* Mathemaica 로 연습해본 분수 계산
TestFraction-01.pdf
* C++ 언어로 구현해본 분수 계산 예제 소스
(참고1: 0으로 나누는 예외상황, 0의 음수 지수 예외상황 처리됨)
(참고2: VC++ 와 g++ 로 모두 컴파일되고 실행됨)
* Filename TestFraction.cpp
*
* Version: 0.4
* Purpose: Calculate fractions.
*
* With VC++
* Compile: cl TestFraction.cpp /EHsc
* Execute: TestFraction
*
* With g++
* Compile: g++ TestFraction.cpp -o TestFraction
* Execute: ./TestFraction
*
* Date: 2011. 10. 9 (Sun)
*/
#include <iostream>
#include <cmath>
#include <cstring>
using namespace std;
class Fraction {
private:
long numer, denom;
public:
Fraction(long _x = 0L, long _y = 1L): numer(_x), denom(_y) {
if (denom < 0) {
simplify();
}
}
~Fraction() {
}
Fraction copy();
void simplify();
void setNumer(long v);
void setDenom(long v);
void set(long a, long b);
long getNumer();
long getDenom();
long *get();
Fraction operator+(const Fraction &other);
Fraction operator+(long other);
Fraction operator-(const Fraction &other);
Fraction operator-(long other);
Fraction operator/(Fraction other);
Fraction operator/(long other);
Fraction operator-();
Fraction operator^(long other);
bool operator==(const Fraction &b);
bool operator<(const Fraction &b);
bool operator<=(const Fraction &b);
bool operator>(const Fraction &b);
bool operator>=(const Fraction &b);
bool operator==(long double v);
bool operator<(long double v);
bool operator<=(long double v);
bool operator>(long double v);
bool operator>=(long double v);
bool isZero();
long double eval();
void show();
};
long gcd(long a, long b) {
long tmp, q, r;
q = abs(a);
r = abs(b);
while (r > 0) {
tmp = q % r;
q = r;
r = tmp;
}
return q;
}
Fraction Fraction::copy() {
Fraction tmp(0, 1);
tmp.numer = numer;
tmp.denom = denom;
return tmp;
}
void Fraction::simplify() {
long x = abs(numer);
long y = abs(denom);
long d = gcd(x, y);
if (denom < 0) {
numer = -numer/d;
denom = -denom/d;
}
else {
numer = numer/d;
denom = denom/d;
}
}
long double Fraction::eval() {
long double tmp = ((long double) numer)/((long double) denom);
return tmp;
}
void Fraction::show() {
if (denom == 1)
cout << numer << endl;
else
cout << "(" << numer << "/" << denom << ")" << endl;
}
bool Fraction::isZero() {
return numer == 0;
}
void printFraction(const char *msg, Fraction a) {
if (msg == NULL || strlen(msg) == 0) {
cout << "(" << a.getNumer() << "/" << a.getDenom() << ")" << endl;
}
else {
cout << msg << "(" << a.getNumer() << "/" << a.getDenom() << ")" << endl;
}
}
void Fraction::setNumer(long v) {
numer = v;
}
void Fraction::setDenom(long v) {
denom = v;
}
void Fraction::set(long a, long b) {
numer = a;
denom = b;
}
long Fraction::getNumer() {
return numer;
}
long Fraction::getDenom() {
return denom;
}
long *Fraction::get() {
static long tmp[2];
tmp[0] = getNumer();
tmp[1] = getDenom();
return (long *)tmp;
}
Fraction Fraction::operator+(const Fraction &other) {
long x = numer*other.denom + denom*other.numer;
long y = denom*other.denom;
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction Fraction::operator+(long other) {
long x = numer + denom*other;
long y = denom;
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction operator+(long other, Fraction a) {
long x = a.getNumer() + a.getDenom()*other;
long y = a.getDenom();
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction Fraction::operator-(const Fraction &other) {
long x = numer*other.denom - denom*other.numer;
long y = denom*other.denom;
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction Fraction::operator-(long other) {
long x = numer - denom*other;
long y = denom;
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction operator-(long other, Fraction a) {
long x = a.getDenom()*other - a.getNumer();
long y = a.getDenom();
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction operator*(long other, Fraction a) {
long x = a.getNumer()*other;
long y = a.getDenom();
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction operator*(Fraction a, Fraction b) {
long x = a.getNumer()*b.getNumer();
long y = a.getDenom()*b.getDenom();
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction Fraction::operator/(Fraction other) {
try {
if (other.isZero()) {
throw "Divided by zero.";
}
long x = numer*other.getDenom();
long y = denom*other.getNumer();
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
catch (const char *msg) {
cout << "Exception: " << msg << endl;
return NULL;
}
}
Fraction Fraction::operator-() {
long x = -numer;
long y = denom;
long d = gcd(x, y);
Fraction tmp(x/d, y/d);
return tmp;
}
Fraction Fraction::operator^(long n) {
try {
if (n <= 0 && numer == 0) {
throw "Nonpositive power of zero does not exist.";
}
Fraction one(1, 1);
Fraction tmp;
if (n == 0) {
tmp.setNumer(1);
tmp.setDenom(1);
return tmp;
