diff --git a/src/api/api_rcf.cpp b/src/api/api_rcf.cpp
index b325c4397..42558ba9e 100644
--- a/src/api/api_rcf.cpp
+++ b/src/api/api_rcf.cpp
@@ -98,13 +98,13 @@ extern "C" {
Z3_CATCH_RETURN(0);
}
- Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(Z3_context c, Z3_string name) {
+ Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(Z3_context c) {
Z3_TRY;
- LOG_Z3_rcf_mk_infinitesimal(c, name);
+ LOG_Z3_rcf_mk_infinitesimal(c);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
- rcfm(c).mk_infinitesimal(name, r);
+ rcfm(c).mk_infinitesimal(r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
@@ -268,13 +268,13 @@ extern "C" {
Z3_CATCH_RETURN(Z3_FALSE);
}
- Z3_string Z3_API Z3_rcf_num_to_string(Z3_context c, Z3_rcf_num a, Z3_bool compact) {
+ Z3_string Z3_API Z3_rcf_num_to_string(Z3_context c, Z3_rcf_num a, Z3_bool compact, Z3_bool html) {
Z3_TRY;
- LOG_Z3_rcf_num_to_string(c, a, compact);
+ LOG_Z3_rcf_num_to_string(c, a, compact, html);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
std::ostringstream buffer;
- rcfm(c).display(buffer, to_rcnumeral(a), compact != 0);
+ rcfm(c).display(buffer, to_rcnumeral(a), compact != 0, html != 0);
return mk_c(c)->mk_external_string(buffer.str());
Z3_CATCH_RETURN("");
}
diff --git a/src/api/python/z3rcf.py b/src/api/python/z3rcf.py
index b9c947b9f..66a6890c3 100644
--- a/src/api/python/z3rcf.py
+++ b/src/api/python/z3rcf.py
@@ -29,8 +29,10 @@ def E(ctx=None):
return RCFNum(Z3_rcf_mk_e(ctx.ref()), ctx)
def MkInfinitesimal(name="eps", ctx=None):
+ # Todo: remove parameter name.
+ # For now, we keep it for backward compatibility.
ctx = z3._get_ctx(ctx)
- return RCFNum(Z3_rcf_mk_infinitesimal(ctx.ref(), name), ctx)
+ return RCFNum(Z3_rcf_mk_infinitesimal(ctx.ref()), ctx)
def MkRoots(p, ctx=None):
ctx = z3._get_ctx(ctx)
@@ -49,6 +51,7 @@ def MkRoots(p, ctx=None):
return r
class RCFNum:
+ html = False
def __init__(self, num, ctx=None):
# TODO: add support for converting AST numeral values into RCFNum
if isinstance(num, RCFNumObj):
@@ -65,10 +68,10 @@ class RCFNum:
return self.ctx.ref()
def __repr__(self):
- return Z3_rcf_num_to_string(self.ctx_ref(), self.num, False)
+ return Z3_rcf_num_to_string(self.ctx_ref(), self.num, False, RCFNum.html)
def compact_str(self):
- return Z3_rcf_num_to_string(self.ctx_ref(), self.num, True)
+ return Z3_rcf_num_to_string(self.ctx_ref(), self.num, True, RCFNum.html)
def __add__(self, other):
v = _to_rcfnum(other, self.ctx)
diff --git a/src/api/z3_rcf.h b/src/api/z3_rcf.h
index 305033690..e2b4b7e05 100644
--- a/src/api/z3_rcf.h
+++ b/src/api/z3_rcf.h
@@ -64,9 +64,9 @@ extern "C" {
/**
\brief Return a new infinitesimal that is smaller than all elements in the Z3 field.
- def_API('Z3_rcf_mk_infinitesimal', RCF_NUM, (_in(CONTEXT), _in(STRING)))
+ def_API('Z3_rcf_mk_infinitesimal', RCF_NUM, (_in(CONTEXT),))
*/
- Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(__in Z3_context c, __in Z3_string name);
+ Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(__in Z3_context c);
/**
\brief Store in roots the roots of the polynomial a[n-1]*x^{n-1} + ... + a[0].
@@ -173,9 +173,9 @@ extern "C" {
/**
\brief Convert the RCF numeral into a string.
