rationals.algebra

Interface SemiRing

All Known Implementing Classes:

BinaryExpr, Letter, Matrix, Plus, Product, RationalExpr

public interface SemiRing

An interface implemented by objects that can be coefficients of a Matrix.

A semi-ring is a structure (R,+,*,0,1) such that:

1. (R,+,0) is a commutative monoid
2. (R,*,1) is a monoid
3. x*(y+z) = x*y + x*z and (y+z)*x = y*x + z*x : multiplication is distributive with respect to addition
4. x*0 = 0*x = 0: 0 is an absorbing element for *

Version:

$Id: SemiRing.java 2 2006-08-24 14:41:48Z oqube $

Author:

nono

See Also:

Matrix

Method Summary

Modifier and Type	Method and Description
SemiRing	mult(SemiRing s2) Multiplication of semiring element with another element.
SemiRing	one() Neutral element for multiplication.
SemiRing	plus(SemiRing s2) Addition of a Semi-ring element with another element.
SemiRing	zero() Neutral element for addition.

Method Detail

plus

SemiRing plus(SemiRing s2)

Addition of a Semi-ring element with another element.

Parameters:

s2 - s2

Returns:

addition

mult

SemiRing mult(SemiRing s2)

Multiplication of semiring element with another element.

Parameters:

s2 - s2

Returns:

multiplication

one

SemiRing one()

Neutral element for multiplication.

Returns:

one

zero

SemiRing zero()

Neutral element for addition.

Returns:

zero