static void tst_isolate_roots(polynomial_ref const & p, anum_manager & am,
polynomial::var x0, anum const & v0, polynomial::var x1, anum const & v1, polynomial::var x2, anum const & v2) {
polynomial::simple_var2value<anum_manager> x2v(am);
x2v.push_back(x0, v0);
x2v.push_back(x1, v1);
x2v.push_back(x2, v2);
std::cout << "--------------\n";
std::cout << "p: " << p << "\n";
std::cout << "x0 -> "; am.display_root(std::cout, v0); std::cout << "\n";
std::cout << "x1 -> "; am.display_root(std::cout, v1); std::cout << "\n";
std::cout << "x2 -> "; am.display_root(std::cout, v2); std::cout << "\n";
scoped_anum_vector roots(am);
svector<int> signs;
am.isolate_roots(p, x2v, roots, signs);
SASSERT(roots.size() + 1 == signs.size());
std::cout << "roots:\n";
for (unsigned i = 0; i < roots.size(); i++) {
am.display_root(std::cout, roots[i]); std::cout << " "; am.display_decimal(std::cout, roots[i]); std::cout << "\n";
}
std::cout << "signs:\n";
for (unsigned i = 0; i < signs.size(); i++) {
if (i > 0)
std::cout << " 0 ";
if (signs[i] < 0) std::cout << "-";
else if (signs[i] == 0) std::cout << "0";
else std::cout << "+";
}
std::cout << "\n";
}
static void ex1() {
unsynch_mpq_manager qm;
polynomial::manager pm(qm);
polynomial_ref x(pm);
polynomial_ref a(pm);
polynomial_ref b(pm);
polynomial_ref c(pm);
x = pm.mk_polynomial(pm.mk_var());
a = pm.mk_polynomial(pm.mk_var());
b = pm.mk_polynomial(pm.mk_var());
c = pm.mk_polynomial(pm.mk_var());
polynomial_ref p(pm);
p = (a + 2*b)*(x^3) + x*a + (b^2);
polynomial_ref p1(pm);
p1 = derivative(p, 0);
polynomial_ref h2(pm);
unsigned d;
h2 = pseudo_remainder(p, p1, 0, d);
std::cout << "d: " << d << "\n";
std::cout << "p: "; pp(p, 0); std::cout << "\np': "; pp(p1, 0); std::cout << "\nh2: "; pp(h2, 0); std::cout << "\n";
polynomial_ref h3(pm);
h3 = pseudo_remainder(p1, h2, 0, d);
std::cout << "d: " << d << "\n";
std::cout << "h3: "; pp(h3, 0); std::cout << "\n";
algebraic_numbers::manager am(qm);
scoped_anum v1(am), v2(am);
am.set(v1, 2);
am.root(v1, 3, v1);
am.set(v2, 3);
am.root(v2, 3, v2);
polynomial::simple_var2value<anum_manager> x2v(am);
x2v.push_back(1, v1);
x2v.push_back(2, v2);
std::cout << "sign(h3(v1,v2)): " << am.eval_sign_at(h3, x2v) << "\n";
scoped_anum v0(am);
am.set(v0, -1);
x2v.push_back(0, v0);
std::cout << "sign(h2(v1,v2)): " << am.eval_sign_at(h2, x2v) << "\n";
std::cout << "sign(p'(v1,v2)): " << am.eval_sign_at(p1, x2v) << "\n";
std::cout << "sign(p(v1,v2)): " << am.eval_sign_at(p, x2v) << "\n";
polynomial::simple_var2value<anum_manager> x2v2(am);
x2v2.push_back(1, v1);
x2v2.push_back(2, v2);
scoped_mpq tmp(qm);
qm.set(tmp, -1);
qm.div(tmp, mpz(2), tmp);
std::cout << "tmp: "; qm.display(std::cout, tmp); std::cout << " "; qm.display_decimal(std::cout, tmp, 10); std::cout << "\n";
am.set(v0, tmp);
x2v2.push_back(0, v0);
std::cout << "v0: " << v0 << "\n";
std::cout << "sign(h2(v1,v2)): " << am.eval_sign_at(h2, x2v2) << "\n";
std::cout << "sign(p'(v1,v2)): " << am.eval_sign_at(p1, x2v2) << "\n";
std::cout << "sign(p(v1,v2)): " << am.eval_sign_at(p, x2v2) << "\n";
}
static void tst_eval_sign(polynomial_ref const & p, anum_manager & am,
polynomial::var x0, anum const & v0, polynomial::var x1, anum const & v1, polynomial::var x2, anum const & v2,
int expected) {
polynomial::simple_var2value<anum_manager> x2v(am);
x2v.push_back(x0, v0);
x2v.push_back(x1, v1);
x2v.push_back(x2, v2);
std::cout << "--------------\n";
std::cout << "p: " << p << "\n";
std::cout << "x0 -> "; am.display_root(std::cout, v0); std::cout << "\n";
std::cout << "x1 -> "; am.display_root(std::cout, v1); std::cout << "\n";
std::cout << "x2 -> "; am.display_root(std::cout, v2); std::cout << "\n";
int s = am.eval_sign_at(p, x2v);
SASSERT((s == 0) == (expected == 0));
SASSERT((s < 0) == (expected < 0));
SASSERT((s > 0) == (expected > 0));
std::cout << "sign: " << s << "\n";
}
vixl::VRegister V(Vreg r) {
return x2v(r);
}