- def_API('Z3_rcf_num_to_string', STRING, (_in(CONTEXT), _in(RCF_NUM), _in(BOOL)))
+ def_API('Z3_rcf_num_to_string', STRING, (_in(CONTEXT), _in(RCF_NUM), _in(BOOL), _in(BOOL)))
*/
- Z3_string Z3_API Z3_rcf_num_to_string(__in Z3_context c, __in Z3_rcf_num a, __in Z3_bool compact);
+ Z3_string Z3_API Z3_rcf_num_to_string(__in Z3_context c, __in Z3_rcf_num a, __in Z3_bool compact, __in Z3_bool html);
/**
\brief Convert the RCF numeral into a string in decimal notation.
diff --git a/src/math/interval/interval.h b/src/math/interval/interval.h
index 1fe797861..ed7654f01 100644
--- a/src/math/interval/interval.h
+++ b/src/math/interval/interval.h
@@ -231,6 +231,7 @@ public:
bool contains(interval const & n, numeral const & v) const;
void display(std::ostream & out, interval const & n) const;
+ void display_pp(std::ostream & out, interval const & n) const;
bool check_invariant(interval const & n) const;
diff --git a/src/math/interval/interval_def.h b/src/math/interval/interval_def.h
index 51c1652d7..89d699f1f 100644
--- a/src/math/interval/interval_def.h
+++ b/src/math/interval/interval_def.h
@@ -643,6 +643,15 @@ void interval_manager::display(std::ostream & out, interval const & n) const
out << (upper_is_open(n) ? ")" : "]");
}
+template
+void interval_manager::display_pp(std::ostream & out, interval const & n) const {
+ out << (lower_is_open(n) ? "(" : "[");
+ ::display_pp(out, m(), lower(n), lower_kind(n));
+ out << ", ";
+ ::display_pp(out, m(), upper(n), upper_kind(n));
+ out << (upper_is_open(n) ? ")" : "]");
+}
+
template
bool interval_manager::check_invariant(interval const & n) const {
if (::eq(m(), lower(n), lower_kind(n), upper(n), upper_kind(n))) {
diff --git a/src/math/realclosure/realclosure.cpp b/src/math/realclosure/realclosure.cpp
index dac4c8e09..8c6a1d232 100644
--- a/src/math/realclosure/realclosure.cpp
+++ b/src/math/realclosure/realclosure.cpp
@@ -298,26 +298,41 @@ namespace realclosure {
struct transcendental : public extension {
symbol m_name;
+ symbol m_pp_name;
unsigned m_k;
mk_interval & m_proc;
- transcendental(unsigned idx, symbol const & n, mk_interval & p):extension(TRANSCENDENTAL, idx), m_name(n), m_k(0), m_proc(p) {}
+ transcendental(unsigned idx, symbol const & n, symbol const & pp_n, mk_interval & p):
+ extension(TRANSCENDENTAL, idx), m_name(n), m_pp_name(pp_n), m_k(0), m_proc(p) {}
- void display(std::ostream & out) const {
- out << m_name;
+ void display(std::ostream & out, bool pp = false) const {
+ if (pp)
+ out << m_pp_name;
+ else
+ out << m_name;
}
};
struct infinitesimal : public extension {
symbol m_name;
+ symbol m_pp_name;
- infinitesimal(unsigned idx, symbol const & n):extension(INFINITESIMAL, idx), m_name(n) {}
+ infinitesimal(unsigned idx, symbol const & n, symbol const & pp_n):extension(INFINITESIMAL, idx), m_name(n), m_pp_name(pp_n) {}
- void display(std::ostream & out) const {
- if (m_name.is_numerical())
- out << "eps!" << m_name.get_num();
- else
- out << m_name;
+ void display(std::ostream & out, bool pp = false) const {
+ if (pp) {
+ if (m_pp_name.is_numerical())
+ out << "ε" << m_pp_name.get_num() << "";
+ else
+ out << m_pp_name;
+
+ }
+ else {
+ if (m_name.is_numerical())
+ out << "eps!" << m_name.get_num();
+ else
+ out << m_name;
+ }
}
};
@@ -1266,9 +1281,9 @@ namespace realclosure {
/**
\brief Create a new infinitesimal.
