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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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 * This file is part of tensorics.
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 * Copyright (c) 2008-2011, CERN. All rights reserved.
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 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
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// @formatter:on

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

import org.tensorics.core.math.structures.grouplike.AbelianGroup;

/**
 * Represents the algebraic structure 'field'. It means that it represents a set of elements together with two binary
 * operations (+, *) with the following properties:
 * 
 * both, + and * are associative: a + (b + c) = (a + b) + c; a * (b * c) = (a * b) * c.
 * 
both, + and * have an identity element (Called '0' for +, '1' for *): a + 0 = a; a * 1 = a.
 * 
both, + and * have an inverse element (Called '-a' for +, '1/a' for *): a + (-a) = 0; a * 1/a = 1.
 * 
both, + and * are commutative: a + b = b + a; a * b = b * a.
 * 
* is distributive over +: a * (b + c) = a * b + a * c.
 * 
 * In other words, both addition and multiplication (without 0) are abelian groups.
 * 
 * @author kfuchsbe
 * @param  the type of elements of the field.
 * @see http://en.wikipedia.org/wiki/Field_(mathematics)
 */
public interface Field extends Ring {

    @Override
    AbelianGroup multiplicationStructure();

}