/// <summary>
/// Test if this polynomial is equal to P.
/// </summary>
/// <param name="P"></param>
/// <returns></returns>
public bool Equals(Polynomial P)
{
int d = Degree;
if (d != P.Degree)
return false;
for (int i = 0; i <= d; ++i)
if (!this[i].Equals(P[i]))
return false;
return true;
}
public static Polynomial Divide(Polynomial N, Polynomial D, out Polynomial R)
{
if (!Equals(N.Variable, D.Variable))
throw new ArgumentException("Polynomials must be of the same variable.", "N/D");
DefaultDictionary<int, Expression> q = new DefaultDictionary<int, Expression>(0);
DefaultDictionary<int, Expression> r = new DefaultDictionary<int, Expression>(0);
foreach (KeyValuePair<int, Expression> i in N.Coefficients)
r.Add(i.Key, i.Value);
while (r.Any() && !r[0].Equals(0) && r.Keys.Max() + 1 >= D.Degree)
{
int rd = r.Keys.Max() + 1;
int dd = D.Degree;
Expression t = r[rd] / D[dd];
int td = rd - dd;
// Compute q += t
q[td] += t;
// Compute r -= d * t
for (int i = 0; i <= dd; ++i)
r[i + td] -= -D[i] * t;
}
R = new Polynomial(r, N.Variable);
return new Polynomial(q, N.Variable);
}
public static Polynomial Multiply(Polynomial L, Polynomial R)
{
if (!Equals(L.Variable, R.Variable))
throw new ArgumentException("Polynomials must be of the same variable.", "L*R");
Dictionary<int, Expression> P = new Dictionary<int, Expression>();
int D = L.Degree + R.Degree;
for (int i = 0; i <= D; ++i)
for (int j = 0; j <= i; ++j)
P[i] += L[j] * R[i - j];
return new Polynomial(P, L.Variable);
}
public static Polynomial Add(Polynomial L, Polynomial R)
{
if (!Equals(L.Variable, R.Variable))
throw new ArgumentException("Polynomials must be of the same variable.", "L+R");
DefaultDictionary<int, Expression> P = new DefaultDictionary<int, Expression>(0);
int D = Math.Max(L.Degree, R.Degree);
for (int i = 0; i <= D; ++i)
P[i] = L[i] + R[i];
return new Polynomial(P, L.Variable);
}
