mirror of
https://github.com/Z3Prover/z3
synced 2025-04-14 04:48:45 +00:00
change lar_terms to use column indices
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
parent
3313590b95
commit
c2e5cd78c8
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@ -109,7 +109,7 @@ public:
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auto & row = m_data[adjust_row(i)];
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lp_assert(row_is_initialized_correctly(row));
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for (const auto & p : c) {
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unsigned j = adjust_column(column_fix(p.var().index()));
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unsigned j = adjust_column(column_fix(p.column().index()));
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row[j] = sign * p.coeff();
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}
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}
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@ -191,7 +191,8 @@ class create_cut {
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void dump_coeff(std::ostream & out, const T& c) const {
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out << "( * ";
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dump_coeff_val(out, c.coeff());
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out << " " << var_name(c.var().index()) << ")";
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auto t = lia.lra.column2tv(c.column());
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out << " " << var_name(t.id()) << ")";
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}
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std::ostream& dump_row_coefficients(std::ostream & out) const {
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@ -221,9 +222,9 @@ class create_cut {
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dump_declaration(out, p.var());
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}
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for (const auto& p : m_t) {
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unsigned v = p.var().index();
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if (lp::tv::is_term(v)) {
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dump_declaration(out, v);
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auto t = lia.lra.column2tv(p.column());
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if (t.is_term()) {
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dump_declaration(out, t.id());
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}
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}
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}
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@ -349,7 +350,6 @@ public:
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// NSB code review: this is also used in nla_core.
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// but it isn't consistent: when theory_lra accesses lar_solver::get_term, the term that is returned uses
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// column indices, not terms.
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lia.lra.subs_term_columns(m_t);
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TRACE("gomory_cut", print_linear_combination_of_column_indices_only(m_t.coeffs_as_vector(), tout << "gomory cut:"); tout << " <= " << m_k << std::endl;);
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return lia_move::cut;
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}
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@ -50,7 +50,8 @@ namespace lp {
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m_constraints_for_explanation.push_back(ci);
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for (const auto &p : *t) {
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m_var_register.add_var(p.var().index(), true); // hnf only deals with integral variables for now
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auto tv = lia.lra.column2tv(p.column());
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m_var_register.add_var(tv.id(), true); // hnf only deals with integral variables for now
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mpq t = abs(ceil(p.coeff()));
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if (t > m_abs_max)
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m_abs_max = t;
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@ -86,7 +86,7 @@ namespace lp {
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bool seen_minus = false;
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bool seen_plus = false;
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for(const auto & p : t) {
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if (!lia.column_is_int(p.var().index()))
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if (!lia.column_is_int(p.column()))
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goto usual_delta;
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const mpq & c = p.coeff();
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if (c == one_of_type<mpq>()) {
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@ -104,7 +104,7 @@ namespace lp {
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usual_delta:
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mpq delta = zero_of_type<mpq>();
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for (const auto & p : t)
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if (lia.column_is_int(p.var().index()))
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if (lia.column_is_int(p.column()))
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delta += abs(p.coeff());
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delta *= mpq(1, 2);
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@ -228,7 +228,7 @@ const lp_settings& int_solver::settings() const {
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return lra.settings();
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}
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bool int_solver::column_is_int(unsigned j) const {
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bool int_solver::column_is_int(column_index const& j) const {
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return lra.column_is_int(j);
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}
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@ -82,7 +82,7 @@ public:
