Java Training Course/JT05 - Revision history

imported>Gfis: JT06 is Ratio

2017-09-26T19:25:07Z

JT06 is Ratio

← Older revision		Revision as of 19:25, 26 September 2017
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	===Prime Number Factorization===		===Prime Number Factorization===
	The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula which relates the LCM to the ''greatest common divisor'' (GCD):		The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula which relates the LCM to the ''greatest common divisor'' (GCD):
	lcm(a,b) = abs(a*b) / gcd(a,b)		:lcm(a,b) = abs(a*b) / gcd(a,b)
	===Euclid's Algorithm for the GCD===		===Euclid's Algorithm for the GCD===
	For the computation of the GCD there was a very simple, famous, fast and important algorithm invented 2300 years ago by the greek mathematician Euclid.		For the computation of the GCD there was a very simple, famous, fast and important algorithm invented 2300 years ago by the greek mathematician Euclid.
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	java GreatestCommonDivisor 4096 256		java GreatestCommonDivisor 4096 256
	[[Java Training Course/JT04\|< Previous: JT04]] Integer Arithmetic<br />		[[Java Training Course/JT04\|< Previous: JT04]] Integer Arithmetic<br />
	[[Java Training Course/JT06\|> Next: JT06]] ~~Skeleton of~~ Class ''~~Rational~~''		[[Java Training Course/JT06\|> Next: JT06]] Preliminary Class ''Ratio''

imported>Gfis at 13:07, 24 September 2017

2017-09-24T13:07:39Z

← Older revision		Revision as of 13:07, 24 September 2017
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	==Greatest Common Divisor==		==Control Structures: The Greatest Common Divisor==
	===Motivation===		===Motivation===
	The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK.		The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK.

imported>Gfis: typo

2017-09-24T10:15:53Z

typo

← Older revision		Revision as of 10:15, 24 September 2017
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	For the computation of the GCD there was a very simple, famous, fast and important algorithm invented 2300 years ago by the greek mathematician Euclid.		For the computation of the GCD there was a very simple, famous, fast and important algorithm invented 2300 years ago by the greek mathematician Euclid.
	* Main task:		* Main task:
	** Read about the [[https://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm].		** Read about the [https://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm].
	** Try to develop the program loop which exchanges the divisor and the rest.		** Try to develop the program loop which exchanges the divisor and the rest.
	** Google several different implementations in Java, and compare them.		** Google several different implementations in Java, and compare them.

imported>Gfis at 10:14, 24 September 2017

2017-09-24T10:14:55Z

← Older revision		Revision as of 10:14, 24 September 2017
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	==Motivation==		==Greatest Common Divisor==
			===Motivation===
	The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK.		The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK.

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	The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula which relates the LCM to the ''greatest common divisor'' (GCD):		The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula which relates the LCM to the ''greatest common divisor'' (GCD):
	lcm(a,b) = abs(a*b) / gcd(a,b)		lcm(a,b) = abs(a*b) / gcd(a,b)
	===~~Greatest Common Divisor (~~GCD)===		===Euclid's Algorithm for the GCD===
	For the GCD, there ~~exists~~ a very simple, famous and important ~~[https://en.wikipedia.org/wiki/Euclidean_algorithm~~ algorithm] invented 2300 years ago by the greek mathematician Euclid.		For the computation of the GCD there was a very simple, famous, fast and important algorithm invented 2300 years ago by the greek mathematician Euclid.
	* Main task:		* Main task:
	** Read about ~~Euclid's~~ algorithm.		** Read about the [[https://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm].
	** Try to develop the program loop which exchanges the divisor and the rest.		** Try to develop the program loop which exchanges the divisor and the rest.
	** Google several different ~~implementation~~ in Java, and compare them.		** Google several different implementations in Java, and compare them.
	** Be careful to obey the conventions for zero and negative numbers.		** Be careful to obey the conventions for zero and negative numbers.
	** Incorporate your solution into a variation of <code>DupInt</code> ~~called~~ <code>GreatestCommonDivisor.java</code>		** Incorporate your solution into a variation of class <code>DupInt</code> in a file <code>GreatestCommonDivisor.java</code>
	** Compile and run it as follows:		** Compile and run that class as follows:
	java GreatestCommonDivisor 0 0		java GreatestCommonDivisor 0 0
	java GreatestCommonDivisor 0 1		java GreatestCommonDivisor 0 1
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	java GreatestCommonDivisor 81 24		java GreatestCommonDivisor 81 24
	java GreatestCommonDivisor 4096 256		java GreatestCommonDivisor 4096 256
			[[Java Training Course/JT04\|< Previous: JT04]] Integer Arithmetic<br />
			[[Java Training Course/JT06\|> Next: JT06]] Skeleton of Class ''Rational''

imported>Gfis: wording

2017-09-23T20:00:34Z

wording

← Older revision		Revision as of 20:00, 23 September 2017
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	* Subtask 2: Explain how you would compute the LCM.		* Subtask 2: Explain how you would compute the LCM.
	===Prime Number Factorization===		===Prime Number Factorization===
	The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula:		The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula which relates the LCM to the ''greatest common divisor'' (GCD):
	lcm(a,b) = abs(a*b) / gcd(a,b)		lcm(a,b) = abs(a*b) / gcd(a,b)
	===Greatest Common Divisor (GCD)===		===Greatest Common Divisor (GCD)===

imported>Gfis: new

2017-09-22T20:25:18Z

new

@@ Line 13: / Line 13: @@
 * Subtask 1: Explain how the 4 arithmetic operations for fractions were done in school.
+===Least Common Multiple (LCM)===
-===Least Common Multiple===
+Multiplication and division of rationals is very simple. But for addition and subtraction, the denominators must first be aligned to their so-called [https://en.wikipedia.org/wiki/Least_common_multiple least common multiple] (LCM).
 * Subtask 2: Explain how you would compute the LCM.
 ===Prime Number Factorization===
-===Greatest Common Divisor===
+The LCM may very easily be determined from the prime number factorization of the 2 denominators, but such a factorization is rather complicated and inefficient for big numbers. There is a simple formula:

imported>Gfis: Created page with "==Motivation== The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK. This class will be named '''Rational 2017-09-22T19:55:51Z Created page with "==Motivation== The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK. This class will be named '''<code>Rational</co..." New page ==Motivation== The goal of the next few sessions is the development of a real, useful Java class that is missing from the JDK. This class will be named '''<code>Rational</code>'''. It will represent a fractional number consisting of: * an integer ''numerator'' displayed above a line (or before a slash), and * a non-zero integer ''denominator'', displayed below that line (or after the slash), * methods for the addition, subtraction, multiplication and division of 2 such <code>Rational</code>s, * some additional, ''helper'' methods which are used internally in the class. If you are not familiar with such rational numbers, you may read the [https://en.wikipedia.org/wiki/Fraction_(mathematics) Wikipedia article] on fractions. A citation from there: : Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10−2 respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implicit denominator of one: 7 equals 7/1. We make a little distinction between fractions (in general; sometimes imprecise 0.33333...) and rationals (with the representation by a numerator and a denominator; 1/3 is always exact). * Subtask 1: Explain how the 4 arithmetic operations for fractions were done in school. ===Least Common Multiple=== Multiplication and division of rationals is very simple. But for addition and subtraction, the denominators must first be aligned to their so-called least common multiple (LCM). * Subtask 2: Explain how you would compute the LCM. ===Prime Number Factorization=== ===Greatest Common Divisor===