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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
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Lev Nachmanson 2025-08-09 14:05:58 -07:00
parent eb7fd9efaa
commit c0ed9b68e0
1 changed files with 45 additions and 1 deletions
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46
src/nlsat/nlsat_types.h
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@ -22,7 +22,7 @@ Revision History:
#include "util/buffer.h"
#include "sat/sat_types.h"
#include "util/z3_exception.h"
#include <vector>
namespace algebraic_numbers {
class anum;
class manager;
@ -143,6 +143,50 @@ namespace nlsat {
struct eq_proc { bool operator()(root_atom const * a1, root_atom const * a2) const; };
};
/**
\brief An indexed root expression designates the i-th real root of a (square-free) polynomial p when regarded as
a univariate over its maximal variable x after substituting the current values for variables < x.
It is a lightweight value object used by projection / sample-cell algorithms. It does not own the polynomial.
*/
struct indexed_root {
poly * m_p; // polynomial whose root is referenced (assumed non-null)
unsigned m_index; // root index (0-based internally; corresponds to paper's i)
var m_var; // the main variable of m_p when treated as univariate
indexed_root(): m_p(nullptr), m_index(0), m_var(null_var) {}
indexed_root(poly* p, unsigned i, var x): m_p(p), m_index(i), m_var(x) {}
poly * p() const { return m_p; }
unsigned index() const { return m_index; }
var x() const { return m_var; }
bool is_null() const { return m_p == nullptr; }
// ordering helper (by variable then polynomial id then index) - total but arbitrary
struct lt {
pmanager & m_pm;
lt(pmanager & pm): m_pm(pm) {}
bool operator()(indexed_root const & a, indexed_root const & b) const {
if (a.m_var != b.m_var) return a.m_var < b.m_var;
if (a.m_p != b.m_p) return m_pm.id(a.m_p) < m_pm.id(b.m_p);
return a.m_index < b.m_index;
}
};
struct hash_proc {
pmanager & m_pm;
hash_proc(pmanager & pm): m_pm(pm) {}
unsigned operator()(indexed_root const & r) const {
return combine(combine(m_pm.id(r.m_p), r.m_index), r.m_var);
}
static unsigned combine(unsigned a, unsigned b) { return a * 1315423911u + b + (a<<5) + (b>>2); }
};
struct eq_proc {
pmanager & m_pm;
eq_proc(pmanager & pm): m_pm(pm) {}
bool operator()(indexed_root const & a, indexed_root const & b) const {
return a.m_var == b.m_var && a.m_index == b.m_index && a.m_p == b.m_p; }
};
};
typedef std::vector<indexed_root> indexed_root_vector;
inline ineq_atom * to_ineq_atom(atom * a) { SASSERT(a->is_ineq_atom()); return static_cast<ineq_atom*>(a); }
inline root_atom * to_root_atom(atom * a) { SASSERT(a->is_root_atom()); return static_cast<root_atom*>(a); }
inline ineq_atom const * to_ineq_atom(atom const * a) { SASSERT(a->is_ineq_atom()); return static_cast<ineq_atom const *>(a); }