*/
- void mk_infinitesimal(symbol const & n, numeral & r) {
+ void mk_infinitesimal(symbol const & n, symbol const & pp_n, numeral & r) {
unsigned idx = next_infinitesimal_idx();
- infinitesimal * eps = alloc(infinitesimal, idx, n);
+ infinitesimal * eps = alloc(infinitesimal, idx, n, pp_n);
m_extensions[extension::INFINITESIMAL].push_back(eps);
set_lower(eps->interval(), mpbq(0));
@@ -1280,12 +1295,12 @@ namespace realclosure {
SASSERT(depends_on_infinitesimals(r));
}
- void mk_infinitesimal(char const * n, numeral & r) {
- mk_infinitesimal(symbol(n), r);
+ void mk_infinitesimal(char const * n, char const * pp_n, numeral & r) {
+ mk_infinitesimal(symbol(n), symbol(pp_n), r);
}
void mk_infinitesimal(numeral & r) {
- mk_infinitesimal(symbol(next_infinitesimal_idx()), r);
+ mk_infinitesimal(symbol(next_infinitesimal_idx()), symbol(next_infinitesimal_idx()), r);
}
void refine_transcendental_interval(transcendental * t) {
@@ -1318,9 +1333,9 @@ namespace realclosure {
}
}
- void mk_transcendental(symbol const & n, mk_interval & proc, numeral & r) {
+ void mk_transcendental(symbol const & n, symbol const & pp_n, mk_interval & proc, numeral & r) {
unsigned idx = next_transcendental_idx();
- transcendental * t = alloc(transcendental, idx, n, proc);
+ transcendental * t = alloc(transcendental, idx, n, pp_n, proc);
m_extensions[extension::TRANSCENDENTAL].push_back(t);
while (contains_zero(t->interval())) {
@@ -1332,12 +1347,12 @@ namespace realclosure {
SASSERT(!depends_on_infinitesimals(r));
}
- void mk_transcendental(char const * p, mk_interval & proc, numeral & r) {
- mk_transcendental(symbol(p), proc, r);
+ void mk_transcendental(char const * p, char const * pp_n, mk_interval & proc, numeral & r) {
+ mk_transcendental(symbol(p), symbol(pp_n), proc, r);
}
void mk_transcendental(mk_interval & proc, numeral & r) {
- mk_transcendental(symbol(next_transcendental_idx()), proc, r);
+ mk_transcendental(symbol(next_transcendental_idx()), symbol(next_transcendental_idx()), proc, r);
}
void mk_pi(numeral & r) {
@@ -1345,7 +1360,7 @@ namespace realclosure {
set(r, m_pi);
}
else {
- mk_transcendental(symbol("pi"), m_mk_pi_interval, r);
+ mk_transcendental(symbol("pi"), symbol("π"), m_mk_pi_interval, r);
m_pi = r.m_value;
inc_ref(m_pi);
}
@@ -1356,7 +1371,7 @@ namespace realclosure {
set(r, m_e);
}
else {
- mk_transcendental(symbol("e"), m_mk_e_interval, r);
+ mk_transcendental(symbol("e"), symbol("e"), m_mk_e_interval, r);
m_e = r.m_value;
inc_ref(m_e);
}
@@ -5762,7 +5777,7 @@ namespace realclosure {
}
template
- void display_polynomial(std::ostream & out, unsigned sz, value * const * p, DisplayVar const & display_var, bool compact) const {
+ void display_polynomial(std::ostream & out, unsigned sz, value * const * p, DisplayVar const & display_var, bool compact, bool pp) const {
if (sz == 0) {
out << "0";
return;
@@ -5778,33 +5793,44 @@ namespace realclosure {
else
out << " + ";
if (i == 0)
- display(out, p[i], compact);
+ display(out, p[i], compact, pp);
else {
if (!is_rational_one(p[i])) {
if (use_parenthesis(p[i])) {
out << "(";
- display(out, p[i], compact);
- out << ")*";
+ display(out, p[i], compact, pp);
+ out << ")";
+ if (pp)
+ out << " ";
+ else
+ out << "*";
}
else {
- display(out, p[i], compact);
- out << "*";
+ display(out, p[i], compact, pp);
+ if (pp)
+ out << " ";
+ else
+ out << "*";
}
}
- display_var(out, compact);
- if (i > 1)
- out << "^" << i;
+ display_var(out, compact, pp);
+ if (i > 1) {