}
else if (n == 1) {
tmp.setNumer(numer);
tmp.setDenom(denom);
return tmp;
}
else {
long mn = n;
if (mn < 0)
mn = -mn;
tmp.setNumer(numer);
tmp.setDenom(denom);
tmp = tmp.operator^(mn/2);
if (mn % 2 == 1) {
tmp.setNumer(tmp.getNumer()*tmp.getNumer()*numer);
tmp.setDenom(tmp.getDenom()*tmp.getDenom()*denom);
}
else {
tmp.setNumer(tmp.getNumer()*tmp.getNumer());
tmp.setDenom(tmp.getDenom()*tmp.getDenom());
}
if (n < 0) {
long t;
t = tmp.numer;
if (t < 0) {
tmp.setNumer(-tmp.getDenom());
tmp.setDenom(-t);
}
else {
tmp.setNumer(tmp.getDenom());
tmp.setDenom(t);
}
}
return tmp;
}
}
catch (const char *msg) {
cout << "Exception: " << msg << endl;
return NULL;
}
}
bool Fraction::operator==(const Fraction &b) {
return numer*b.denom == denom*b.numer;
}
bool Fraction::operator<(const Fraction &b) {
return numer*b.denom < denom*b.numer;
}
bool Fraction::operator<=(const Fraction &b) {
return numer*b.denom <= denom*b.numer;
}
bool Fraction::operator>(const Fraction &b) {
return numer*b.denom > denom*b.numer;
}
bool Fraction::operator>=(const Fraction &b) {
return numer*b.denom >= denom*b.numer;
}
bool Fraction::operator==(long double v) {
return eval() - v == 0;
}
bool Fraction::operator<(long double v) {
return eval() < v;
}
bool Fraction::operator<=(long double v) {
return eval() <= v;
}
bool Fraction::operator>(long double v) {
return eval() > v;
}
bool Fraction::operator>=(long double v) {
return eval() >= v;
}
int main() {
Fraction a(1, 6);
printFraction("a = ", a);
Fraction b(3, 4);
printFraction("b = ", b);
Fraction c = a + b;
printFraction("c = a + b = ", c);
c = a - b;
printFraction("c = a - b = ", c);
c = a * b;
printFraction("c = a * b = ", c);
c = a / b;
printFraction("c = a / b = ", c);
printFraction("-a = ", -a);
printFraction("a + 1 = ", a + 1);
printFraction("1 + a = ", 1 + a);
printFraction("a - 1 = ", a - 1);
printFraction("1 - a = ", 1 - a);
printFraction("a * 2 = ", a * 2);
printFraction("-3 * a = ", -3 * a);
printFraction("1 + a - 3 = ", 1 + a - 3);
printFraction("a^2 = ", a^2);
printFraction("b^3 = ", b^3);
printFraction("-b^-3 = ", -b^-3);
c = a.copy();
printFraction("a = ", a);
printFraction("b = ", b);
printFraction("c = ", c);
cout << " a == c ? " << (a == c) << endl;
cout << " a < c ? " << (a < c) << endl;
cout << " a <= c ? " << (a <= c) << endl;
cout << " a > c ? " << (a > c) << endl;
cout << " a >= c ? " << (a >= c) << endl;
cout << " a == b ? " << (a == b) << endl;
cout << " a < b ? " << (a < b) << endl;
cout << " a <= b ? " << (a <= b) << endl;
cout << " a > b ? " << (a > b) << endl;
cout << " a >= b ? " << (a >= b) << endl;
a.setNumer(3);
cout << "Comapre again!" << endl;
printFraction("a = ", a);
printFraction("c = ", c);
cout << " a == c ? " << (a == c) << endl;
Fraction d(5, -10);
printFraction("d = ", d);
printFraction("a = ", a);
a.simplify();
printFraction("Simplified, a = ", a);
cout << " a.eval() = " << a.eval() << endl;
int i;
long *pval;
printFraction("a = ", a);
pval = a.get();
for (i = 0; i < 2; i++) {
cout << " pval[" << i << "] = " << pval[i] << endl;
}
printFraction("c = ", c);
pval = c.get();
for (i = 0; i < 2; i++) {
cout << " pval[" << i << "] = " << pval[i] << endl;
}
printFraction("d = ", d);
pval = d.get();
for (i = 0; i < 2; i++) {
cout << " pval[" << i << "] = " << pval[i] << endl;
}
printFraction("a = ", a);
cout << " a == 0.1 ? " << (a == 0.1) << endl;
cout << " a < 0.1 ? " << (a < 0.1) << endl;
cout << " a <= 0.1 ? " << (a <= 0.1) << endl;
cout << " a > 0.1 ? " << (a > 0.1) << endl;
cout << " a >= 0.1 ? " << (a >= 0.1) << endl;
Fraction e = a/(b - b);
printFraction("e = ", e);
e = (b - b)^-2;
printFraction("e = ", e);
return 0;
}
/*
a = (1/6)
b = (3/4)
c = a + b = (11/12)
c = a - b = (-7/12)
c = a * b = (1/8)
c = a / b = (2/9)
-a = (-1/6)
a + 1 = (7/6)
1 + a = (7/6)
a - 1 = (-5/6)
1 - a = (5/6)
a * 2 = (1/3)
-3 * a = (-1/2)
1 + a - 3 = (-11/6)
a^2 = (1/36)
b^3 = (27/64)
-b^-3 = (-64/27)
a = (1/6)
b = (3/4)
c = (1/6)
a == c ? 1
a < c ? 0
a <= c ? 1
a > c ? 0
a >= c ? 1
a == b ? 0
a < b ? 1
a <= b ? 1
a > b ? 0
a >= b ? 0
Comapre again!
a = (3/6)
c = (1/6)
a == c ? 0
d = (-1/2)
a = (3/6)
Simplified, a = (1/2)
a.eval() = 0.5
a = (1/2)
pval[0] = 1
pval[1] = 2
c = (1/6)
pval[0] = 1
pval[1] = 6
d = (-1/2)
pval[0] = -1
pval[1] = 2
a = (1/2)
a == 0.1 ? 0
a < 0.1 ? 0
a <= 0.1 ? 0
a > 0.1 ? 1
a >= 0.1 ? 1
Exception: Divided by zero.
e = (0/1)
Exception: Nonpositive power of zero does not exist.
e = (0/1)
*/
* Groovy 언어로 작성된 분수 계산용 Fraction 클래스 (Java에서도 사용 가능)
(참고: Groovy 1.8.0 & Java 7 및 Groovy 1.8.2 & Java 7 에소 테스트되었음)
* Filename: Fraction.groovy
*
* Purpose:
* A class, supporting fraction calculations,
* which depends on the long types of Java.