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bool is_real(unsigned j) const;
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const impq & lower_bound(unsigned j) const;
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const impq & upper_bound(unsigned j) const;
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bool column_is_int(unsigned j) const;
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bool column_is_int(column_index const& j) const;
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const impq & get_value(unsigned j) const;
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bool at_lower(unsigned j) const;
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bool at_upper(unsigned j) const;
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@ -115,13 +115,13 @@ bool lar_solver::implied_bound_is_correctly_explained(implied_bound const & be,
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} else {
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lar_term const& t = get_term(be.m_j);
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auto first_coeff = t.begin();
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unsigned j = (*first_coeff).var().index();
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unsigned j = (*first_coeff).column();
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auto it = coeff_map.find(j);
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if (it == coeff_map.end())
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return false;
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mpq ratio = it->second / (*first_coeff).coeff();
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for (auto p : t) {
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it = coeff_map.find(p.var().index());
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it = coeff_map.find(p.column());
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if (it == coeff_map.end())
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return false;
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if (p.coeff() * ratio != it->second)
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@ -231,6 +231,7 @@ void lar_solver::explain_implied_bound(implied_bound & ib, lp_bound_propagator &
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}
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// lp_assert(implied_bound_is_correctly_explained(ib, explanation));
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}
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// here i is just the term index
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bool lar_solver::term_is_used_as_row(unsigned i) const {
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SASSERT(i < m_terms.size());
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@ -246,7 +247,6 @@ void lar_solver::propagate_bounds_on_terms(lp_bound_propagator & bp) {
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}
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}
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// goes over touched rows and tries to induce bounds
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void lar_solver::propagate_bounds_for_touched_rows(lp_bound_propagator & bp) {
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if (!use_tableau())
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@ -423,7 +423,7 @@ void lar_solver::set_costs_to_zero(const lar_term& term) {
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lp_assert(jset.is_empty());
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for (const auto & p : term) {
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unsigned j = p.var().index();
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unsigned j = p.column();
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rslv.m_costs[j] = zero_of_type<mpq>();
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int i = rslv.m_basis_heading[j];
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if (i < 0)
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@ -454,7 +454,7 @@ void lar_solver::prepare_costs_for_r_solver(const lar_term & term) {
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lp_assert(reduced_costs_are_zeroes_for_r_solver());
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rslv.m_costs.resize(A_r().column_count(), zero_of_type<mpq>());
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for (const auto & p : term) {
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unsigned j = p.var().index();
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unsigned j = p.column();
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rslv.m_costs[j] = p.coeff();
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if (rslv.m_basis_heading[j] < 0)
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rslv.m_d[j] += p.coeff();
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@ -681,7 +681,7 @@ void lar_solver::substitute_terms_in_linear_expression(const vector<std::pair<mp
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const lar_term & term = * m_terms[tv::unmask_term(t.second)];
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for (auto p : term){
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register_monoid_in_map(coeffs, t.first * p.coeff() , p.var().index());
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register_monoid_in_map(coeffs, t.first * p.coeff() , p.column());
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}
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}
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}
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@ -917,7 +917,7 @@ void lar_solver::fill_last_row_of_A_r(static_matrix<mpq, numeric_pair<mpq>> & A,
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lp_assert(A.m_rows[last_row].size() == 0);
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for (auto t : *ls) {
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lp_assert(!is_zero(t.coeff()));
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var_index j = t.var().index();
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var_index j = t.column();
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A.set(last_row, j, - t.coeff());
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}
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unsigned basis_j = A.column_count() - 1;
