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added polynomial evaluation at algebraic point

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2012-12-08 20:39:16 -08:00
parent bf2340850a
commit 0d230375be
9 changed files with 266 additions and 26 deletions
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80
src/ast/expr2polynomial.cpp
View file

@ -49,21 +49,24 @@ struct expr2polynomial::imp {
polynomial::polynomial_ref_vector m_presult_stack;
polynomial::scoped_numeral_vector m_dresult_stack;
bool m_use_var_idxs;
volatile bool m_cancel;
imp(expr2polynomial & w, ast_manager & am, polynomial::manager & pm, expr2var * e2v):
imp(expr2polynomial & w, ast_manager & am, polynomial::manager & pm, expr2var * e2v, bool use_var_idxs):
m_wrapper(w),
m_am(am),
m_autil(am),
m_pm(pm),
m_expr2var(e2v == 0 ? alloc(expr2var, am) : e2v),
m_expr2var_owner(e2v == 0),
m_expr2var(e2v == 0 && !use_var_idxs ? alloc(expr2var, am) : e2v),
m_expr2var_owner(e2v == 0 && !use_var_idxs),
m_var2expr(am),
m_cached_domain(am),
m_cached_polynomials(pm),
m_cached_denominators(pm.m()),
m_presult_stack(pm),
m_dresult_stack(pm.m()),
m_use_var_idxs(use_var_idxs),
m_cancel(false) {
}
@ -95,6 +98,14 @@ struct expr2polynomial::imp {
cooperate("expr2polynomial");
}
void throw_not_polynomial() {
throw default_exception("the given expression is not a polynomial");
}
void throw_no_int_var() {
throw default_exception("integer variables are not allowed in the given polynomial");
}
void push_frame(app * t) {
m_frame_stack.push_back(frame(t));
}
@ -127,14 +138,26 @@ struct expr2polynomial::imp {
}
void store_var_poly(expr * t) {
polynomial::var x = m_expr2var->to_var(t);
if (x == UINT_MAX) {
bool is_int = m_autil.is_int(t);
x = m_wrapper.mk_var(is_int);
m_expr2var->insert(t, x);
if (x >= m_var2expr.size())
m_var2expr.resize(x+1, 0);
m_var2expr.set(x, t);
polynomial::var x;
if (m_use_var_idxs) {
SASSERT(::is_var(t));
if (m_autil.is_int(t))
throw_no_int_var();
unsigned idx = to_var(t)->get_idx();
while (idx >= m_pm.num_vars())
m_pm.mk_var();
x = static_cast<polynomial::var>(idx);
}
else {
x = m_expr2var->to_var(t);
if (x == UINT_MAX) {
bool is_int = m_autil.is_int(t);
x = m_wrapper.mk_var(is_int);
m_expr2var->insert(t, x);
if (x >= m_var2expr.size())
m_var2expr.resize(x+1, 0);
m_var2expr.set(x, t);
}
}
polynomial::numeral one(1);
store_result(t, pm().mk_polynomial(x), one);
@ -160,7 +183,10 @@ struct expr2polynomial::imp {
rational k;
SASSERT(t->get_num_args() == 2);
if (!m_autil.is_numeral(t->get_arg(1), k) || !k.is_int() || !k.is_unsigned()) {
store_var_poly(t);
if (m_use_var_idxs)
throw_not_polynomial();
else
store_var_poly(t);
return true;
}
push_frame(t);
@ -168,6 +194,8 @@ struct expr2polynomial::imp {
}
default:
// can't handle operator
if (m_use_var_idxs)
throw_not_polynomial();
store_var_poly(t);
return true;
}
@ -190,6 +218,8 @@ struct expr2polynomial::imp {
SASSERT(is_app(t));
if (!m_autil.is_arith_expr(t)) {
if (m_use_var_idxs)
throw_not_polynomial();
store_var_poly(t);
return true;
}
@ -378,19 +408,25 @@ struct expr2polynomial::imp {
for (unsigned i = 0; i < sz; i++) {
margs.reset();
polynomial::monomial * m = pm().get_monomial(p, i);
polynomial::monomial * _m = pm().get_monomial(p, i);
polynomial::numeral const & a = pm().coeff(p, i);
if (!nm().is_one(a)) {
margs.push_back(m_autil.mk_numeral(rational(a), is_int));
}
unsigned msz = pm().size(m);
unsigned msz = pm().size(_m);
for (unsigned j = 0; j < msz; j++) {
polynomial::var x = pm().get_var(m, j);
expr * t = m_var2expr.get(x);
if (m_wrapper.is_int(x) && !is_int) {
t = m_autil.mk_to_real(t);
polynomial::var x = pm().get_var(_m, j);
expr * t;
if (m_use_var_idxs) {
t = m().mk_var(x, m_autil.mk_real());
}
unsigned d = pm().degree(m, j);
else {
t = m_var2expr.get(x);
if (m_wrapper.is_int(x) && !is_int) {
t = m_autil.mk_to_real(t);
}
}
unsigned d = pm().degree(_m, j);
if (use_power && d > 1) {
margs.push_back(m_autil.mk_power(t, m_autil.mk_numeral(rational(d), is_int)));
}
@ -426,8 +462,8 @@ struct expr2polynomial::imp {
}
};
expr2polynomial::expr2polynomial(ast_manager & am, polynomial::manager & pm, expr2var * e2v) {
m_imp = alloc(imp, *this, am, pm, e2v);
expr2polynomial::expr2polynomial(ast_manager & am, polynomial::manager & pm, expr2var * e2v, bool use_var_idxs) {
m_imp = alloc(imp, *this, am, pm, e2v, use_var_idxs);
}
expr2polynomial::~expr2polynomial() {
@ -451,10 +487,12 @@ void expr2polynomial::to_expr(polynomial::polynomial_ref const & p, bool use_pow
}
bool expr2polynomial::is_var(expr * t) const {
SASSERT(!m_imp->m_use_var_idxs);
return m_imp->m_expr2var->is_var(t);
}
expr2var const & expr2polynomial::get_mapping() const {
SASSERT(!m_imp->m_use_var_idxs);
return *(m_imp->m_expr2var);
}

25
src/ast/expr2polynomial.h
View file

@ -29,7 +29,24 @@ class expr2polynomial {
struct imp;
imp * m_imp;
public:
expr2polynomial(ast_manager & am, polynomial::manager & pm, expr2var * e2v);
expr2polynomial(ast_manager & am,
polynomial::manager & pm,
expr2var * e2v,
/*
If true, the expressions converted into
polynomials should only contain Z3 free variables.
A Z3 variable x, with idx i, is converted into
the variable i of the polynomial manager pm.
An exception is thrown if there is a mismatch between
the sorts x and the variable in the polynomial manager.
The argument e2v is ignored when use_var_idxs is true.
Moreover, only real variables are allowed.
*/
bool use_var_idxs = false
);
virtual ~expr2polynomial();
ast_manager & m() const;
@ -63,6 +80,8 @@ public:
/**
\brief Return the mapping from expressions to variables
\pre the object was created using use_var_idxs = false.
*/
expr2var const & get_mapping() const;
@ -74,10 +93,10 @@ public:
/**
\brief Return true if the variable is associated with an expression of integer sort.
*/
virtual bool is_int(polynomial::var x) const = 0;
virtual bool is_int(polynomial::var x) const { UNREACHABLE(); return false; }
protected:
virtual polynomial::var mk_var(bool is_int) = 0;
virtual polynomial::var mk_var(bool is_int) { UNREACHABLE(); return polynomial::null_var; }
};
class default_expr2polynomial : public expr2polynomial {