*
* Setting Environment Variables:
* set JAVA_HOME=c:\Java7
* set GROOVY_HOME=c:\groovy182
* set PATH=c:%GROOVY_HOME%\bin;%PATH%
*
* Execute Only: groovy Fraction.groovy
* Compile for Java: groovyc -d . Fraction.groovy
*
* Author: Copyright (c) 2011. 10. 7 (Fri) PH Kim ( pkim (AT) scripts (DOT) pe (DOT) kr )
***********************************************************************************/
package kr.pe.scripts.numeric.fraction
public class Fraction {
public long numer;
public long denom;
final public static Fraction ZERO = new Fraction(0, 1);
final public static Fraction ONE = new Fraction(1, 1);
final public static Fraction TWO = new Fraction(2, 1);
final public static Fraction THREE = new Fraction(3, 1);
final public static Fraction TEN = new Fraction(10, 1);
public Fraction(long numer, long denom) {
this.numer = numer;
this.denom = denom;
}
public boolean isZero() {
return this.numer == 0L;
}
public Fraction plus(Fraction other) {
long a = this.numer*other.denom + this.denom*other.numer;
long b = this.denom*other.denom;
Fraction z = new Fraction(a, b);
z.simplify();
return z;
}
public Fraction minus(Fraction other) {
long a = this.numer*other.denom - this.denom*other.numer;
long b = this.denom*other.denom;
Fraction z = new Fraction(a, b);
simplify(z);
return z;
}
public Fraction multiply(Fraction other) {
long a = this.numer*other.numer;
long b = this.denom*other.denom;
if (b < 0) {
a = -a;
b = -b;
}
Fraction z = new Fraction(a, b);
simplify(z);
return z;
}
public Fraction div(Fraction other) {
if (other.isZero()) {
throw new RuntimeException("Cannot divide by the fraction " + other + ", since it is zero.");
}
long a = this.numer*other.denom;
long b = this.denom*other.numer;
if (b < 0) {
a = -a;
b = -b;
}
Fraction z = new Fraction(a, b);
simplify(z);
return z;
}
public void simplify() {
long c = gcd(this.numer, this.denom);
// if (c < 0)
// c = -c;
this.numer = (this.numer / c) as long;
this.denom = (this.denom / c) as long;
if (this.numer == 0) {
this.denom = 1;
}
}
public static void simplify(Fraction z) {
long c = gcd(z.numer, z.denom);
z.numer = (z.numer / c) as long;
z.denom = (z.denom / c) as long;
if (z.numer == 0) {
z.denom = 1;
}
}
public static long gcd(long a, long b) {
long q = Math.abs(a);
long r = Math.abs(b);
long t;
while (r != 0L) {
t = r;
r = q % r
q = t;
}
return q;
}
/*
public Complex power(long n) {
long mn = n;
if (mn < 0.0)
mn = -mn;
Complex tmp = new Complex(1, 0);
for (int i = 0; i < mn; i++) {
tmp = tmp*this;
}
if (n < 0) {
tmp = new Complex(1, 0) / tmp;
}
return tmp;
}
*/
public Fraction power(long n) {
if (n < 0 && this.isZero()) {
throw new RuntimeException("Negative power of " + this + " dose not exist, since it is zero.");
}
if (n == 0)
return new Fraction(1, 1);
else if (n == 1)
return new Fraction(this.numer, this.denom);
long mn = n;
if (mn < 0L)
mn = -mn;
Fraction tmp = this.power((mn/2) as long);
if (mn % 2 == 1) {
tmp = tmp*tmp*this;
}
else {
tmp = tmp*tmp;
}
if (n < 0) {
// println(" : tmp = " + tmp);
tmp = Fraction.ONE / tmp;
// println(" ----> tmp = " + tmp);
}
return tmp;
}
public static Fraction square(Fraction z) {
return z*z;
}
public static Fraction cube(Fraction z) {
return z*z*z;
}
public Fraction inverse() {
if (this.isZero()) {
throw new RuntimeException("The multiplicative inverse of " + this + " does not exist, since it is zero.");
}
if (this.numer < 0)
return new Fraction(-this.denom, -this.numer);
else
return new Fraction(this.denom, this.numer);
}
public Fraction abs() {
return new Fraction(Math.abs(this.numer), this.denom)
}
public static Fraction abs(Fraction z) {
return new Fraction(Math.abs(z.numer), z.denom)
}
public Fraction negative() {
return new Fraction(-this.numer, this.denom)
}
public boolean equals(Fraction other) {
return this.numer*other.denom == other.numer*this.denom;
}
public String toString() {
if (this.denom == 1)
return "" + this.numer;
return "(" + this.numer + "/" + this.denom + ")";
}
public static void println(String s) {
System.out.println(s);
}
public static void main(String[] args) {
Fraction z = new Fraction(1, 2);
Fraction w = new Fraction(5, 4);
println("z = " + z);
println("w = " + w);
println(" z + w = " + (z + w));
println(" z - w = " + (z - w));
println(" z * w = " + (z * w));
println(" z / w = " + (z / w));
println(" z**2 = " + (z**2));
println(" z**3 = " + (z**3));
println(" z.inverse() = " + z.inverse());
println(" 1/z = " + (ONE/z));
println(" z**-1 = " + (z**-1));
println(" z**-2 = " + (z**-2));
println(" z**-3 = " + (z**-3));
println(" -z = " + (-z));
println(" z.abs() = (" + z + ").abs() = " + z.abs());
println(" z == " + new Fraction(1, 2) + " ? " + (z == new Fraction(1,2)));
println(" z - z = " + (z - z));
println(" (z - z).isZero() ? " + (z - z).isZero());
println(" Fraction.ZERO = " + Fraction.ZERO);
println(" Fraction.ONE = " + Fraction.ONE);
println(" Fraction.TWO = " + Fraction.TWO);