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@ -1147,7 +1147,7 @@ bool lar_solver::has_value(var_index var, mpq& value) const {
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lar_term const& t = get_term(var);
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value = 0;
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for (auto const& cv : t) {
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impq const& r = get_column_value(cv.var().index());
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impq const& r = get_column_value(cv.column());
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if (!numeric_traits<mpq>::is_zero(r.y)) return false;
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value += r.x * cv.coeff();
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}
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@ -1306,7 +1306,7 @@ std::ostream& lar_solver::print_term(lar_term const& term, std::ostream & out) c
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out << " - ";
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else if (val != numeric_traits<mpq>::one())
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out << T_to_string(val);
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out << this->get_variable_name(p.var().index());
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out << this->get_variable_name(p.column());
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}
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return out;
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}
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@ -1530,7 +1530,7 @@ bool lar_solver::model_is_int_feasible() const {
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bool lar_solver::term_is_int(const lar_term * t) const {
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for (auto const p : *t)
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if (! (column_is_int(p.var().index()) && p.coeff().is_int()))
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if (! (column_is_int(p.column()) && p.coeff().is_int()))
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return false;
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return true;
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}
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@ -1691,19 +1691,9 @@ bool lar_solver::term_coeffs_are_ok(const vector<std::pair<mpq, var_index>> & co
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}
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#endif
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void lar_solver::push_term(lar_term* t) {
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// SASSERT(well_formed(*t));
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m_terms.push_back(t);
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}
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bool lar_solver::well_formed(lar_term const& t) const {
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for (auto const& ti : t) {
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if (!ti.var().is_term() &&
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column_corresponds_to_term(ti.var().index())) {
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return false;
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}
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}
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return true;
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}
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// terms
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@ -1956,7 +1946,7 @@ void lar_solver::fill_last_row_of_A_d(static_matrix<double, double> & A, const l
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for (auto t : *ls) {
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lp_assert(!is_zero(t.coeff()));
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var_index j = t.var().index();
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var_index j = t.column();
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A.set(last_row, j, -t.coeff().get_double());
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}
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@ -2257,7 +2247,7 @@ void lar_solver::fix_terms_with_rounded_columns() {
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bool need_to_fix = false;
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const lar_term & t = *m_terms[i];
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for (const auto & p : t) {
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if (m_incorrect_columns.contains(p.var().index())) {
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if (m_incorrect_columns.contains(p.column())) {
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need_to_fix = true;
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break;
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}
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@ -2274,7 +2264,7 @@ void lar_solver::fix_terms_with_rounded_columns() {
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bool lar_solver::sum_first_coords(const lar_term& t, mpq & val) const {
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val = zero_of_type<mpq>();
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for (const auto & c : t) {
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const auto & x = m_mpq_lar_core_solver.m_r_x[c.var().index()];
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const auto & x = m_mpq_lar_core_solver.m_r_x[c.column()];
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if (!is_zero(x.y))
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return false;
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val += x.x * c.coeff();
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@ -60,7 +60,7 @@ class lar_solver : public column_namer {
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size_t seed = 0;
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int i = 0;
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for (const auto p : t) {
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hash_combine(seed, p.var().index());
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hash_combine(seed, (unsigned)p.column());
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hash_combine(seed, p.coeff());
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if (i++ > 10)
