/* * $Id: Series.java,v 1.9 2004/12/23 15:55:08 jdc Exp $ * $Date: 2004/12/23 15:55:08 $ * $Author: jdc $ * $Revision: 1.9 $ * */ package org.dawley_carr.math; import java.math.BigInteger; import java.util.ArrayList; /** * @author Jacob Dawley-Carr * @version $Revision: 1.9 $ */ public abstract class Series { public static final BigInteger ZERO = BigInteger.ZERO; public static final BigInteger ONE = BigInteger.ONE; public static final BigInteger TEN = BigInteger.TEN; /** * f(n) = 1/n! + 1/(n - 1)! + 1/(n - 2)! ... + 1/0! * * @return f(n) * pow(10, newPrecision) */ public static BigInteger euler(BigInteger newPrecision) { BigInteger mult = ONE; BigInteger prev = TEN; // some bogus entry BigInteger next = ZERO; if (newPrecision.compareTo(ZERO) <= 0) { throw new IllegalArgumentException("Argument must be positive"); } for (BigInteger i = ZERO; i.compareTo(newPrecision) < 0; i = i.add(ONE)) { mult = mult.multiply(TEN); } // add until it doesn't make any difference for (BigInteger i = ZERO; next.compareTo(prev) != 0; i = i.add(ONE)) { BigInteger tmpFactorial = Series.factorial(i); BigInteger tmpInverseFactorial = mult.divide(tmpFactorial); prev = next; next = next.add(tmpInverseFactorial); } return next; } /** * n! = n * (n - 1) * (n - 2) * ... * 1 * * @return n! */ public static BigInteger factorial(BigInteger newArg) { if (newArg.compareTo(ZERO) < 0) { throw new IllegalArgumentException("Argument must be non-negative"); } else if (newArg.compareTo(ZERO) == 0) { return ONE; } else if (newArg.compareTo(ONE) == 0) { return ONE; } else { BigInteger tmpBigInteger = ONE; for (BigInteger i = ONE; i.compareTo(newArg) <= 0; i = i.add(ONE)) { tmpBigInteger = tmpBigInteger.multiply(i); } return tmpBigInteger; } } /** * f(0) = 0 *

* f(1) = 1 *

* f(n) = f(n-1) + f(n-2) for n > 1 *

* f(n) undefined for n < 0 * * @return f(n) */ public static BigInteger fibonacci(BigInteger newArg) { BigInteger tmpBigInteger = null; if (newArg.compareTo(ZERO) < 0) { throw new IllegalArgumentException("Argument must be non-negative"); } else if (newArg.compareTo(ZERO) == 0) { tmpBigInteger = ZERO; } else if (newArg.compareTo(ONE) == 0) { tmpBigInteger = ONE; } else { BigInteger f_2 = ZERO; // f(x-2) BigInteger f_1 = ONE; // f(x-1) BigInteger f_0 = ONE; // f(x) for (BigInteger i = ONE; i.compareTo(newArg) < 0; i = i.add(ONE)) { f_0 = f_1.add(f_2); f_2 = f_1; f_1 = f_0; } tmpBigInteger = f_0; } return tmpBigInteger; } /** * The 10 digit prime numbers from consecutive digits of "e" * * @return array of the first couple google numbers */ public static Object[] google() { BigInteger tmpEulerPrecision = new BigInteger(new String("1000")); BigInteger tmpEuler = Series.euler(tmpEulerPrecision); String tmpSeriesString = tmpEuler.toString(); ArrayList tmpArrayList = new ArrayList(); for (int i = 0; i < tmpSeriesString.length() - 10; ++i) { String tmpSubSeriesString = tmpSeriesString.substring(i, i + 10); BigInteger tmpSubSeries = new BigInteger(tmpSubSeriesString); if (tmpSubSeries.isProbablePrime(100000)) { tmpArrayList.add(tmpSubSeriesString); } } return tmpArrayList.toArray(); } /** * demo of usage */ public static void main(String[] argv) { String[] tmpArgvs = argv; if (tmpArgvs.length == 0) { tmpArgvs = new String[1]; tmpArgvs[0] = new String("1000"); } for (int i = 0; i < tmpArgvs.length; ++i) { try { BigInteger tmpArgv = new BigInteger(tmpArgvs[i]); BigInteger tmpValue; System.out.println("fibonacci(" + tmpArgv.toString() + ") ="); tmpValue = Series.fibonacci(tmpArgv); System.out.println(" length = " + tmpValue.toString().length()); System.out.println(" value = " + tmpValue.toString()); System.out.println(); System.out.println("euler(" + tmpArgv.toString() + ") ="); tmpValue = Series.euler(tmpArgv); System.out.println(" length = " + tmpValue.toString().length()); System.out.println(" value = " + tmpValue.toString()); System.out.println(); } catch (NumberFormatException e) { System.out.println(tmpArgvs[i] + ": not a number"); } } System.out.println("google series is:"); Object[] tmpValues = Series.google(); for (int i = 0; i < tmpValues.length; ++i) { System.out.println(" value = " + tmpValues[i].toString()); } } }