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https://github.com/Z3Prover/z3
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Add accessors for RCF numeral internals (#7013)
This commit is contained in:
Christoph M. Wintersteiger
GitHub
parent
9382b96a32
commit
16753e43f1
7 changed files with 845 additions and 117 deletions
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@ -2498,6 +2498,35 @@ namespace realclosure {
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}
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}
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/**
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\brief Return true if a is an algebraic number.
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*/
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bool is_algebraic(numeral const & a) {
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return is_rational_function(a) && to_rational_function(a)->ext()->is_algebraic();
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}
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/**
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\brief Return true if a represents an infinitesimal.
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*/
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bool is_infinitesimal(numeral const & a) {
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return is_rational_function(a) && to_rational_function(a)->ext()->is_infinitesimal();
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}
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/**
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\brief Return true if a is a transcendental.
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*/
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bool is_transcendental(numeral const & a) {
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return is_rational_function(a) && to_rational_function(a)->ext()->is_transcendental();
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}
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/**
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\brief Return true if a is a rational.
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*/
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bool is_rational(numeral const & a) {
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return a.m_value->is_rational();
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}
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/**
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\brief Return true if a depends on infinitesimal extensions.
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*/
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@ -3330,6 +3359,151 @@ namespace realclosure {
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set(q, _q);
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}
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unsigned extension_index(numeral const & a) {
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if (!is_rational_function(a))
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return -1;
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return to_rational_function(a)->ext()->idx();
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}
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symbol transcendental_name(numeral const & a) {
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if (!is_transcendental(a))
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return symbol();
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return to_transcendental(to_rational_function(a)->ext())->m_name;
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}
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symbol infinitesimal_name(numeral const & a) {
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if (!is_infinitesimal(a))
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return symbol();
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return to_infinitesimal(to_rational_function(a)->ext())->m_name;
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}
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unsigned num_coefficients(numeral const & a) {
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if (!is_algebraic(a))
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return 0;
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return to_algebraic(to_rational_function(a)->ext())->p().size();
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}
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numeral get_coefficient(numeral const & a, unsigned i)
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{
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if (!is_algebraic(a))
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return numeral();
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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if (i >= ext->p().size())
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return numeral();
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value_ref v(*this);
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v = ext->p()[i];
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numeral r;
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set(r, v);
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return r;
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}
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unsigned num_sign_conditions(numeral const & a) {
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unsigned r = 0;
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if (is_algebraic(a)) {
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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const sign_det * sdt = ext->sdt();
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if (sdt) {
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sign_condition * sc = sdt->sc(ext->sc_idx());
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while (sc) {
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r++;
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sc = sc->prev();
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}
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}
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}
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return r;
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}
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int get_sign_condition_sign(numeral const & a, unsigned i)
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{
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if (!is_algebraic(a))
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return 0;
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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const sign_det * sdt = ext->sdt();
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if (!sdt)
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return 0;
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else {
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sign_condition * sc = sdt->sc(ext->sc_idx());
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while (i) {
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if (sc) sc = sc->prev();
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i--;
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}
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return sc ? sc->sign() : 0;
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}
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}
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bool get_interval(numeral const & a, int & lower_is_inf, int & lower_is_open, numeral & lower, int & upper_is_inf, int & upper_is_open, numeral & upper)
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{
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if (!is_algebraic(a))
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return false;
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lower = numeral();
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upper = numeral();
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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mpbqi &ivl = ext->iso_interval();
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lower_is_inf = ivl.lower_is_inf();
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lower_is_open = ivl.lower_is_open();
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if (!m_bqm.is_zero(ivl.lower()))
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set(lower, mk_rational(ivl.lower()));
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upper_is_inf = ivl.upper_is_inf();
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upper_is_open = ivl.upper_is_open();
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if (!m_bqm.is_zero(ivl.upper()))
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set(upper, mk_rational(ivl.upper()));
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return true;
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}
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unsigned get_sign_condition_size(numeral const &a, unsigned i) {
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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const sign_det * sdt = ext->sdt();
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if (!sdt)