println(" Fraction.THREE = " + Fraction.THREE);
println(" Fraction.TEN = " + Fraction.TEN);
println(" z = " + z);
println(" w.negative() = " + w.negative());
println(" z**0 = " + (z**0));
println(" z**1 = " + (z**1));
println(" z**2 = " + (z**2));
println(" z**3 = " + (z**3));
println(" z**4 = " + (z**4));
println(" z**10 = " + (z**10));
println(" z**-1 = " + (z**-1));
println(" z**-2 = " + (z**-2));
println(" z**-3 = " + (z**-3));
println(" z**-4 = " + (z**-4));
println(" z**-10 = " + (z**-10));
println(" w.negative()**0 = " + (w.negative()**0));
println(" w.negative()**1 = " + (w.negative()**1));
println(" w.negative()**2 = " + (w.negative()**2));
println(" w.negative()**3 = " + (w.negative()**3));
println(" w.negative()**4 = " + (w.negative()**4));
println(" w.negative()**10 = " + (w.negative()**10));
println(" w.negative()**-1 = " + (w.negative()**-1));
println(" w.negative()**-2 = " + (w.negative()**-2));
println(" w.negative()**-3 = " + (w.negative()**-3));
println(" w.negative()**-4 = " + (w.negative()**-4));
println(" w.negative()**-10 = " + (w.negative()**-10));
println(" (z - w)**0 = " + ((z - w)**0));
println(" (z - w)**1 = " + ((z - w)**1));
println(" (z - w)**2 = " + ((z - w)**2));
println(" (z - w)**3 = " + ((z - w)**3));
println(" (z - w)**-1 = " + ((z - w)**-1));
println(" (z - w)**-2 = " + ((z - w)**-2));
println(" (z - w)**-3 = " + ((z - w)**-3));
}
}
/*
Execution Result:
z = (1/2)
w = (5/4)
z + w = (7/4)
z - w = (-3/4)
z * w = (5/8)
z / w = (2/5)
z**2 = (1/4)
z**3 = (1/8)
z.inverse() = 2
1/z = 2
z**-1 = 2
z**-2 = 4
z**-3 = 8
-z = (-1/2)
z.abs() = ((1/2)).abs() = (1/2)
z == (1/2) ? true
z - z = 0
(z - z).isZero() ? true
Fraction.ZERO = 0
Fraction.ONE = 1
Fraction.TWO = 2
Fraction.THREE = 3
Fraction.TEN = 10
z = (1/2)
w.negative() = (-5/4)
z**0 = 1
z**1 = (1/2)
z**2 = (1/4)
z**3 = (1/8)
z**4 = (1/16)
z**10 = (1/1024)
z**-1 = 2
z**-2 = 4
z**-3 = 8
z**-4 = 16
z**-10 = 1024
w.negative()**0 = 1
w.negative()**1 = (-5/4)
w.negative()**2 = (25/16)
w.negative()**3 = (-125/64)
w.negative()**4 = (625/256)
w.negative()**10 = (9765625/1048576)
w.negative()**-1 = (-4/5)
w.negative()**-2 = (16/25)
w.negative()**-3 = (-64/125)
w.negative()**-4 = (256/625)
w.negative()**-10 = (1048576/9765625)
(z - w)**0 = 1
(z - w)**1 = (-3/4)
(z - w)**2 = (9/16)
(z - w)**3 = (-27/64)
(z - w)**-1 = (-4/3)
(z - w)**-2 = (16/9)
(z - w)**-3 = (-64/27)
*/
* Groovy 언어로 작성된 Fraction 클래스를 테스트하는 Java 예제 소스
(참고: Groovy 1.8.0 & Java 7 및 Groovy 1.8.2 & Java 7 에서 테스트되었음)
/**********************************************************************************
* Filename: TestFraction.java
*
* Purpose:
* Testing the Fraction class made by Groovy,
*
* Setting Environment Variables:
* set JAVA_HOME=c:\Java7
* set GROOVY_HOME=c:\groovy182
* set PATH=c:%GROOVY_HOME%\bin;%PATH%
*
* Compile: javac -d . TestFraction.java
* Execute: java -cp .;%GROOVY_HOME%\embeddable\groovy-all-1.8.2.jar
* kr.pe.scripts.numeric.fraction.TestFraction
*
* Author: Copyright (c) 2011. 10. 7 (Fri) PH Kim ( pkim (AT) scripts (DOT) pe (DOT) kr )
***********************************************************************************/
package kr.pe.scripts.numeric.fraction;
import kr.pe.scripts.numeric.fraction.Fraction;
public class TestFraction {
public static void println(String s) {
System.out.println(s);
}
public static void main(String[] args) {
Fraction z = new Fraction(1, 2);
Fraction w = new Fraction(5, 4);
println("z = " + z);
println("w = " + w);
println(" z + w = " + z.plus(w));
println(" z - w = " + z.minus(w));
println(" z * w = " + z.multiply(w));
println(" z / w = " + z.div(w));
println(" z**2 = " + z.power(2));
println(" z**3 = " + z.power(3));
println(" z.inverse() = " + z.inverse());
println(" 1/z = " + Fraction.ONE.div(z));
println(" z**-1 = " + z.power(-1));
println(" z**-2 = " + z.power(-2));
println(" z**-3 = " + z.power(-3));
println(" -z = " + z.negative());
println(" z.abs() = (" + z + ").abs() = " + z.abs());
println(" z == " + new Fraction(1, 2) + " ? " + (z == new Fraction(1,2)));
println(" z - z = " + z.minus(z));
println(" (z - z).isZero() ? " + z.minus(z).isZero());
println(" Fraction.ZERO = " + Fraction.ZERO);
println(" Fraction.ONE = " + Fraction.ONE);
println(" Fraction.TWO = " + Fraction.TWO);
println(" Fraction.THREE = " + Fraction.THREE);
println(" Fraction.TEN = " + Fraction.TEN);
println(" z = " + z);
println(" w.negative() = " + w.negative());
println(" z**0 = " + z.power(0));
println(" z**1 = " + z.power(1));
println(" z**2 = " + z.power(2));
println(" z**3 = " + z.power(3));
println(" z**4 = " + z.power(4));
println(" z**10 = " + z.power(10));
println(" z**-1 = " + z.power(-1));
println(" z**-2 = " + z.power(-2));
println(" z**-3 = " + z.power(-3));
println(" z**-4 = " + z.power(-4));
println(" z**-10 = " + z.power(-10));
println(" w.negative()**0 = " + w.negative().power(0));
println(" w.negative()**1 = " + w.negative().power(1));