+ if (pp)
+ out << "" << i << "";
+ else
+ out << "^" << i;
+ }
}
}
}
template
- void display_polynomial(std::ostream & out, polynomial const & p, DisplayVar const & display_var, bool compact) const {
- display_polynomial(out, p.size(), p.c_ptr(), display_var, compact);
+ void display_polynomial(std::ostream & out, polynomial const & p, DisplayVar const & display_var, bool compact, bool pp) const {
+ display_polynomial(out, p.size(), p.c_ptr(), display_var, compact, pp);
}
struct display_free_var_proc {
- void operator()(std::ostream & out, bool compact) const {
+ void operator()(std::ostream & out, bool compact, bool pp) const {
out << "x";
}
};
@@ -5813,13 +5839,13 @@ namespace realclosure {
imp const & m;
extension * m_ref;
display_ext_proc(imp const & _m, extension * r):m(_m), m_ref(r) {}
- void operator()(std::ostream & out, bool compact) const {
- m.display_ext(out, m_ref, compact);
+ void operator()(std::ostream & out, bool compact, bool pp) const {
+ m.display_ext(out, m_ref, compact, pp);
}
};
- void display_polynomial_expr(std::ostream & out, polynomial const & p, extension * ext, bool compact) const {
- display_polynomial(out, p, display_ext_proc(*this, ext), compact);
+ void display_polynomial_expr(std::ostream & out, polynomial const & p, extension * ext, bool compact, bool pp) const {
+ display_polynomial(out, p, display_ext_proc(*this, ext), compact, pp);
}
static void display_poly_sign(std::ostream & out, int s) {
@@ -5846,7 +5872,7 @@ namespace realclosure {
out << "}";
}
- void display_sign_conditions(std::ostream & out, sign_condition * sc, array const & qs, bool compact) const {
+ void display_sign_conditions(std::ostream & out, sign_condition * sc, array const & qs, bool compact, bool pp) const {
bool first = true;
out << "{";
while (sc) {
@@ -5854,21 +5880,28 @@ namespace realclosure {
first = false;
else
out << ", ";
- display_polynomial(out, qs[sc->qidx()], display_free_var_proc(), compact);
+ display_polynomial(out, qs[sc->qidx()], display_free_var_proc(), compact, pp);
display_poly_sign(out, sc->sign());
sc = sc->prev();
}
out << "}";
}
- void display_algebraic_def(std::ostream & out, algebraic * a, bool compact) const {
+ void display_interval(std::ostream & out, mpbqi const & i, bool pp) const {
+ if (pp)
+ bqim().display_pp(out, i);
+ else
+ bqim().display(out, i);
+ }
+
+ void display_algebraic_def(std::ostream & out, algebraic * a, bool compact, bool pp) const {
out << "root(";
- display_polynomial(out, a->p(), display_free_var_proc(), compact);
+ display_polynomial(out, a->p(), display_free_var_proc(), compact, pp);
out << ", ";
- bqim().display(out, a->iso_interval());
+ display_interval(out, a->iso_interval(), pp);
out << ", ";
if (a->sdt() != 0)
- display_sign_conditions(out, a->sdt()->sc(a->sc_idx()), a->sdt()->qs(), compact);
+ display_sign_conditions(out, a->sdt()->sc(a->sc_idx()), a->sdt()->qs(), compact, pp);
else
out << "{}";
out << ")";
@@ -5878,28 +5911,33 @@ namespace realclosure {
collect_algebraic_refs c;
for (unsigned i = 0; i < n; i++)
c.mark(p[i]);
- display_polynomial(out, n, p, display_free_var_proc(), true);
+ display_polynomial(out, n, p, display_free_var_proc(), true, false);
std::sort(c.m_found.begin(), c.m_found.end(), rank_lt_proc());
for (unsigned i = 0; i < c.m_found.size(); i++) {
algebraic * ext = c.m_found[i];
out << "\n r!" << ext->idx() << " := ";
- display_algebraic_def(out, ext, true);
+ display_algebraic_def(out, ext, true, false);
