bool SimpleReductor::reduceStep (Polynomial& r, const Polynomial& p) {
Polynomial t;
r.copy(p);
Monomial lm = r.lm();
int i, i0 = -1;
for (i = 0; i < g.size(); ++i) {
Monomial m = g[i].lm();
if (MP.divides(lm, m)) {
t.mul(g[i], MP.div(lm, m));
Cf f;
Ring::neg(f, r.lc());
r.add(t, t.lc(), f);
return true;
}
}
return false;
}
void Tester::test_polynomials()
{
Polynomial ZERO = Polynomial::ZERO();
cout << ZERO << endl;
Polynomial p = ZERO.copy();
p.addTrailingTerm(3);
p.addTrailingTerm(-5);
p.addTrailingTerm(10);
p.addTrailingTerm(-3);
Polynomial p2 = ZERO;//ZERO.copy();//new Polynomial();
p2.addTrailingTerm(3);
p2.addTrailingTerm(1);
// p2 -> addTrailingTerm(10);
cout << "a: " << p << endl;
cout << "b: " << p2 << endl;
Polynomial p12 = p + p2;
cout << "a+b: " << p12 << endl;
Polynomial sub = p - p2;
cout << "a-b: " << sub << endl;
Polynomial scale = p *.5;
cout << "a*.5: " << scale << endl;
Polynomial mult = p*p2;
cout << "a*b: " << mult << endl;
// Division and Remainder.
Polynomial div = p/p2;
cout << "a/b: " << p/p2 << endl;
// cout << "a%b: " << p%p2 << endl;
// WARNING: Memory Explosion if not handled with care.
std::vector<double> roots;
/*
p -> computeRealRoots(roots,
-1000, 1000,
.000001);
*/
Polynomial p3 = ZERO;
// This polynomial has roots 1, 2, 3, 4, 5. They are all found accuratly.
p3.addTrailingTerm(1);
p3.addTrailingTerm(-15);
p3.addTrailingTerm(85);
p3.addTrailingTerm(-225);
p3.addTrailingTerm(274);
p3.addTrailingTerm(-120);
// This polynomial has roots:
// -1.32, 1.32, 4.56, 4.58, 4.6.
// Thus far we only find -1.32, 1.32, and 4.53658.
// We don't find the close last 3 values accuratly.
/*
p3.addTrailingTerm(1);
p3.addTrailingTerm(-13.74);
p3.addTrailingTerm(61.1864);
p3.addTrailingTerm(-72.1295);
p3.addTrailingTerm(-109.647);
p3.addTrailingTerm(167.393);
*/
std::cout << "Quintic Polynomial: " << p3 << std::endl;
p3.computeRealRoots(roots,
-1000, 1000,
.0000001);
for(auto iter = roots.begin(); iter != roots.end(); ++iter)
{
cout << "Root: " << *iter << " -> " << p3.eval(*iter)<< endl;
}
Polynomial x, y, z;
x.addTrailingTerm(1);
x.addTrailingTerm(1);
y.addTrailingTerm(2);
y.addTrailingTerm(2);
z.addTrailingTerm(3);
z.addTrailingTerm(3);
PolynomialVector3D vec(x, y, z);
cout << "vec - vec = " << vec - vec << endl;
cout << "vec + vec = " << vec + vec << endl;
cout << vec << endl;
vec = dot(vec, vec);
cout << vec << endl;
}