println(" w.negative()**2 = " + w.negative().power(2));
println(" w.negative()**3 = " + w.negative().power(3));
println(" w.negative()**4 = " + w.negative().power(4));
println(" w.negative()**10 = " + w.negative().power(10));
println(" w.negative()**-1 = " + w.negative().power(-1));
println(" w.negative()**-2 = " + w.negative().power(-2));
println(" w.negative()**-3 = " + w.negative().power(-3));
println(" w.negative()**-4 = " + w.negative().power(-4));
println(" w.negative()**-10 = " + w.negative().power(-10));
println(" (z - w)**0 = " + z.minus(w).power(0));
println(" (z - w)**1 = " + z.minus(w).power(1));
println(" (z - w)**2 = " + z.minus(w).power(2));
println(" (z - w)**3 = " + z.minus(w).power(3));
println(" (z - w)**-1 = " + z.minus(w).power(-1));
println(" (z - w)**-2 = " + z.minus(w).power(-2));
println(" (z - w)**-3 = " + z.minus(w).power(-3));
}
}
/*
Execution Result:
z = (1/2)
w = (5/4)
z + w = (7/4)
z - w = (-3/4)
z * w = (5/8)
z / w = (2/5)
z**2 = (1/4)
z**3 = (1/8)
z.inverse() = 2
1/z = 2
z**-1 = 2
z**-2 = 4
z**-3 = 8
-z = (-1/2)
z.abs() = ((1/2)).abs() = (1/2)
z == (1/2) ? false
z - z = 0
(z - z).isZero() ? true
Fraction.ZERO = 0
Fraction.ONE = 1
Fraction.TWO = 2
Fraction.THREE = 3
Fraction.TEN = 10
z = (1/2)
w.negative() = (-5/4)
z**0 = 1
z**1 = (1/2)
z**2 = (1/4)
z**3 = (1/8)
z**4 = (1/16)
z**10 = (1/1024)
z**-1 = 2
z**-2 = 4
z**-3 = 8
z**-4 = 16
z**-10 = 1024
w.negative()**0 = 1
w.negative()**1 = (-5/4)
w.negative()**2 = (25/16)
w.negative()**3 = (-125/64)
w.negative()**4 = (625/256)
w.negative()**10 = (9765625/1048576)
w.negative()**-1 = (-4/5)
w.negative()**-2 = (16/25)
w.negative()**-3 = (-64/125)
w.negative()**-4 = (256/625)
w.negative()**-10 = (1048576/9765625)
(z - w)**0 = 1
(z - w)**1 = (-3/4)
(z - w)**2 = (9/16)
(z - w)**3 = (-27/64)
(z - w)**-1 = (-4/3)
(z - w)**-2 = (16/9)
(z - w)**-3 = (-64/27)
*/
* Python 언어로 분수 계산하는 예제
(참고: 파이썬에는 분수 계산용 모듈 fractions 이 기본적으로 있으므로,
별도로 분수 계산용 클래스를 만들지 않았다.
from fractions import *
이 구문만 추가하면 Fraction 클래스를 사용할 수 있다. )
"""
Filename: TestFraction.py
Test fraction calculations, wgich works on Python 2.6 or 2.7.
Execute: python TestFraction.py
Date: 2011. 10. 10
"""
from fractions import *
z = Fraction(1, 2)
w = Fraction("5/4")
print "z = %s, w=%s" % (z, w)
print "z + w = %s" % (z + w)
print "z - w = %s" % (z - w)
print "z * w = %s" % (z * w)
print "z / w = %s" % (z / w)
print "z**2 = %s" % (z**2)
print "z**3 = %s" % (z**3)
print "1/z = %s" % (1/z)
print "z**-1 = %s" % (z**-1)
print "z**-2 = %s" % (z**-2)
print "z**-3 = %s" % (z**-3)
print "-z = %s" % (-z)
print "abs(z) = %s" % abs(z)
print "z == Fraction(\"1/2\") ? %s" % (z == Fraction("1/2"))
print "z == Fraction(1, 2) ? %s" % (z == Fraction(1, 2))
print "Fraction(3, 6) = %s" % (Fraction(3, 6))
print "z == Fraction(3, 6) ? %s" % (z == Fraction(3, 6))
print "z - z == 0 ? %s" % (z - z == 0)
print "(z - w)**0 = %s" % ((z - w)**0)
print "(z - w)**1 = %s" % ((z - w)**1)
print "(z - w)**2 = %s" % ((z - w)**2)
print "(z - w)**3 = %s" % ((z - w)**3)
print "(z - w)**-1 = %s" % ((z - w)**-1)
print "(z - w)**-2 = %s" % ((z - w)**-2)
print "(z - w)**-3 = %s" % ((z - w)**-3)
"""
Execute Result:
z = 1/2, w=5/4
z + w = 7/4
z - w = -3/4
z * w = 5/8
z / w = 2/5
z**2 = 1/4
z**3 = 1/8
1/z = 2
z**-1 = 2
z**-2 = 4
z**-3 = 8
-z = -1/2
abs(z) = 1/2
z == Fraction("1/2") ? True
z == Fraction(1, 2) ? True
Fraction(3, 6) = 1/2
z == Fraction(3, 6) ? True
z - z == 0 ? True
(z - w)**0 = 1
(z - w)**1 = -3/4
(z - w)**2 = 9/16
(z - w)**3 = -27/64
(z - w)**-1 = -4/3
(z - w)**-2 = 16/9
(z - w)**-3 = -64/27
"""
* Lua 언어로 분수 계산을 하기 위한 fraction 클래스 소스
-- fraction 0.1.0
-- Lua 5.1
-- Filename: fraction.lua
--
-- 'fraction' provides common tasks with fractional numbers
-- function fraction.new( numer, denom )
-- returns a fraction number on success, nil on failure
-- numer := numerator
-- denom := denominator
-- e.g. fraction.new( -3, 5 )
-- function fraction.to( arg ); fraction( arg )
-- returns a fraction number on success, nil on failure
-- arg := number or { number,number }
-- or ( "(-)<number>" and/or "(+/-)<number>/(+/-)<number>" )
-- e.g. 5; {2,3}; "2/3", "2 / 3", "+2/ 3", "-5 / 4 "
-- function fraction.parseApart( arg )
-- returns a fraction number on success, nil on failure
-- arg := number or { number, number, number }
-- or ( "(-)<number>" and/or "(+/-)<number> (+/-)<number>/(+/-)<number>"
-- and/or "(+/-)<number> + (+/-)<number>/(+/-)<number>" )
-- e.g. {-2, 3, 5}; "-2 3/5", "-2 + 3/5", "-2 + +3/5"
-- a fraction number is defined as numerator over denomnator
-- fraction number := { numer, denom }
-- this gives fast access to both parts of the number for calculation
-- the access is faster than in a hash table
-- the metatable is just a add on, when it comes to speed, one is faster using a direct function call
-- See: http://scripting.tistory.com
--
-- Licensed under the same terms as Lua itself.
