/*
 * Zorbage: an algebraic data hierarchy for use in numeric processing.
 *
 * Copyright (C) 2016-2018 Barry DeZonia
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 
 * 1. Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */
package nom.bdezonia.zorbage.algorithm;

import nom.bdezonia.zorbage.type.algebra.AbsoluteValue;
import nom.bdezonia.zorbage.type.algebra.Group;
import nom.bdezonia.zorbage.type.algebra.ModularDivision;
import nom.bdezonia.zorbage.type.algebra.Multiplication;
import nom.bdezonia.zorbage.type.algebra.Ordered;

/**
 * Least Common Multiple algorithm
 * 
 * @author Barry DeZonia
 *
 */
public class Lcm {
	
	/**
	 * Do not instantiate. Private constructor for utility class.
	 */
	private Lcm() {}
	
	/**
	 * Sets the result to the least common multiple of a and b. Result is always nonnegative.
	 * 
	 * @param group
	 * @param a
	 * @param b
	 * @param result
	 */
	public static <T extends Group<T,U> & AbsoluteValue<U> & ModularDivision<U> & Multiplication<U> & Ordered<U>, U>
		void compute(T group, U a, U b, U result)
	{
		U n = group.construct();
		U d = group.construct();
		group.multiply(a, b, n); // TODO: overflow prone?
		group.abs(n, n);
		Gcd.compute(group, a, b, d);
		group.div(n, d, result);
	}

}

@@ -2256,17 +2256,19 @@
 %0A%09%7B%0A%09%09U 
-n
+gcd
  = group
@@ -2285,17 +2285,18 @@
 ();%0A%09%09U 
-d
+a1
  = group
@@ -2315,105 +2315,190 @@
 ;%0A%09%09
-group.multiply(a, b, n); // TODO: overflow prone?%0A%09%09group.abs(n, n);%0A%09%09Gcd.compute(group, a
+U b1 = group.construct();%0A%09%09Gcd.compute(group, a, b, gcd);%0A%09%09group.div(a, gcd, a1);%0A%09%09group.div(b, gcd, b1);%0A%09%09group.abs(a1, a1);%0A%09%09group.abs(b1, b1);%0A%09%09group.multiply(a1
 , b
+1
 , 
-d
+result
 );%0A%09
@@ -2508,15 +2508,27 @@
 oup.
-div(n, 
+multiply(result, gc
 d, r

Make Lcm algorithm less susceptible to overflow