}
}
- void display_ext(std::ostream & out, extension * r, bool compact) const {
+ void display_ext(std::ostream & out, extension * r, bool compact, bool pp) const {
switch (r->knd()) {
- case extension::TRANSCENDENTAL: to_transcendental(r)->display(out); break;
- case extension::INFINITESIMAL: to_infinitesimal(r)->display(out); break;
+ case extension::TRANSCENDENTAL: to_transcendental(r)->display(out, pp); break;
+ case extension::INFINITESIMAL: to_infinitesimal(r)->display(out, pp); break;
case extension::ALGEBRAIC:
- if (compact)
- out << "r!" << r->idx();
- else
- display_algebraic_def(out, to_algebraic(r), compact);
+ if (compact) {
+ if (pp)
+ out << "α" << r->idx() << "";
+ else
+ out << "r!" << r->idx();
+ }
+ else {
+ display_algebraic_def(out, to_algebraic(r), compact, pp);
+ }
}
}
- void display(std::ostream & out, value * v, bool compact) const {
+ void display(std::ostream & out, value * v, bool compact, bool pp=false) const {
if (v == 0)
out << "0";
else if (is_nz_rational(v))
@@ -5907,51 +5945,50 @@ namespace realclosure {
else {
rational_function_value * rf = to_rational_function(v);
if (is_denominator_one(rf)) {
- display_polynomial_expr(out, rf->num(), rf->ext(), compact);
+ display_polynomial_expr(out, rf->num(), rf->ext(), compact, pp);
}
else if (is_rational_one(rf->num())) {
out << "1/(";
- display_polynomial_expr(out, rf->den(), rf->ext(), compact);
+ display_polynomial_expr(out, rf->den(), rf->ext(), compact, pp);
out << ")";
}
else {
out << "(";
- display_polynomial_expr(out, rf->num(), rf->ext(), compact);
+ display_polynomial_expr(out, rf->num(), rf->ext(), compact, pp);
out << ")/(";
- display_polynomial_expr(out, rf->den(), rf->ext(), compact);
+ display_polynomial_expr(out, rf->den(), rf->ext(), compact, pp);
out << ")";
}
}
}
- void display_compact(std::ostream & out, value * a) const {
+ void display_compact(std::ostream & out, value * a, bool pp=false) const {
collect_algebraic_refs c;
c.mark(a);
if (c.m_found.empty()) {
- display(out, a, true);
+ display(out, a, true, pp);
}
else {
std::sort(c.m_found.begin(), c.m_found.end(), rank_lt_proc());
out << "[";
- display(out, a, true);
+ display(out, a, true, pp);
for (unsigned i = 0; i < c.m_found.size(); i++) {
algebraic * ext = c.m_found[i];
- out << "; r!" << ext->idx() << " := ";
- display_algebraic_def(out, ext, true);
+ if (pp)
+ out << "; α" << ext->idx() << " := ";
+ else
+ out << "; r!" << ext->idx() << " := ";
+ display_algebraic_def(out, ext, true, pp);
}
out << "]";
}
}
- void display_compact(std::ostream & out, numeral const & a) const {
- display_compact(out, a.m_value);
- }
-
- void display(std::ostream & out, numeral const & a, bool compact=false) const {
+ void display(std::ostream & out, numeral const & a, bool compact=false, bool pp=false) const {
if (compact)
- display_compact(out, a);
+ display_compact(out, a.m_value, pp);
else
- display(out, a.m_value, false);
+ display(out, a.m_value, false, pp);
}
void display_non_rational_in_decimal(std::ostream & out, numeral const & a, unsigned precision) {
@@ -5989,7 +6026,7 @@ namespace realclosure {
if (is_zero(a))
out << "[0, 0]";
else
- bqim().display(out, interval(a.m_value));
+ display_interval(out, interval(a.m_value), false);
}
};
@@ -6029,16 +6066,16 @@ namespace realclosure {
m_imp->del(a);
}
- void manager::mk_infinitesimal(char const * n, numeral & r) {
- m_imp->mk_infinitesimal(n, r);
+ void manager::mk_infinitesimal(char const * n, char const * pp_n, numeral & r) {