--
-- Author: PH Kim ( pkim [AT] scripts [DOT] pe [DOT] kr )
--/////////////--
--// fraction //--
--/////////////--
-- link to fraction table
local fraction = {}
-- link to fraction metatable
local fraction_meta = {}
-- fraction.to( arg )
-- return a fraction number on success
-- return nil on failure
local _retone = function() return 1 end
local _retminusone = function() return -1 end
function fraction.to( num )
-- check for table type
-- print( type( num ) )
if type( num ) == "table" then
-- check for a fractionnumber
if getmetatable( num ) == fraction_meta then
return num
end
local numer, denom = tonumber( num[1] ), tonumber( num[2] )
if not denom then
denim = 1
end
-- print(numer, denom)
if numer and denom then
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
if denom < 0 then
return setmetatable( { -numer, -denom }, fraction_meta )
else
return setmetatable( { numer, denom }, fraction_meta )
end
end
return
end
-- check for number
local isnum = tonumber( num )
if isnum then
return setmetatable( { isnum, 1 }, fraction_meta )
end
-- print( type( num ) )
if type( num ) == "string" then
-- print( " >" .. type( num ) )
-- check for digits
-- number chars [%-%+%*%^%d/%*%^%d]
-- local numer, denom = string.match( num, "^(%-%+%d+)[ ](%d+)$" )
local numer, denom = string.match( num, "([%+%-%*%^%d]*%d)[\\/ ]*([%+%-%*%^%d]*%d)[, ]*" )
-- print(numer, denom)
-- print( type( num ) )
if numer and denom then
numer, denom = tonumber(numer), tonumber(denom)
-- print(" ", numer, denom)
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
-- print(" ---> ", numer, denom)
if denom < 0 then
return setmetatable( { -numer, -denom }, fraction_meta )
else
return setmetatable( { numer, denom }, fraction_meta )
end
elseif numer then
numer = tonumber(numer)
return setmetatable( { numer, 1 }, fraction_meta )
end
end
return nil
end
-- fraction( arg )
-- same as fraction.to( arg )
-- set __call behaviour of fraction
setmetatable( fraction, { __call = function( _,num ) return fraction.to( num ) end } )
-- fraction.new( numer, denom )
-- fast function to get a complex number, not invoking any checks
function fraction.new( ... )
return setmetatable( { ... }, fraction_meta )
end
function fraction.parseApart( num )
-- check for table type
-- print( type( num ) )
if type( num ) == "table" then
-- check for a fractionnumber
if getmetatable( num ) == fraction_meta then
return num
end
local ipart, numer, denom = tonumber( num[1] ), tonumber( num[2] ), tonumber( num[3] )
if not denom then
denom = 1
end
-- print(numer, denom)
if ipart and numer and denom then
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
if denom < 0 then
numer = numer + ipart*(-denom)
return setmetatable( { -numer, -denom }, fraction_meta )
else
numer = numer + ipart*denom
return setmetatable( { numer, denom }, fraction_meta )
end
elseif numer and denom then
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
if denom < 0 then
return setmetatable( { -numer, -denom }, fraction_meta )
else
return setmetatable( { numer, denom }, fraction_meta )
end
end
return
end
-- check for number
local isnum = tonumber( num )
if isnum then
return setmetatable( { isnum, 1 }, fraction_meta )
end
-- print( type( num ) )
if type( num ) == "string" then
-- print( " >" .. type( num ) )
-- check for digits
-- number chars [%-%+%*%^%d %-%+%*%^%d/%-%+%*%^%d]
-- local numer, denom = string.match( num, "^(%-%+%d+)[ ](%d+)$" )
---- print( num )
local ipart, numer, denom = string.match( num, "([%+%-%*%^%d]*%d)[$+ ]*([%+%-%*%^%d]*%d)[\\/ ]*([%+%-%*%^%d]*%d)[, ]*" )
---- print( ipart, numer, denom )
-- print(numer, denom)
-- print( type( num ) )
if ipart and numer and denom then
ipart, numer, denom = tonumber(ipart), tonumber(numer), tonumber(denom)
-- print(" ", numer, denom)
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
-- print(" ---> ", numer, denom)
if denom < 0 then
numer = numer + ipart*(-denom)
return setmetatable( { -numer, -denom }, fraction_meta )
else
numer = numer + ipart*denom
return setmetatable( { numer, denom }, fraction_meta )
end
elseif numer and denom then
numer, denom = tonumber(numer), tonumber(denom)
-- print(" ", numer, denom)
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
-- print(" ---> ", numer, denom)
if denom < 0 then
return setmetatable( { -numer, -denom }, fraction_meta )
else
return setmetatable( { numer, denom }, fraction_meta )
end
elseif numer then
numer = tonumber(numer)
return setmetatable( { numer, 1 }, fraction_meta )
end
end
return nil
end
function fraction.tostring( x )
local numer, denom = x[1], x[2]
-- print(numer, denom)
---- print(x)
if denom == 1 then
return "" .. numer
else
return "(" .. numer .. "/" .. denom .. ")"
end
end
function fraction.toApart( x )
local numer, denom = x[1], x[2]
-- print(numer, denom)
if denom == 1 then
return "" .. numer
else
local q, r
q = math.floor(numer/denom)
