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Tensorics is a java framework which uses a tensor as a central object. A tensor represents a set of values placed in an N-dimensional space. Wherever you are tempted to use maps of maps, a tensor might be a good choice ;-) Tensorics provides methods to create, transform and performing calculations with those tensors.

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package org.tensorics.core.math.structures.ringlike;

import org.tensorics.core.math.structures.grouplike.CommutativeMonoid;
import org.tensorics.core.math.structures.grouplike.Monoid;

/**
 * The algebraic structure of a semiring, which has the following properties:
 * 
 * R is the underlying set; a, b, c are elements of R.
 * 

 * (R, +) is a commutative monoid with identity element 0:
 * 
 * (a + b) + c = a + (b + c)
 * 

 * 0 + a = a + 0 = a
 * 

 * a + b = b + a
 * 

 * 
(R, *) is a monoid with identity element 1:
 * 
 * (a*b)*c = a*(b*c)
 * 

 * 1*a = a*1 = a
 * 

 * 
Multiplication left and right distributes over addition:
 * 
 * a*(b + c) = (a*b) + (a*c) = (a + b)*c = (a*c) + (b*c)
 * 
Multiplication by 0 annihilates R:
 * 
 * 
 * 
 * @author kfuchsbe
 * @param  the type of the elements of the structure
 */
public interface Semiring extends RinglikeStructure {

    @Override
    CommutativeMonoid additionStructure();

    @Override
    Monoid multiplicationStructure();

}