & t = c().m_lar_solver.get_term(ls.local_to_external(j));
|
|
for (auto p : t) {
|
|
if (ret.find(p.var()) == ret.end())
|
|
added.push_back(p.var());
|
|
}
|
|
}
|
|
}
|
|
if (added.size() == 0)
|
|
return ret;
|
|
for (lpvar j: added)
|
|
ret.insert(j);
|
|
added.clear();
|
|
} while (true);
|
|
}
|
|
|
|
void nla_grobner::assert_eq_0(nex* e, ci_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);
|
|
for (unsigned j : get_vars_of_expr_with_opening_terms(e)) {
|
|
tout << "(";
|
|
c().print_var(j, tout) << ")\n";
|
|
});
|
|
insert_to_simplify(eq);
|
|
}
|
|
|
|
void nla_grobner::init_equation(equation* eq, nex*e, ci_dependency * dep) {
|
|
unsigned bidx = m_equations_to_delete.size();
|
|
eq->m_bidx = bidx;
|
|
eq->dep() = dep;
|
|
eq->expr() = e;
|
|
m_equations_to_delete.push_back(eq);
|
|
SASSERT(m_equations_to_delete[eq->m_bidx] == eq);
|
|
}
|
|
|
|
nla_grobner::~nla_grobner() {
|
|
del_equations(0);
|
|
}
|
|
|
|
std::ostream& nla_grobner::display_dependency(std::ostream& out, ci_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_core->print_explanation(e, out);
|
|
out << "\n";
|
|
}
|
|
}
|
|
|
|
return out;
|
|
}
|
|
|
|
} // end of nla namespace
|