public virtual Polynomial divideWithRemainder(Polynomial p)
{
if (Coefficients.Count == 0 || p.Coefficients.Count == 0)
return null; //null
var answer = new Polynomial[2];
int prime = Coefficients[0].Prime;
int m = Degree;
int n = p.Degree;
if (m < n)
return null;
var quotient = new Zp[m - n + 1];
var coeffs = new Zp[m + 1];
for (int k = 0; k <= m; k++)
coeffs[k] = new Zp(Coefficients[k]);
var norm = p.Coefficients[n].MultipInverse;
for (int k = m - n; k >= 0; k--)
{
quotient[k] = new Zp(prime, coeffs[n + k].Value * norm.Value);
for (int j = n + k - 1; j >= k; j--)
coeffs[j] = new Zp(prime,
coeffs[j].Value - quotient[k].Value * p.Coefficients[j - k].Value);
}
var remainder = new Zp[n];
for (int k = 0; k < n; k++)
remainder[k] = new Zp(coeffs[k]);
answer[0] = new Polynomial(quotient);
answer[1] = new Polynomial(remainder);
foreach (Zp zp in answer[1].Coefficients)
{
if (zp.Value != 0)
return null;
}
return answer[0];
}
public virtual Polynomial multiply(Polynomial p)
{
Debug.Assert(Degree > p.Degree && Coefficients.Count > 0);
int prime = Coefficients[0].Prime;
var coeffs = new SortedDictionary<int, Zp>();
for (int deg1 = 0; deg1 <= Degree; deg1++)
{
for (int deg2 = 0; deg2 <= p.Degree; deg2++)
{
int deg = deg1 + deg2;
var curr = coeffs[deg];
var newValue = new Zp(prime, Coefficients[deg1].Value * p.Coefficients[deg2].Value);
if (curr == null)
curr = newValue;
else
curr = new Zp(prime, curr.Value + newValue.Value);
coeffs[deg] = curr;
}
}
return new Polynomial(new List<Zp>(coeffs.Values));
}
