// FILE. . . . . d:/hak/hlt/src/hlt/math/matrix/sources/StandardAlgebra.java
// EDIT BY . . . Hassan Ait-Kaci
// ON MACHINE. . Hak-Laptop
// STARTED ON. . Tue Dec 3 17:40:58 2019
package hlt.math.matrix;
/**
* package hlt.math.matrix
* documentation listing
*/
/**
* This is a concrete subclass of NumberAlgebra redefining its
* operations as those of standard arithmetic to be final methods:
*
* zero() ≝ 0.0
* one() ≝ 1.0
* sum(x,y) ≝ x+y
* product(x,y) ≝ \*
* negation(x) ≝ -x
* difference(x,y) ≝ x-y
*
*
* @see NumberAlgebra
* @see Matrix
*
* @version Last modified on Fri Dec 13 10:01:27 2019 by hak
* @author Hassan Aït-Kaci
* @copyy © by the author
*/
public class StandardAlgebra extends NumberAlgebra
{
/**
* Return the zero of this algebra as 0.0. It
* should always verify sum(x,zero()) =
* sum(zero(),x) = x, for any double
* x.
*/
public final double zero ()
{
return 0.0;
}
/**
* Return the one of this algebra as 1.0. It should
* always verify product(x,one()) = product(one(),x)
* = x, for any double
*/
public final double one ()
{
return 1.0;
}
/**
* Return the sum of the arguments as +.
*/
public final double sum (double x, double y)
{
return x + y;
}
/**
* Return the product of the arguments as ×.
*/
public final double product (double x, double y)
{
return x * y;
}
/**
* Return the difference of the arguments as binary -.
*/
public final double difference (double x, double y)
{
return x - y;
}
/**
* Return the negation of the argument as unary -.
*/
public final double negation (double x)
{
return -x;
}
/**
* Define a String form for this StandardAlgebra. It is
* final so it cannot be redefined in any subclass.
*/
public final String toString ()
{
return "Standard Algebra";
}
}