Below is the syntax highlighted version of RationalPolynomial.java
from §9.2 Floating Point.
/****************************************************************************** * Compilation: javac RationalPolynomial.java * Execution: java RationalPolynomial * * A polynomial with arbitrary precision rational coefficients. * ******************************************************************************/ public class RationalPolynomial { public final static RationalPolynomial ZERO = new RationalPolynomial(BigRational.ZERO, 0); private BigRational[] coef; // coefficients private int deg; // degree of polynomial (0 for the zero polynomial) // a * x^b public RationalPolynomial(BigRational a, int b) { coef = new BigRational[b+1]; for (int i = 0; i < b; i++) coef[i] = BigRational.ZERO; 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].compareTo(BigRational.ZERO) != 0) d = i; return d; } // return c = a + b public RationalPolynomial plus(RationalPolynomial b) { RationalPolynomial a = this; RationalPolynomial c = new RationalPolynomial(BigRational.ZERO, Math.max(a.deg, b.deg)); for (int i = 0; i <= a.deg; i++) c.coef[i] = c.coef[i].plus(a.coef[i]); for (int i = 0; i <= b.deg; i++) c.coef[i] = c.coef[i].plus(b.coef[i]); c.deg = c.degree(); return c; } // return c = a - b public RationalPolynomial minus(RationalPolynomial b) { RationalPolynomial a = this; RationalPolynomial c = new RationalPolynomial(BigRational.ZERO, Math.max(a.deg, b.deg)); for (int i = 0; i <= a.deg; i++) c.coef[i] = c.coef[i].plus(a.coef[i]); for (int i = 0; i <= b.deg; i++) c.coef[i] = c.coef[i].minus(b.coef[i]); c.deg = c.degree(); return c; } // return (a * b) public RationalPolynomial times(RationalPolynomial b) { RationalPolynomial a = this; RationalPolynomial c = new RationalPolynomial(BigRational.ZERO, a.deg + b.deg); for (int i = 0; i <= a.deg; i++) for (int j = 0; j <= b.deg; j++) c.coef[i+j] = c.coef[i+j].plus(a.coef[i].times(b.coef[j])); c.deg = c.degree(); return c; } // return (a / b) public RationalPolynomial divides(RationalPolynomial b) { RationalPolynomial a = this; if ((b.deg == 0) && (b.coef[0].compareTo(BigRational.ZERO) == 0)) throw new ArithmeticException("call divides() with denominator that is the zero polynomial"); if (a.deg < b.deg) return ZERO; BigRational coefficient = a.coef[a.deg].divides(b.coef[b.deg]); int exponent = a.deg - b.deg; RationalPolynomial c = new RationalPolynomial(coefficient, exponent); return c.plus( (a.minus(b.times(c)).divides(b)) ); } // truncate to degree d public RationalPolynomial truncate(int d) { RationalPolynomial p = new RationalPolynomial(BigRational.ZERO, d); for (int i = 0; i <= d; i++) p.coef[i] = coef[i]; p.deg = p.degree(); return p; } // use Horner's method to compute and return the polynomial evaluated at x public BigRational evaluate(BigRational x) { BigRational p = BigRational.ZERO; for (int i = deg; i >= 0; i--) p = coef[i].plus(x.times(p)); return p; } // differentiate this polynomial and return it public RationalPolynomial differentiate() { if (deg == 0) return ZERO; RationalPolynomial deriv = new RationalPolynomial(BigRational.ZERO, deg-1); for (int i = 0; i < deg; i++) deriv.coef[i] = coef[i+1].times(new BigRational(i + 1)); deriv.deg = deriv.degree(); return deriv; } // return antiderivative public RationalPolynomial integrate() { RationalPolynomial integral = new RationalPolynomial(BigRational.ZERO, deg + 1); for (int i = 0; i <= deg; i++) integral.coef[i+1] = coef[i].divides(new BigRational(i + 1)); integral.deg = integral.degree(); return integral; } // return integral from a to b public BigRational integrate(BigRational a, BigRational b) { RationalPolynomial integral = integrate(); return integral.evaluate(b).minus(integral.evaluate(a)); } // 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--) { int cmp = coef[i].compareTo(BigRational.ZERO); if (cmp == 0) continue; else if (cmp > 0) s = s + " + " + ( coef[i]); else if (cmp < 0) s = s + " - " + (coef[i].negate()); if (i == 1) s = s + " x"; else if (i > 1) s = s + " x^" + i; } return s; } // test client public static void main(String[] args) { BigRational half = new BigRational(1, 2); BigRational three = new BigRational(3, 1); RationalPolynomial p = new RationalPolynomial(half, 1); RationalPolynomial q = new RationalPolynomial(three, 2); RationalPolynomial r = p.plus(q); RationalPolynomial s = p.times(q); RationalPolynomial t = r.times(r); RationalPolynomial u = t.minus(q.times(q)); RationalPolynomial v = t.divides(q); RationalPolynomial w = v.times(q); StdOut.println("p(x) = " + p); StdOut.println("q(x) = " + q); StdOut.println("r(x) = p(x) + q(x) = " + r); StdOut.println("s(x) = p(x) * q(x) = " + s); StdOut.println("t(x) = r(x) * r(x) = " + t); StdOut.println("u(x) = t(x) - q^2(x) = " + u); StdOut.println("v(x) = t(x) / q(x) = " + v); StdOut.println("w(x) = v(x) * q(x) = " + w); StdOut.println("t(3) = " + t.evaluate(three)); StdOut.println("t'(x) = " + t.differentiate()); StdOut.println("t''(x) = " + t.differentiate().differentiate()); StdOut.println("f(x) = int of t(x) = " + t.integrate()); StdOut.println("integral(t(x), 1/2..3) = " + t.integrate(half, three)); } }