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in the middle

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Lev Nachmanson 2024-08-20 16:01:07 -10:00 • committed by Lev Nachmanson
parent 122e0135d2
commit 5a36e02c58
1 changed files with 104 additions and 26 deletions
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130
src/math/lp/dioph_eq.cpp
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@ -7,32 +7,91 @@
namespace lp {
// This class represents a term with an added constant number c, in form sum {x_i*a_i} + c.
class term_o:public lar_term {
mpq m_c;
public:
const mpq& c() const { return m_c; }
mpq& c() { return m_c; }
term_o():m_c(0) {}
term_o& operator*=(mpq const& k) {
for (auto & t : m_coeffs)
t.m_value *= k;
return *this;
}
};
class dioph_eq::imp {
class term_o:public lar_term {
mpq m_c;
public:
const mpq& c() const { return m_c; }
mpq& c() { return m_c; }
term_o():m_c(0) {}
term_o& operator*=(mpq const& k) {
for (auto & t : m_coeffs)
t.m_value *= k;
return *this;
}
void substitute(const term_o& t, unsigned term_column) {
auto it = this->m_coeffs.find_core(term_column);
if (it == nullptr) return;
mpq a = it->get_data().m_value;
this->m_coeffs.erase(term_column);
for (auto p : t) {
this->add_monomial(a * p.coeff(), p.j());
}
this->c() += a * t.c();
}
};
std::ostream& print_term(term_o const& term, std::ostream& out, const std::string & var_prefix) const {
if (term.size() == 0) {
out << "0";
return out;
}
bool first = true;
for (const auto p : term) {
mpq val = p.coeff();
if (first) {
first = false;
}
else if (is_pos(val)) {
out << " + ";
}
else {
out << " - ";
val = -val;
}
if (val == -numeric_traits<mpq>::one())
out << " - ";
else if (val != numeric_traits<mpq>::one())
out << T_to_string(val);
out << var_prefix << p.j();
}
if (!term.c().is_zero())
out << " + " << term.c();
return out;
}
/*
An annotated state is a triple ⟨E′, λ, σ⟩, where E′ is a set of pairs ⟨e, ℓ⟩ in which
e is an equation and ℓ is a linear combination of variables from L
*/
struct eprime_pair {
term_o * m_e;
lar_term * m_l;
};
vector<eprime_pair> m_eprime;
/*
Let L be a set of variables disjoint from X, and let λ be a mapping from variables in
L to linear combinations of variables in X and of integer constants
*/
u_map<unsigned> m_lambda; // maps to the index of the term in m_eprime
/* let σ be a partial mapping from variables in L united with X to linear combinations
of variables in X and of integer constants showing the substitutions
*/
u_map<lar_term*> m_sigma;
public:
int_solver& lia;
lar_solver& lra;
unsigned m_fresh_x_vars_start;
unsigned m_last_fresh_x_var;
// set F
std::list<term_o*> m_f;
std::list<unsigned> m_f; // F = {λ(t):t in m_f}
// set S
std::list<term_o*> m_s;
std::list<unsigned> m_s; // S = {λ(t): t in m_s}
t imp(int_solver& lia, lar_solver& lra): lia(lia), lra(lra) {
m_fresh_x_vars_start = lra.number_of_vars();
imp(int_solver& lia, lar_solver& lra): lia(lia), lra(lra) {
m_last_fresh_x_var = -1;
}
@ -71,7 +130,14 @@ namespace lp {
t->c() += lia.lower_bound(p.var()).x;
}
}
m_f.push_back(t);
unsigned lvar = static_cast<unsigned>(m_f.size());
lar_term* lt = new lar_term();
lt->add_var(lvar);
eprime_pair pair = {t, lt};
m_eprime.push_back(pair);
m_lambda.insert(lvar, lvar);
m_f.push_back(lvar);
}
}
@ -103,7 +169,8 @@ namespace lp {
}
// returns true if no conflict is found and false otherwise
bool normalize_by_gcd() {
for (auto * e: m_f) {
for (unsigned l: m_f) {
term_o* e = m_eprime[l].m_e;
if (!normalize_e_by_gcd(*e)) {
return false;
}
@ -120,17 +187,27 @@ namespace lp {
}
return lia_move::sat;
}
std::list<term_o*>::iterator pick_eh() {
std::list<unsigned>::iterator pick_eh() {
return m_f.begin(); // TODO: make a smarter joice
}
void substitute(unsigned k, term_o* s) {
NOT_IMPLEMENTED_YET();
print_term(*s, std::cout<< k<< "->", "x") << std::endl;
for (unsigned e_index: m_f) {
term_o* e = m_eprime[e_index].m_e;
if (!e->contains(k)) continue;
print_term(*e, std::cout << "before:", "x") << std::endl;
e->substitute(*s, k);
print_term(*e, std::cout << "after :", "x") << std::endl;
}
}
// this is the step 6 or 7 of the algorithm
void rewrite_eqs() {
auto eh_it = pick_eh();
term_o* eh = *eh_it;
auto eh_it = pick_eh();
auto eprime_entry = m_eprime[*eh_it];
std
term_o* eh = m_eprime[*eh_it].m_e;
// looking for minimal in absolute value coefficient
bool first = true;
mpq ahk;
@ -154,14 +231,15 @@ namespace lp {
if (p.j() == k) continue;
s_term->add_monomial(-k_sign*p.coeff(), p.j());
}
m_s.push_back(*eh_it);
m_f.erase(eh_it);
m_s.push_back(s_term);
m_sigma.insert(k, s_term);
substitute(k, s_term);
} else {
// step 7
// the fresh variable
unsigned xt = m_last_fresh_x_var == -1? m_fresh_x_vars_start: m_last_fresh_x_var++;
unsigned xt = m_last_fresh_x_var++;
NOT_IMPLEMENTED_YET();
}