public Polynome Dérivée () {
var poly = new Polynome ();
for (int k = 1; k <= Degré; k++) {
poly.AddCoefficient (k - 1, k * GetCoefficient (k));
}
return poly;
}
public static Polynome operator /(Polynome A, Polynome B) {
var Q = new Polynome ();
while (A.Degré >= B.Degré) {
var C = new Polynome ();
C.AddCoefficient ((A.Degré - B.Degré) * Convert.ToInt32(A.Degré >= B.Degré), A.GetCoefficient (A.Degré) / B.GetCoefficient (B.Degré));
A -= B * C;
Q += C;
}
return Q;
}
public static Polynome operator *(Polynome A, Polynome B) {
var poly = new Polynome ();
for (int k = 0; k <= A.Degré; k++) {
for (int l = 0; l <= B.Degré; l++) {
poly.AddCoefficient (k+l, A.GetCoefficient (k) * B.GetCoefficient (l));
}
}
return poly;
}
public static Polynome operator -(Polynome A, Polynome B) {
var poly = new Polynome ();
for (int k = 0; k <= Math.Max(A.Degré, B.Degré); k++) {
poly.AddCoefficient (k, A.GetCoefficient(k)-B.GetCoefficient(k));
}
return poly;
}
public static Polynome[] Bezout(Polynome A, Polynome B) {
Polynome Uk = 1;
Polynome Vk = 0;
Polynome UkPlus1 = 0;
Polynome VkPlus1 = 1;
while (B != 0) {
var Uk_save = Uk;
var Vk_save = Vk;
Uk = UkPlus1;
Vk = VkPlus1;
UkPlus1 = Uk_save - UkPlus1 * (A / B);
VkPlus1 = Vk_save - VkPlus1 * (A / B);
var X = B;
B = A % B;
A = X;
}
return new Polynome[] { Uk / A.GetCoefficient (A.Degré), Vk / A.GetCoefficient (A.Degré) };
}
public static Polynome[] Bezout (Polynome[] polynomes) {
if (polynomes.Length == 1)
return polynomes;
var bezouts = new Polynome[polynomes.Length];
for (int i = 0; i < bezouts.Length; i++) {
bezouts [i] = 1;
}
for (int k = 1; k <= polynomes.Length; k++) {
var pgcd = polynomes [0];
for (int i = 1; i < polynomes.Length - k; i++) {
pgcd = PGCD(pgcd, polynomes[i]);
}
var b = Bezout (pgcd, polynomes [polynomes.Length - k]);
bezouts [bezouts.Length - k] *= b [1];
for (int l = 0; l < bezouts.Length-k; l++) {
bezouts [l] *= b [0];
}
}
return bezouts;
}
public static Polynome PGCD (Polynome[] polynomes) {
var pgcd = polynomes [0];
for (int k = 1; k < polynomes.Length; k++) {
pgcd = PGCD (polynomes [k], pgcd);
}
return pgcd;
}
public static Polynome PGCD (Polynome A, Polynome B) {
while (B != 0) {
var X = B;
B = A % B;
A = X;
}
return A / A.GetCoefficient (A.Degré);
}