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return 0;
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sign_condition * sc = sdt->sc(ext->sc_idx());
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while (i) {
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if (sc) sc = sc->prev();
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i--;
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}
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return ext->sdt()->qs()[sc->qidx()].size();
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}
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int num_sign_condition_coefficients(numeral const &a, unsigned i)
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{
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if (!is_algebraic(a))
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return 0;
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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const sign_det * sdt = ext->sdt();
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if (!sdt)
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return 0;
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sign_condition * sc = sdt->sc(ext->sc_idx());
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while (i) {
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if (sc) sc = sc->prev();
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i--;
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}
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const polynomial & q = ext->sdt()->qs()[sc->qidx()];
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return q.size();
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}
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numeral get_sign_condition_coefficient(numeral const &a, unsigned i, unsigned j)
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{
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if (!is_algebraic(a))
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return numeral();
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algebraic * ext = to_algebraic(to_rational_function(a)->ext());
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const sign_det * sdt = ext->sdt();
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if (!sdt)
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return numeral();
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sign_condition * sc = sdt->sc(ext->sc_idx());
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while (i) {
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if (sc) sc = sc->prev();
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i--;
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}
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const polynomial & q = ext->sdt()->qs()[sc->qidx()];
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if (j >= q.size())
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return numeral();
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value_ref v(*this);
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v = q[j];
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numeral r;
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set(r, v);
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return r;
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}
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// ---------------------------------
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//
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// GCD of integer coefficients
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@ -6103,6 +6277,22 @@ namespace realclosure {
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return m_imp->is_int(a);
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}
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bool manager::is_rational(numeral const & a) {
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return m_imp->is_rational(a);
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}
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bool manager::is_algebraic(numeral const & a) {
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return m_imp->is_algebraic(a);
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}
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bool manager::is_infinitesimal(numeral const & a) {
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return m_imp->is_infinitesimal(a);
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}
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bool manager::is_transcendental(numeral const & a) {
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return m_imp->is_transcendental(a);
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}
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bool manager::depends_on_infinitesimals(numeral const & a) {
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return m_imp->depends_on_infinitesimals(a);
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}
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@ -6251,6 +6441,56 @@ namespace realclosure {
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save_interval_ctx ctx(this);
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m_imp->clean_denominators(a, p, q);
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}
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unsigned manager::extension_index(numeral const & a)
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{
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return m_imp->extension_index(a);
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}
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symbol manager::transcendental_name(numeral const &a)
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{
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return m_imp->transcendental_name(a);
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}
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symbol manager::infinitesimal_name(numeral const &a)
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{
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return m_imp->infinitesimal_name(a);
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}
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unsigned manager::num_coefficients(numeral const &a)
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{
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return m_imp->num_coefficients(a);
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}
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manager::numeral manager::get_coefficient(numeral const &a, unsigned i)
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{
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return m_imp->get_coefficient(a, i);
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}
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unsigned manager::num_sign_conditions(numeral const &a)
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{
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return m_imp->num_sign_conditions(a);
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}
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int manager::get_sign_condition_sign(numeral const &a, unsigned i)
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{
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return m_imp->get_sign_condition_sign(a, i);
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}
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bool manager::get_interval(numeral const & a, int & lower_is_inf, int & lower_is_open, numeral & lower, int & upper_is_inf, int & upper_is_open, numeral & upper)
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{
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return m_imp->get_interval(a, lower_is_inf, lower_is_open, lower, upper_is_inf, upper_is_open, upper);
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}
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unsigned manager::num_sign_condition_coefficients(numeral const &a, unsigned i)
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{
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return m_imp->num_sign_condition_coefficients(a, i);
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}
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manager::numeral manager::get_sign_condition_coefficient(numeral const &a, unsigned i, unsigned j)
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{
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return m_imp->get_sign_condition_coefficient(a, i, j);
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}
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};
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void pp(realclosure::manager::imp * imp, realclosure::polynomial const & p, realclosure::extension * ext) {
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@ -70,14 +70,14 @@ namespace realclosure {
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*/
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void mk_infinitesimal(char const * name, char const * pp_name, numeral & r);
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void mk_infinitesimal(numeral & r);
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/**
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\brief Add a new transcendental real value to the field.