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break;
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@ -125,15 +125,11 @@ public:
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static bool valid_index(unsigned j){ return static_cast<int>(j) >= 0;}
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bool column_is_int(unsigned j) const;
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bool column_value_is_int(unsigned j) const {
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return m_mpq_lar_core_solver.m_r_x[j].is_int();
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}
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bool column_is_int(column_index const& j) const { return column_is_int((unsigned)j); }
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const impq& get_column_value(unsigned j) const {
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return m_mpq_lar_core_solver.m_r_x[j];
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}
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bool column_is_int(unsigned j) const;
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bool column_value_is_int(unsigned j) const { return m_mpq_lar_core_solver.m_r_x[j].is_int(); }
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const impq& get_column_value(unsigned j) const { return m_mpq_lar_core_solver.m_r_x[j]; }
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void set_column_value(unsigned j, const impq& v) {
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m_mpq_lar_core_solver.m_r_x[j] = v;
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@ -583,23 +579,9 @@ public:
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return m_columns_to_ul_pairs()[j].lower_bound_witness();
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}
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// NSB code review - seems superfluous to translate back and forth because
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// get_term(..) that is exposed over API does not ensure that columns that
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// are based on terms are translated back to term indices.
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// would be better to have consistent typing, either lar_term uses cv (and not tv)
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// or they are created to use tv consistently.
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void subs_term_columns(lar_term& t) {
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svector<std::pair<unsigned,unsigned>> columns_to_subs;
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for (const auto & m : t) {
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unsigned tj = adjust_column_index_to_term_index(m.var().index());
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if (tj == m.var().index()) continue;
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columns_to_subs.push_back(std::make_pair(m.var().index(), tj));
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}
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for (const auto & p : columns_to_subs) {
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t.subst_index(p.first, p.second);
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}
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tv column2tv(column_index const& c) const {
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return tv::raw(adjust_column_index_to_term_index(c));
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}
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std::ostream& print_column_info(unsigned j, std::ostream& out) const {
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m_mpq_lar_core_solver.m_r_solver.print_column_info(j, out);
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@ -123,8 +123,7 @@ public:
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const mpq & m_coeff;
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public:
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ival(unsigned var, const mpq & val) : m_var(var), m_coeff(val) { }
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unsigned raw() const { return m_var; }
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tv var() const { return tv::raw(m_var); }
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column_index column() const { return column_index(m_var); }
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const mpq & coeff() const { return m_coeff; }
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};
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@ -143,13 +142,13 @@ public:
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lpvar min_var = -1;
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mpq c;
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for (const auto & p : *this) {
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if (p.var().index() < min_var) {
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min_var = p.var().index();
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if (p.column() < min_var) {
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min_var = p.column();
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}
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}
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lar_term r;
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for (const auto & p : *this) {
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if (p.var().index() == min_var) {
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if (p.column() == min_var) {
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return p.coeff().is_one();
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}
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}
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@ -21,6 +21,11 @@ Revision History:
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#include <sstream>
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namespace nla {
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class core;
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}
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namespace lp {
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typedef unsigned var_index;
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typedef unsigned constraint_index;
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@ -62,8 +67,23 @@ public:
