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diff --git a/src/main/java/org/unitConverter/math/ObjectProduct.java b/src/main/java/org/unitConverter/math/ObjectProduct.java
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+/**
+ * Copyright (C) 2018 Adrien Hopkins
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Affero General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU Affero General Public License for more details.
+ *
+ * You should have received a copy of the GNU Affero General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+package org.unitConverter.math;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.HashSet;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Set;
+import java.util.function.Function;
+
+/**
+ * An immutable product of multiple objects of a type, such as base units. The objects can be multiplied and
+ * exponentiated.
+ * 
+ * @author Adrien Hopkins
+ * @since 2019-10-16
+ */
+public final class ObjectProduct<T> {
+	/**
+	 * Returns an empty ObjectProduct of a certain type
+	 * 
+	 * @param <T>
+	 *            type of objects that can be multiplied
+	 * @return empty product
+	 * @since 2019-10-16
+	 */
+	public static final <T> ObjectProduct<T> empty() {
+		return new ObjectProduct<>(new HashMap<>());
+	}
+
+	/**
+	 * Gets an {@code ObjectProduct} from an object-to-integer mapping
+	 * 
+	 * @param <T>
+	 *            type of object in product
+	 * @param map
+	 *            map mapping objects to exponents
+	 * @return object product
+	 * @since 2019-10-16
+	 */
+	public static final <T> ObjectProduct<T> fromExponentMapping(final Map<T, Integer> map) {
+		return new ObjectProduct<>(new HashMap<>(map));
+	}
+
+	/**
+	 * Gets an ObjectProduct that has one of the inputted argument, and nothing else.
+	 * 
+	 * @param object
+	 *            object that will be in the product
+	 * @return product
+	 * @since 2019-10-16
+	 * @throws NullPointerException
+	 *             if object is null
+	 */
+	public static final <T> ObjectProduct<T> oneOf(final T object) {
+		Objects.requireNonNull(object, "object must not be null.");
+		final Map<T, Integer> map = new HashMap<>();
+		map.put(object, 1);
+		return new ObjectProduct<>(map);
+	}
+
+	/**
+	 * The objects that make up the product, mapped to their exponents. This map treats zero as null, and is immutable.
+	 * 
+	 * @since 2019-10-16
+	 */
+	final Map<T, Integer> exponents;
+
+	/**
+	 * Creates the {@code ObjectProduct}.
+	 * 
+	 * @param exponents
+	 *            objects that make up this product
+	 * @since 2019-10-16
+	 */
+	private ObjectProduct(final Map<T, Integer> exponents) {
+		this.exponents = Collections.unmodifiableMap(ConditionalExistenceCollections.conditionalExistenceMap(exponents,
+				e -> !Integer.valueOf(0).equals(e.getValue())));
+	}
+
+	/**
+	 * Calculates the quotient of two products
+	 *
+	 * @param other
+	 *            other product
+	 * @return quotient of two products
+	 * @since 2019-10-16
+	 * @throws NullPointerException
+	 *             if other is null
+	 */
+	public ObjectProduct<T> dividedBy(final ObjectProduct<T> other) {
+		Objects.requireNonNull(other, "other must not be null.");
+		// get a list of all objects in both sets
+		final Set<T> objects = new HashSet<>();
+		objects.addAll(this.getBaseSet());
+		objects.addAll(other.getBaseSet());
+
+		// get a list of all exponents
+		final Map<T, Integer> map = new HashMap<>(objects.size());
+		for (final T key : objects) {
+			map.put(key, this.getExponent(key) - other.getExponent(key));
+		}
+
+		// create the product
+		return new ObjectProduct<>(map);
+	}
+
+	// this method relies on the use of ZeroIsNullMap
+	@Override
+	public boolean equals(final Object obj) {
+		if (this == obj)
+			return true;
+		if (!(obj instanceof ObjectProduct))
+			return false;
+		final ObjectProduct<?> other = (ObjectProduct<?>) obj;
+		return Objects.equals(this.exponents, other.exponents);
+	}
+
+	/**
+	 * @return immutable map mapping objects to exponents
+	 * @since 2019-10-16
+	 */
+	public Map<T, Integer> exponentMap() {
+		return this.exponents;
+	}
+
+	/**
+	 * @return a set of all of the base objects with non-zero exponents that make up this dimension.