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\brief Add a new transcendental real value to the field.
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The functor \c mk_interval is used to compute approximations of the transcendental value.
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This procedure should be used with care, if the value is not really transcendental with respect to the current
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field, computations with the new numeral may not terminate.
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Example: we extended the field with Pi. Pi is transcendental with respect to a field that contains only algebraic real numbers.
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So, this step is fine. Let us call the resultant field F.
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So, this step is fine. Let us call the resultant field F.
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Then, we extend the field F with 1 - Pi. 1 - Pi is transcendental with respect to algebraic real numbers, but it is NOT transcendental
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with respect to F, since F contains Pi.
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*/
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@ -109,12 +109,12 @@ namespace realclosure {
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\brief Return the sign of a.
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*/
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int sign(numeral const & a);
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/**
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\brief Return true if a is zero.
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*/
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bool is_zero(numeral const & a);
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/**
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\brief Return true if a is positive.
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*/
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@ -129,13 +129,33 @@ namespace realclosure {
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\brief Return true if a is an integer.
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*/
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bool is_int(numeral const & a);
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/**
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\brief Return true if a is a rational.
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*/
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bool is_rational(numeral const & a);
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/**
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\brief Return true if a is an algebraic number.
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*/
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bool is_algebraic(numeral const & a);
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/**
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\brief Return true if a represents an infinitesimal.
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*/
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bool is_infinitesimal(numeral const & a);
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/**
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\brief Return true if a is a transcendental.
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*/
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bool is_transcendental(numeral const & a);
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/**
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\brief Return true if the representation of \c a depends on
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infinitesimal extensions.
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*/
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bool depends_on_infinitesimals(numeral const & a);
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/**
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\brief a <- n
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*/
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@ -148,14 +168,14 @@ namespace realclosure {
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/**
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\brief Return a^{1/k}
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Throws an exception if (a is negative and k is even) or (k is zero).
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*/
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*/
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void root(numeral const & a, unsigned k, numeral & b);
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/**
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\brief Return a^k
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Throws an exception if 0^0.
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*/
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void power(numeral const & a, unsigned k, numeral & b);
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@ -180,7 +200,7 @@ namespace realclosure {
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\brief a <- -a
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*/
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void neg(numeral & a);
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/**
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\brief b <- -a
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*/
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@ -190,7 +210,7 @@ namespace realclosure {
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\brief a <- 1/a if a != 0
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*/
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void inv(numeral & a);
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/**
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\brief b <- 1/a if a != 0
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*/
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@ -207,7 +227,7 @@ namespace realclosure {
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Return 1 if a > b
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*/
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int compare(numeral const & a, numeral const & b);
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/**
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\brief a == b
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*/
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@ -249,7 +269,7 @@ namespace realclosure {
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bool ge(numeral const & a, numeral const & b) { return !lt(a, b); }
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bool ge(numeral const & a, mpq const & b) { return !lt(a, b); }
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bool ge(numeral const & a, mpz const & b) { return !lt(a, b); }
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void display(std::ostream & out, numeral const & a, bool compact=false, bool pp=false) const;
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/**
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@ -259,10 +279,30 @@ namespace realclosure {
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*/
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void display_decimal(std::ostream & out, numeral const & a, unsigned precision = 10) const;
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void display_interval(std::ostream & out, numeral const & a) const;
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void clean_denominators(numeral const & a, numeral & p, numeral & q);
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unsigned extension_index(numeral const & a);
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symbol transcendental_name(numeral const &a);
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symbol infinitesimal_name(numeral const &a);
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unsigned num_coefficients(numeral const &a);
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numeral get_coefficient(numeral const &a, unsigned i);
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unsigned num_sign_conditions(numeral const &a);
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int get_sign_condition_sign(numeral const &a, unsigned i);
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bool get_interval(numeral const & a, int & lower_is_inf, int & lower_is_open, numeral & lower, int & upper_is_inf, int & upper_is_open, numeral & upper);
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unsigned num_sign_condition_coefficients(numeral const &a, unsigned i);
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numeral get_sign_condition_coefficient(numeral const &a, unsigned i, unsigned j);
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};
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struct value;
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