r = math.fmod(numer, denom)
-- print( " q = " .. q .. ", r = " .. r )
if r < 0 then
q = q - 1
r = r + denom
end
-- print( " --> q = " .. q .. ", r = " .. r )
if q == 0 then
return "(" .. numer .. "/" .. denom .. ")"
else
return "(" .. q .. "+" .. r .. "/" .. denom .. ")"
end
end
end
function fraction.toDecimal( x )
local numer, denom = x[1], x[2]
return numer/denom
end
-- fraction.print( cx [, formatstr] )
-- print a fraction number
function fraction.print( ... )
print( fraction.tostring( ... ) )
end
-- fraction.abs( cx )
-- get the absolute value of a fraction number
function fraction.abs( x )
return fraction.new(x.numer, x.denom )
end
--// functions returning a new complex number
-- fraction.copy( x )
-- copy fraction number
function fraction.copy( x )
return setmetatable( { cx[1], cx[2] }, fraction_meta )
end
function fraction.simplify( x )
local numer = x[1]
local denom = x[2]
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
if denom < 0 then
x[1] = -numer
x[2] = -denom
else
x[1] = numer
x[2] = denom
end
end
function gcd( a, b )
local tmp
local q, r = math.abs(a), math.abs(b)
-- print( " q : " .. q .. ", r : " .. r )
tmp = math.fmod(q, r)
while tmp > 0 do
q = r
r = tmp
tmp = math.fmod(q, r)
-- print( " --> q : " .. q .. ", r : " .. r )
end
-- print( " r = " .. r )
return r
end
-- fraction.add( x1, x2 )
-- add two numbers; x1 + x2
function fraction.add( x1,x2 )
local numer = x1[1]*x2[2] + x1[2]*x2[1]
local denom = x1[2]*x2[2]
local d = gcd(math.abs(numer), math.abs(denom))
return setmetatable( { numer/d, denom/d }, fraction_meta )
end
-- fraction.sub( x1, x2 )
-- subtract two numbers; x1 - x2
function fraction.sub( x1, x2 )
local numer = x1[1]*x2[2] - x1[2]*x2[1]
local denom = x1[2]*x2[2]
local d = gcd(math.abs(numer), math.abs(denom))
return setmetatable( { numer/d, denom/d }, fraction_meta )
end
-- fraction.mul( x1, x2 )
-- multiply two numbers; x1 * x2
function fraction.mul( x1, x2 )
-- return setmetatable( { x1[1]*x2[1], x1[2]*x2[2] }, fraction_meta )
local numer = x1[1]*x2[1]
local denom = x1[2]*x2[2]
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
if denom < 0 then
return setmetatable( { -numer, -denom }, fraction_meta )
else
return setmetatable( { numer, denom }, fraction_meta )
end
end
-- fraction.div( x1, x2 )
-- divide two numbers; x1 / x2
function fraction.div( x1, x2 )
-- return setmetatable( { x1[1]*x2[2], x1[2]*x2[1] }, fraction_meta )
local numer = x1[1]*x2[2]
local denom = x1[2]*x2[1]
local d = gcd(numer, denom)
if d > 1 then
numer = numer / d
denom = denom / d
end
if denom < 0 then
return setmetatable( { -numer, -denom }, fraction_meta )
end
return setmetatable( { numer, denom }, fraction_meta )
end
-- fraction.pow( c, num )
-- get the power of a fraction number
function fraction.pow( x, num )
return setmetatable( { x[1]^num, x[2]^num }, fraction_meta )
end
-- function fraction.lt_event( x1, x2 )
-- print(" --- ", type(x1), type(x2))
-- return fraction_meta.__lt( x1, x2 )
-- end
--// metatable functions
fraction_meta.__add = function( x1, x2 )
local x1, x2 = fraction.to( x1 ), fraction.to( x2 )
return fraction.add( x1, x2 )
end
fraction_meta.__sub = function( x1, x2 )
local x1, x2 = fraction.to( x1 ), fraction.to( x2 )
return fraction.sub( x1, x2 )
end
fraction_meta.__mul = function( x1, x2 )
local x1, x2 = fraction.to( x1 ), fraction.to( x2 )
return fraction.mul( x1, x2 )
end
fraction_meta.__div = function( x1, x2 )
local x1, x2 = fraction.to( x1 ), fraction.to( x2 )
return fraction.div( x1, x2 )
end
fraction_meta.__pow = function( x, num )
local x = fraction.to( x )
return fraction.pow( x, num )
end
fraction_meta.__unm = function( x )
-- print("called UNM here!" )
return setmetatable( { -x[1], x[2] }, fraction_meta )
end
fraction_meta.__eq = function( x1, x2 )
-- print("called here!" )
return x1[1]*x2[2] - x1[2]*x2[1] == 0
end
fraction_meta.__lt = function( x1, x2 )
return x1[1]*x2[2] - x1[2]*x2[1] < 0
end
fraction_meta.__ltt = function( x1, x2 )
local x1, x2 = fraction.to( x1 ), fraction.to( x2 )
print(type(x1), type(x2))
print(type(x1) == "number", type(x2) == "number")
if type(x2) == "number" then
return x1[1] - x1[2]*x2 < 0
elseif type(x1) == "number" then
return x1*x2[2] - x2[1] < 0
end
return x1[1]*x2[2] - x1[2]*x2[1] < 0
end
fraction_meta.__gt = function( x1, x2 )
return x1[1]*x2[2] - x1[2]*x2[1] > 0
end
fraction_meta.__le = function( x1, x2 )
return x1[1]*x2[2] - x1[2]*x2[1] <= 0
end
fraction_meta.__ge = function( x1, x2 )
return x1[1]*x2[2] - x1[2]*x2[1] >= 0
end
fraction_meta.__tostring = function( x )
return tostring( fraction.tostring( x ) )
end
fraction_meta.__concat = function( x, x2 )
return tostring(x)..tostring(x2)
end
fraction_meta.__call = function( ... )
print( fraction.tostring( ... ) )
end
fraction_meta.__index = {}
for k,v in pairs( fraction ) do
fraction_meta.__index[k] = v
end
return fraction