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}
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};
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class column_index {
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unsigned m_index;
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friend class lar_solver;
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friend class lar_term;
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friend nla::core;
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operator unsigned() const { return m_index; }
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public:
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column_index(unsigned j): m_index(j) {}
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unsigned index() const { return m_index; }
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};
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}
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inline std::ostream& operator<<(std::ostream& out, lp::tv const& t) {
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return out << (t.is_term() ? "t":"j") << t.id() << "\n";
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}
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@ -50,7 +50,7 @@ bool core::compare_holds(const rational& ls, llc cmp, const rational& rs) const
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rational core::value(const lp::lar_term& r) const {
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rational ret(0);
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for (const auto & t : r) {
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ret += t.coeff() * val(t.var().index());
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ret += t.coeff() * val(t.column());
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}
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return ret;
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}
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@ -58,7 +58,7 @@ rational core::value(const lp::lar_term& r) const {
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lp::lar_term core::subs_terms_to_columns(const lp::lar_term& t) const {
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lp::lar_term r;
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for (const auto& p : t) {
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lpvar j = p.var().index();
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lpvar j = p.column();
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if (lp::tv::is_term(j))
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j = m_lar_solver.map_term_index_to_column_index(j);
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r.add_monomial(p.coeff(), j);
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@ -323,25 +323,25 @@ bool core:: explain_coeff_lower_bound(const lp::lar_term::ival& p, rational& bou
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SASSERT(!a.is_zero());
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unsigned c; // the index for the lower or the upper bound
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if (a.is_pos()) {
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unsigned c = m_lar_solver.get_column_lower_bound_witness(p.var().index());
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unsigned c = m_lar_solver.get_column_lower_bound_witness(p.column());
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if (c + 1 == 0)
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return false;
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bound = a * m_lar_solver.get_lower_bound(p.var().index()).x;
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bound = a * m_lar_solver.get_lower_bound(p.column()).x;
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e.add(c);
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return true;
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}
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// a.is_neg()
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c = m_lar_solver.get_column_upper_bound_witness(p.var().index());
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c = m_lar_solver.get_column_upper_bound_witness(p.column());
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if (c + 1 == 0)
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return false;
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bound = a * m_lar_solver.get_upper_bound(p.var().index()).x;
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bound = a * m_lar_solver.get_upper_bound(p.column()).x;
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e.add(c);
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return true;
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}
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bool core::explain_coeff_upper_bound(const lp::lar_term::ival& p, rational& bound, lp::explanation& e) const {
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const rational& a = p.coeff();
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lpvar j = p.var().is_term()? m_lar_solver.map_term_index_to_column_index(p.var().index()) : p.var().index();
|
||||
lpvar j = p.column();
|
||||
SASSERT(!a.is_zero());
|
||||
unsigned c; // the index for the lower or the upper bound
|
||||
if (a.is_neg()) {
|
||||
|
@ -426,7 +426,6 @@ bool core:: explain_by_equiv(const lp::lar_term& t, lp::explanation& e) const {
|
|||
void core::mk_ineq(lp::lar_term& t, llc cmp, const rational& rs) {
|
||||
TRACE("nla_solver_details", m_lar_solver.print_term_as_indices(t, tout << "t = "););
|
||||
if (!explain_ineq(t, cmp, rs)) {
|
||||
m_lar_solver.subs_term_columns(t);
|
||||
current_lemma().push_back(ineq(cmp, t, rs));
|
||||
CTRACE("nla_solver", ineq_holds(ineq(cmp, t, rs)), print_ineq(ineq(cmp, t, rs), tout) << "\n";);
|
||||
SASSERT(!ineq_holds(ineq(cmp, t, rs)));
|
||||
|
@ -435,7 +434,6 @@ void core::mk_ineq(lp::lar_term& t, llc cmp, const rational& rs) {
|
|||
|
||||
void core::mk_ineq_no_expl_check(lp::lar_term& t, llc cmp, const rational& rs) {
|
||||
TRACE("nla_solver_details", m_lar_solver.print_term_as_indices(t, tout << "t = "););
|
||||
m_lar_solver.subs_term_columns(t);
|
||||
current_lemma().push_back(ineq(cmp, t, rs));
|
||||
CTRACE("nla_solver", ineq_holds(ineq(cmp, t, rs)), print_ineq(ineq(cmp, t, rs), tout) << "\n";);
|
||||