+	 * @since 2018-12-12
+	 * @since v0.1.0
+	 */
+	public final Set<T> getBaseSet() {
+		final Set<T> dimensions = new HashSet<>();
+
+		// add all dimensions with a nonzero exponent - zero exponents shouldn't be there in the first place
+		for (final T dimension : this.exponents.keySet()) {
+			if (!this.exponents.get(dimension).equals(0)) {
+				dimensions.add(dimension);
+			}
+		}
+
+		return dimensions;
+	}
+
+	/**
+	 * Gets the exponent for a specific dimension.
+	 * 
+	 * @param dimension
+	 *            dimension to check
+	 * @return exponent for that dimension
+	 * @since 2018-12-12
+	 * @since v0.1.0
+	 */
+	public int getExponent(final T dimension) {
+		return this.exponents.getOrDefault(dimension, 0);
+	}
+
+	@Override
+	public int hashCode() {
+		return Objects.hash(this.exponents);
+	}
+
+	/**
+	 * @return true if this product is a single object, i.e. it has one exponent of one and no other nonzero exponents
+	 * @since 2019-10-16
+	 */
+	public boolean isSingleObject() {
+		int oneCount = 0;
+		boolean twoOrMore = false; // has exponents of 2 or more
+		for (final T b : this.getBaseSet()) {
+			if (this.getExponent(b) == 1) {
+				oneCount++;
+			} else if (this.getExponent(b) != 0) {
+				twoOrMore = true;
+			}
+		}
+		return oneCount == 1 && !twoOrMore;
+	}
+
+	/**
+	 * Multiplies this product by another
+	 *
+	 * @param other
+	 *            other product
+	 * @return product of two products
+	 * @since 2019-10-16
+	 * @throws NullPointerException
+	 *             if other is null
+	 */
+	public ObjectProduct<T> times(final ObjectProduct<T> other) {
+		Objects.requireNonNull(other, "other must not be null.");
+		// get a list of all objects in both sets
+		final Set<T> objects = new HashSet<>();
+		objects.addAll(this.getBaseSet());
+		objects.addAll(other.getBaseSet());
+
+		// get a list of all exponents
+		final Map<T, Integer> map = new HashMap<>(objects.size());
+		for (final T key : objects) {
+			map.put(key, this.getExponent(key) + other.getExponent(key));
+		}
+
+		// create the product
+		return new ObjectProduct<>(map);
+	}
+
+	/**
+	 * Returns this product, but to an exponent
+	 * 
+	 * @param exponent
+	 *            exponent
+	 * @return result of exponentiation
+	 * @since 2019-10-16
+	 */
+	public ObjectProduct<T> toExponent(final int exponent) {
+		final Map<T, Integer> map = new HashMap<>(this.exponents);
+		for (final T key : this.exponents.keySet()) {
+			map.put(key, this.getExponent(key) * exponent);
+		}
+		return new ObjectProduct<>(map);
+	}
+
+	/**
+	 * Converts this product to a string using the objects' {@link Object#toString()} method. If objects have a long
+	 * toString representation, it is recommended to use {@link #toString(Function)} instead to shorten the returned
+	 * string.
+	 * 
+	 * <p>
+	 * {@inheritDoc}
+	 */
+	@Override
+	public String toString() {
+		return this.toString(Object::toString);
+	}
+
+	/**
+	 * Converts this product to a string. The objects that make up this product are represented by
+	 * {@code objectToString}
+	 * 
+	 * @param objectToString
+	 *            function to convert objects to strings
+	 * @return string representation of product
+	 * @since 2019-10-16
+	 */
+	public String toString(final Function<T, String> objectToString) {
+		final List<String> positiveStringComponents = new ArrayList<>();
+		final List<String> negativeStringComponents = new ArrayList<>();
+
+		// for each base object that makes up this object, add it and its exponent
+		for (final T object : this.getBaseSet()) {
+			final int exponent = this.exponents.get(object);
+			if (exponent > 0) {
+				positiveStringComponents.add(String.format("%s^%d", objectToString.apply(object), exponent));
+			} else if (exponent < 0) {
+				negativeStringComponents.add(String.format("%s^%d", objectToString.apply(object), -exponent));
+			}
+		}
+
+		final String positiveString = positiveStringComponents.isEmpty() ? "1"
+				: String.join(" * ", positiveStringComponents);
+		final String negativeString = negativeStringComponents.isEmpty() ? ""
+				: " / " + String.join(" * ", negativeStringComponents);
+
+		return positiveString + negativeString;
+	}
+}