** 위의 fraction 클래스를 테스트하는 Lua 예제
--// Filename: TestFraction-01.lua
--// Using the 'fraction' class given at http://scripting.tistory.com
--// Execute: lua TestFraction-01.lua
local fraction = require "fraction"
function printFraction(msg, a)
if type(msg) == "string" and #(msg) > 0 then
print( msg .. a )
else
print( a )
end
end
function fraction:eq_event (x1, x2)
print("... eq_event() called here!" )
if x1[1]*x2[2] - x1[2]*x2[1] == 0 then
return true
else
return false
end
end
local a, b, c, d
-- instantiate of matrices
a = fraction.new(6, 9)
printFraction( "a = ", a )
fraction.simplify( a )
printFraction( "Simplified, a = ", a )
b = fraction {120, 150}
printFraction( "b = ", b )
fraction.simplify( b )
printFraction( "Simplified, b = ", b )
-- c = fraction"2/5"
c = fraction"-2 / 5"
printFraction( "c = ", c )
printFraction( "-c = ", -c )
printFraction( "5 - c = ", 5 - c )
printFraction( "5 + c - 2 = ", 5 + c - 2 )
printFraction( "3*c = ", 3*c )
printFraction( "2/c = ", 2/c )
print( 3 - fraction"1/10" - 1 )
print( fraction"3" - fraction"1/10" + fraction"-1" )
print( fraction {-3, -1} - fraction {1, 10} + fraction {-1, 1} )
print( fraction"-5/-10" )
printFraction( "a^2 = ", a^2 )
printFraction( "1/a = ", 1/a )
printFraction( "1/a^2 = ", 1/a^2 )
printFraction( "a = ", a )
printFraction( "b = ", b )
printFraction( "b/a = ", b/a )
printFraction( "b/a^2 = ", b/a^2 )
print( "fraction.toApart(b/a^2) = " .. fraction.toApart(b/a^2) )
print( "fraction.toDecimal(b/a^2) = " .. fraction.toDecimal(b/a^2) )
printFraction( "-b/a^2 = ", -b/a^2 )
print( "fraction.toApart(-b/a^2) = " .. fraction.toApart(-b/a^2) )
print( "fraction.toDecimal(-b/a^2) = " .. fraction.toDecimal(-b/a^2) )
a = fraction.new(12, 6)
printFraction( "Changed, a = ", a )
printFraction( "a[1] = ", a[1] )
printFraction( "a[2] = ", a[2] )
print( "a == b ?", a == b )
print( "a ~= b ?", a ~= b )
print( "a == fraction\"2\" ?", a == fraction"2" )
print( "a ~= fraction\"2\" ?", a ~= fraction"2" )
print( "not (a == fraction\"2\") ?", not (a == fraction"2") )
print( "a < b ?", a < b )
print( "a < fraction\"2\" ?", a < fraction"2" )
print( "fraction\"2\" > a ?", fraction"2" > a )
print( "a > fraction\"2\" ?", a > fraction"2" )
print( "a > b ?", a > b )
print( "a <= b ?", a <= b )
print( "a >= b ?", a >= b )
print( "a <= fraction\"2\" ?", a <= fraction"2" )
print( "a >= fraction\"2\" ?", a >= fraction"2" )
print( "a <= fraction.to(2) ?", a <= fraction.to(2) )
print( "a >= fraction.to(2) ?", a >= fraction.to(2) )
print( "a <= fraction.to(-1) ?", a <= fraction.to(-1) )
print( "a >= fraction.to(-1) ?", a >= fraction.to(-1) )
printFraction( "fraction.parseApart { 1, 2, 3 } = ", fraction.parseApart { 1, 2, 3 } )
printFraction( "fraction.parseApart { -1, 2, 3 } = ", fraction.parseApart { -1, 2, 3 } )
printFraction( "fraction.parseApart\"1+2/3\" = ", fraction.parseApart { -1, -2, 3 } )
printFraction( "fraction.parseApart\"1+2/3\" = ", fraction.parseApart"1+2/3" )
printFraction( "fraction.parseApart\"1+2/3\" = ", fraction.parseApart"1+2/3" )
printFraction( "fraction.parseApart\"-1 2/3\" = ", fraction.parseApart"-1 2/3" )
printFraction( "fraction.parseApart\"-1 -2/3\" = ", fraction.parseApart"-1 -2/3" )
printFraction( "fraction.parseApart\"-1 + -2/3\" = ", fraction.parseApart"-1 + -2/3" )
printFraction( "fraction.parseApart\"-1 + 2/3\" = ", fraction.parseApart"-1 + 2/3" )
printFraction( "fraction.parseApart\"-1 + +2/3\" = ", fraction.parseApart"-1 + +2/3" )
printFraction( "fraction.parseApart\"-1 +2/3\" = ", fraction.parseApart"-1 +2/3" )
--[[
Execute Result:
a = (6/9)
Simplified, a = (2/3)
b = (4/5)
Simplified, b = (4/5)
c = (-2/5)
-c = (2/5)
5 - c = (27/5)
5 + c - 2 = (13/5)
3*c = (-6/5)
2/c = -5
(19/10)
(19/10)
(19/10)
(1/2)
a^2 = (4/9)
1/a = (3/2)
1/a^2 = (9/4)
a = (2/3)
b = (4/5)
b/a = (6/5)
b/a^2 = (9/5)
fraction.toApart(b/a^2) = (1+4/5)
fraction.toDecimal(b/a^2) = 1.8
-b/a^2 = (-9/5)
fraction.toApart(-b/a^2) = (-3+1/5)
fraction.toDecimal(-b/a^2) = -1.8
Changed, a = (12/6)
a[1] = 12
a[2] = 6
a == b ? false
a ~= b ? true
a == fraction"2" ? true
a ~= fraction"2" ? false
not (a == fraction"2") ? false
a < b ? false
a < fraction"2" ? false
fraction"2" > a ? false
a > fraction"2" ? false
a > b ? true
a <= b ? false
a >= b ? true
a <= fraction"2" ? true
a >= fraction"2" ? true
a <= fraction.to(2) ? true
a >= fraction.to(2) ? true
a <= fraction.to(-1) ? false
a >= fraction.to(-1) ? true
fraction.parseApart { 1, 2, 3 } = (5/3)
fraction.parseApart { -1, 2, 3 } = (-1/3)
fraction.parseApart"1+2/3" = (-5/3)
fraction.parseApart"1+2/3" = (5/3)
fraction.parseApart"1+2/3" = (5/3)
fraction.parseApart"-1 2/3" = (-1/3)
fraction.parseApart"-1 -2/3" = (-5/3)
fraction.parseApart"-1 + -2/3" = (-5/3)
fraction.parseApart"-1 + 2/3" = (-1/3)
fraction.parseApart"-1 + +2/3" = (-1/3)
fraction.parseApart"-1 +2/3" = (-1/3)
--]]
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