SASSERT(!ineq_holds(ineq(cmp, t, rs)));
|
||||
|
@ -681,7 +679,7 @@ std::ostream & core::print_ineqs(const lemma& l, std::ostream & out) const {
|
|||
print_ineq(in, out);
|
||||
if (i + 1 < l.ineqs().size()) out << " or ";
|
||||
for (const auto & p: in.m_term)
|
||||
vars.insert(p.var().index());
|
||||
vars.insert(p.column());
|
||||
}
|
||||
out << std::endl;
|
||||
for (lpvar j : vars) {
|
||||
|
@ -864,9 +862,9 @@ bool core:: is_octagon_term(const lp::lar_term& t, bool & sign, lpvar& i, lpvar
|
|||
return false;
|
||||
}
|
||||
if (i == static_cast<lpvar>(-1))
|
||||
i = p.var().index();
|
||||
i = p.column();
|
||||
else
|
||||
j = p.var().index();
|
||||
j = p.column();
|
||||
}
|
||||
SASSERT(j != static_cast<unsigned>(-1));
|
||||
sign = (seen_minus && seen_plus)? false : true;
|
||||
|
@ -987,7 +985,7 @@ std::unordered_set<lpvar> core::collect_vars(const lemma& l) const {
|
|||
|
||||
for (const auto& i : current_lemma().ineqs()) {
|
||||
for (const auto& p : i.term()) {
|
||||
insert_j(p.var().index());
|
||||
insert_j(p.column());
|
||||
}
|
||||
}
|
||||
for (const auto& p : current_expl()) {
|
||||
|
@ -1754,9 +1752,9 @@ std::unordered_set<lpvar> core::get_vars_of_expr_with_opening_terms(const nex *e
|
|||
if (ls.column_corresponds_to_term(j)) {
|
||||
const auto& t = m_lar_solver.get_term(lp::tv::raw(ls.local_to_external(j)));
|
||||
for (auto p : t) {
|
||||
if (ret.find(p.var().index()) == ret.end()) {
|
||||
added.push_back(p.var().index());
|
||||
ret.insert(p.var().index());
|
||||
if (ret.find(p.column()) == ret.end()) {
|
||||
added.push_back(p.column());
|
||||
ret.insert(p.column());
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
@ -357,14 +357,14 @@ public:
|
|||
// we use the form -it + 1 = 0
|
||||
m_work_vector.set_value(one_of_type<T>(), bj);
|
||||
for (auto p : row) {
|
||||
m_work_vector.set_value(-p.coeff(), p.var().index());
|
||||
m_work_vector.set_value(-p.coeff(), p.column().index());
|
||||
// but take care of the basis 1 later
|
||||
}
|
||||
|
||||
// now iterate with pivoting
|
||||
fill_last_row_with_pivoting_loop_block(bj, basis_heading);
|
||||
for (auto p : row) {
|
||||
fill_last_row_with_pivoting_loop_block(p.var().index(), basis_heading);
|
||||
fill_last_row_with_pivoting_loop_block(p.column().index(), basis_heading);
|
||||
}
|
||||
lp_assert(m_work_vector.is_OK());
|
||||
unsigned last_row = row_count() - 1;
|
||||
|
|
|
@ -1523,7 +1523,7 @@ public:
|
|||
if (t.is_term()) {
|
||||
const lp::lar_term& term = lp().get_term(t);
|
||||
for (const auto & i: term) {
|
||||
m_todo_terms.push_back(std::make_pair(i.var(), coeff * i.coeff()));
|
||||
m_todo_terms.push_back(std::make_pair(lp().column2tv(i.column()), coeff * i.coeff()));
|
||||
}
|
||||
}
|
||||
else {
|
||||
|
@ -1555,11 +1555,12 @@ public:
|
|||
if (t2.is_term()) {
|
||||
const lp::lar_term& term = lp().get_term(t2);
|
||||
for (const auto & i : term) {
|
||||
if (m_variable_values.count(i.var().index()) > 0) {
|
||||
result += m_variable_values[i.var().index()] * coeff * i.coeff();
|
||||
auto tv = lp().column2tv(i.column());
|
||||
if (m_variable_values.count(tv.index()) > 0) {
|
||||
result += m_variable_values[tv.index()] * coeff * i.coeff();
|
||||
}
|
||||
else {
|
||||
m_todo_terms.push_back(std::make_pair(i.var(), coeff * i.coeff()));
|
||||
m_todo_terms.push_back(std::make_pair(tv, coeff * i.coeff()));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
@ -1955,7 +1956,7 @@ public:
|
|||
expr_ref t(m);
|
||||
expr_ref_vector ts(m);
|
||||
for (auto const& p : term) {
|
||||
auto ti = p.var();
|
||||
auto ti = lp().column2tv(p.column());
|
||||
if (ti.is_term()) {
|
||||
ts.push_back(multerm(p.coeff(), term2expr(lp().get_term(ti))));
|
||||
}
|
||||
|
@ -1997,7 +1998,7 @@ public:
|
|||
lp().print_term(term, out << "bound: ");
|
||||
out << (upper?" <= ":" >= ") << k << "\n";
|
||||
for (auto const& p : term) {
|
||||
auto ti = p.var();
|
||||
auto ti = lp().column2tv(p.column());
|
||||
out << p.coeff() << " * ";
|
||||
if (ti.is_term()) {
|
||||
lp().print_term(lp().get_term(ti), out) << "\n";
|
||||
|
@ -2798,7 +2799,7 @@ public:
|
|||
m_todo_vars.pop_back();
|
||||
lp::lar_term const& term = lp().get_term(ti);
|
||||
for (auto const& p : term) {
|
||||
lp::tv wi = p.var();
|
||||
lp::tv wi = lp().column2tv(p.column());
|
||||
if (wi.is_term()) {
|
||||
m_todo_vars.push_back(wi);
|
||||
}
|
||||
|
@ -2824,7 +2825,7 @@ public:
|
|||
m_todo_vars.pop_back();
|
||||
lp::lar_term const& term = lp().get_term(ti);
|
||||
for (auto const& coeff : term) {
|
||||
auto wi = coeff.var();
|
||||
auto wi = lp().column2tv(coeff.column());
|
||||
if (wi.is_term()) {
|
||||
m_todo_vars.push_back(wi);
|
||||
}
|
||||
|
@ -2914,7 +2915,7 @@ public:
|
|||
SASSERT(ti.is_term());
|
||||
lp::lar_term const& term = m_solver->get_term(ti);
|
||||
for (auto const mono : term) {
|
||||
auto wi = mono.var();
|
||||
auto wi = lp().column2tv(mono.column());
|
||||
lp::constraint_index ci;
|
||||
rational value;
|
||||
bool is_strict;
|
||||
|
@ -3377,7 +3378,7 @@ public:
|
|||
m_nra->am().set(r1, c1.to_mpq());
|
||||
m_nra->am().add(r, r1, r);
|
||||
for (auto const & arg : term) {
|
||||
auto wi = arg.var();
|
||||
auto wi = lp().column2tv(arg.column());
|
||||
c1 = arg.coeff() * wcoeff;
|
||||
if (wi.is_term()) {
|
||||
m_todo_terms.push_back(std::make_pair(wi, c1));
|
||||
|
@ -3658,23 +3659,17 @@ public:
|
|||
TRACE("arith", lp().print_term(term, tout) << "\n";);
|
||||
for (const auto & ti : term) {
|
||||
theory_var w;
|
||||
if (ti.var().is_term()) {
|
||||
lp::lar_term const& term1 = lp().get_term(ti.var());
|
||||
auto tv = lp().column2tv(ti.column());
|
||||
if (tv.is_term()) {
|
||||
lp::lar_term const& term1 = lp().get_term(tv);
|
||||
rational coeff2 = coeff * ti.coeff();
|
||||
term2coeffs(term1, coeffs, coeff2);
|
||||
continue;
|
||||
}
|
||||
else if (lp().column_corresponds_to_term(ti.var().index())) {
|
||||
lp::tv t = lp::tv::term(ti.var().index());
|
||||
lp::lar_term const& term1 = lp().get_term(t);
|
||||
rational coeff2 = coeff * ti.coeff();
|
||||
term2coeffs(term1, coeffs, coeff2);
|
||||
continue;
|
||||
}
|
||||
else {
|
||||
w = lp().local_to_external(ti.var().index());
|
||||
w = lp().local_to_external(tv.id());
|
||||
SASSERT(w >= 0);
|
||||
TRACE("arith", tout << (ti.var().index()) << ": " << w << "\n";);
|
||||
TRACE("arith", tout << (tv.id()) << ": " << w << "\n";);
|
||||
}
|
||||
rational c0(0);
|
||||
coeffs.find(w, c0);
|
||||
|
|
Loading…
Reference in a new issue