我试图通过创建多项式的除法类来找到多项式的GCD。我理解如何添加，减号，乘法和创建多项式，但我不知道如何划分两者（使用代码）。谁能帮助我？
到目前为止，这是我的代码：
public class Polynomial2 {
private int[] coef; // coefficients
private int deg; // degree of polynomial (0 for the zero polynomial)
// a * x^b
public Polynomial2(int a, int b) {
coef = new int[b+1];
coef[b] = a;
deg = degree();
}
// return the degree of this polynomial (0 for the zero polynomial)
public int degree() {
int d = 0;
for (int i = 0; i < coef.length; i++)
if (coef[i] != 0) d = i;
return d;
}
// return c = a + b
public Polynomial2 plus(Polynomial2 b) {
Polynomial2 a = this;
Polynomial2 c = new Polynomial2(0, Math.max(a.deg, b.deg));
for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];
for (int i = 0; i <= b.deg; i++) c.coef[i] += b.coef[i];
c.deg = c.degree();
return c;
}
// return (a - b)
public Polynomial2 minus(Polynomial2 b) {
Polynomial2 a = this;
Polynomial2 c = new Polynomial2(0, Math.max(a.deg, b.deg));
for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];
for (int i = 0; i <= b.deg; i++) c.coef[i] -= b.coef[i];
c.deg = c.degree();
return c;
}
// return (a * b)
public Polynomial2 times(Polynomial2 b) {
Polynomial2 a = this;
Polynomial2 c = new Polynomial2(0, a.deg + b.deg);
for (int i = 0; i <= a.deg; i++)
for (int j = 0; j <= b.deg; j++)
c.coef[i+j] += (a.coef[i] * b.coef[j]);
c.deg = c.degree();
return c;
}
// return a(b(x)) - compute using Horner's method
public Polynomial2 compose(Polynomial2 b) {
Polynomial2 a = this;
Polynomial2 c = new Polynomial2(0, 0);
for (int i = a.deg; i >= 0; i--) {
Polynomial2 term = new Polynomial2(a.coef[i], 0);
c = term.plus(b.times(c));
}
return c;
}
// do a and b represent the same polynomial?
public boolean eq(Polynomial2 b) {
Polynomial2 a = this;
if (a.deg != b.deg) return false;
for (int i = a.deg; i >= 0; i--)
if (a.coef[i] != b.coef[i]) return false;
return true;
}
// use Horner's method to compute and return the polynomial evaluated at x
public int evaluate(int x) {
int p = 0;
for (int i = deg; i >= 0; i--)
p = coef[i] + (x * p);
return p;
}
// differentiate this polynomial and return it
public Polynomial2 differentiate() {
if (deg == 0) return new Polynomial2(0, 0);
Polynomial2 deriv = new Polynomial2(0, deg - 1);
deriv.deg = deg - 1;
for (int i = 0; i < deg; i++)
deriv.coef[i] = (i + 1) * coef[i + 1];
return deriv;
}
// convert to string representation
public String toString() {
if (deg == 0) return "" + coef[0];
if (deg == 1) return coef[1] + "x + " + coef[0];
String s = coef[deg] + "x^" + deg;
for (int i = deg-1; i >= 0; i--) {
if (coef[i] == 0) continue;
else if (coef[i] > 0) s = s + " + " + ( coef[i]);
else if (coef[i] < 0) s = s + " - " + (-coef[i]);
if (i == 1) s = s + "x";
else if (i > 1) s = s + "x^" + i;
}
return s;
}
//method for division
public Polynomial2 divides(Polynomial2 b) {
}
// test client
public static void main(String[] args) {
/*first polynomial*/
Polynomial2 p1 = new Polynomial2(1, 13);
Polynomial2 p2 = new Polynomial2(-12, 12);
Polynomial2 p3 = new Polynomial2(55, 11);
Polynomial2 p4 = new Polynomial2(-148, 10);
Polynomial2 p5 = new Polynomial2(337, 9);
Polynomial2 p6 = new Polynomial2(-460, 8);
Polynomial2 p7 = new Polynomial2(55, 7);
Polynomial2 p8 = new Polynomial2(-148, 6);
Polynomial2 p9 = new Polynomial2(336, 5);
Polynomial2 p10 = new Polynomial2(-448, 4);
Polynomial2 p = p1.plus(p2).plus(p3).plus(p4).plus(p5).plus(p6).plus(p7).
plus(p8).plus(p9).plus(p10);
//x^13 - 12x^12 - 55x^11 - 148x^10 + 337x^9 + 460x^8 + 55x^7 - 148x^5 + 336x^5 - 448x^4
/*second polynomial*/
Polynomial2 q1 = new Polynomial2(1, 20);
Polynomial2 q2 = new Polynomial2(-12, 19);
Polynomial2 q3 = new Polynomial2(55, 18);
Polynomial2 q4 = new Polynomial2(-148, 17);
Polynomial2 q5 = new Polynomial2(335, 16);
Polynomial2 q6 = new Polynomial2(-436, 15);
Polynomial2 q7 = new Polynomial2(-55, 14);
Polynomial2 q8 = new Polynomial2(148, 13);
Polynomial2 q9 = new Polynomial2(-336, 12);
Polynomial2 q10 = new Polynomial2(448, 11);
Polynomial2 q11 = new Polynomial2(1, 7);
Polynomial2 q12 = new Polynomial2(-12, 6);
Polynomial2 q13 = new Polynomial2(55, 5);
Polynomial2 q14 = new Polynomial2(-148, 4);
Polynomial2 q15 = new Polynomial2(336, 3);
Polynomial2 q16 = new Polynomial2(-448, 2);
Polynomial2 q = q1.plus(q2).plus(q3).plus(q4).plus(q5).plus(q6).plus(q7).
plus(q8).plus(q9).plus(q10).plus(q11).plus(q12).plus(q13).
plus(q14).plus(q15).plus(q16);
//x^20 - 12x^19 + 55x^18 - 148x^17 + 335x^16 - 436x^15 - 55x^14 + 148x^13 - 336x^12
//448x^11 + x^7 - 12x^6 + 55x^5 - 148x^4 + 336x^3 - 448x^2;
System.out.println("p(x) = " + p);
System.out.println("q(x) = " + q);
}
}
答案 0 :(得分：1)
你需要在两个多项式中除以匹配度的系数，如：
public Polynomial2 divides(Polynomial2 b) {
Polynomial2 a = this;
if ((b.deg == 0) && (b.coef[0] == 0))
throw new RuntimeException("Divide by zero polynomial"); //Zero polynomial is the one having coeff and degree both zero.
if (a.deg < b.deg) return new Polynomial2(0,0);
int coefficient = a.coef[a.deg]/(b.coef[b.deg]);
int exponent = a.deg - b.deg;
Polynomial2 c = new Polynomial2(coefficient, exponent);
return c.plus( (a.minus(b.times(c)).divides(b)) );
}
此代码应该按照您的意愿执行。您可能需要根据您的要求进行小的改进。上面的代码是this的轻微修改版本。
答案 1 :(得分：1)
这里有一些伪代码，基于Princeton archives
// return (a / b)
public Polynomial2 divides(Polynomial2 b) {
Polynomial2 a = this;
if ((b.deg == 0) && (b.coef[0] == 0))
throw new RuntimeException("Divide by zero polynomial");
if (a.deg < b.deg) return ZERO;
int coefficient = a.coef[a.deg].divides(b.coef[b.deg]);
int exponent = a.deg - b.deg;
Polynomial2 c = new Polynomial2(coefficient, exponent);
return c.plus( (a.minus(b.times(c)).divides(b)) );
}