+ m_imp->mk_infinitesimal(n, pp_n, r);
}
void manager::mk_infinitesimal(numeral & r) {
m_imp->mk_infinitesimal(r);
}
- void manager::mk_transcendental(char const * n, mk_interval & proc, numeral & r) {
- m_imp->mk_transcendental(n, proc, r);
+ void manager::mk_transcendental(char const * n, char const * pp_n, mk_interval & proc, numeral & r) {
+ m_imp->mk_transcendental(n, pp_n, proc, r);
}
void manager::mk_transcendental(mk_interval & proc, numeral & r) {
@@ -6212,9 +6249,9 @@ namespace realclosure {
return gt(a, _b);
}
- void manager::display(std::ostream & out, numeral const & a, bool compact) const {
+ void manager::display(std::ostream & out, numeral const & a, bool compact, bool pp) const {
save_interval_ctx ctx(this);
- m_imp->display(out, a, compact);
+ m_imp->display(out, a, compact, pp);
}
void manager::display_decimal(std::ostream & out, numeral const & a, unsigned precision) const {
@@ -6234,7 +6271,7 @@ namespace realclosure {
};
void pp(realclosure::manager::imp * imp, realclosure::polynomial const & p, realclosure::extension * ext) {
- imp->display_polynomial_expr(std::cout, p, ext, false);
+ imp->display_polynomial_expr(std::cout, p, ext, false, false);
std::cout << std::endl;
}
@@ -6278,6 +6315,6 @@ void pp(realclosure::manager::imp * imp, mpq const & n) {
}
void pp(realclosure::manager::imp * imp, realclosure::extension * x) {
- imp->display_ext(std::cout, x, false);
+ imp->display_ext(std::cout, x, false, false);
std::cout << std::endl;
}
diff --git a/src/math/realclosure/realclosure.h b/src/math/realclosure/realclosure.h
index 2b70d3be0..2a1b0dc20 100644
--- a/src/math/realclosure/realclosure.h
+++ b/src/math/realclosure/realclosure.h
@@ -70,7 +70,7 @@ namespace realclosure {
/**
\brief Add a new infinitesimal to the current field. The new infinitesimal is smaller than any positive element in the field.
*/
- void mk_infinitesimal(char const * name, numeral & r);
+ void mk_infinitesimal(char const * name, char const * pp_name, numeral & r);
void mk_infinitesimal(numeral & r);
/**
@@ -83,7 +83,7 @@ namespace realclosure {
Then, we extend the field F with 1 - Pi. 1 - Pi is transcendental with respect to algebraic real numbers, but it is NOT transcendental
with respect to F, since F contains Pi.
*/
- void mk_transcendental(char const * name, mk_interval & proc, numeral & r);
+ void mk_transcendental(char const * name, char const * pp_name, mk_interval & proc, numeral & r);
void mk_transcendental(mk_interval & proc, numeral & r);
/**
@@ -252,7 +252,7 @@ namespace realclosure {
bool ge(numeral const & a, mpq const & b) { return !lt(a, b); }
bool ge(numeral const & a, mpz const & b) { return !lt(a, b); }
- void display(std::ostream & out, numeral const & a, bool compact=false) const;
+ void display(std::ostream & out, numeral const & a, bool compact=false, bool pp=false) const;
/**
\brief Display a real number in decimal notation.
diff --git a/src/util/ext_numeral.h b/src/util/ext_numeral.h
index af4b7ac10..83d326243 100644
--- a/src/util/ext_numeral.h
+++ b/src/util/ext_numeral.h
@@ -332,4 +332,16 @@ void display(std::ostream & out,
}
}
+template
+void display_pp(std::ostream & out,
+ numeral_manager & m,
+ typename numeral_manager::numeral const & a,
+ ext_numeral_kind ak) {
+ switch (ak) {
+ case EN_MINUS_INFINITY: out << "-∞"; break;
+ case EN_NUMERAL: m.display(out, a); break;
+ case EN_PLUS_INFINITY: out << "+∞"; break;
+ }
+}
+
#endif