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 * Copyright (c) 2013, SRI International
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 * Licensed under the The BSD 3-Clause License;
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package com.sri.ai.grinder.sgdpllt.group;

import java.util.List;

import com.google.common.annotations.Beta;
import com.sri.ai.expresso.api.Expression;
import com.sri.ai.grinder.sgdpllt.api.Context;

/**
 * Object representing an associative commutative semi-ring.
 * 
 * @author braz
 *
 */
@Beta
public interface AssociativeCommutativeSemiRing extends AssociativeCommutativeGroup {

	/** Returns the functor of the multiplicative operation. */
	String multiplicativeFunctor();
	
	/** The multiplicative operation identity element. */
	Expression multiplicativeIdentityElement();

	/** 
	 * The multiplicative operation identity element.
	 * This reason this is not a test like {@link AssociativeCommutativeGroup#isAdditiveAbsorbingElement}
	 * is that semi-rings are required to have a multiplicative absorbing element,
	 * but not required to have an additive one.
	 */
	Expression multiplicativeAbsorbingElement();

	/**
	 * Given an expression, returns its arguments if it is an application of the multiplicative operation,
	 * or the expression itself otherwise.
	 * This is useful when the multiplicative operator is implicit when applied to a single argument.
	 */
	List getFactors(Expression expression);
	
	/**
	 * Performs the semi-rings's multiplicative operation on a function application of the multiplicative operator.
	 */
	Expression multiply(Expression multiplication, Context context);

	/**
	 * Returns the n-th root for an expression, if an exact value exists, or null otherwise. 
	 * @param n
	 * @param expression
	 * @return
	 */
	Expression getNthRoot(int n, Expression expression);

	/**
	 * The result of multiplying a value to itself n times, where both value and n may be symbolic expressions.
	 */
	Expression multiplyNTimes(Expression value, Expression n, Context context);
}