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package org.apache.commons.math3;

Interface representing a field.

Classes implementing this interface will often be singletons.

Type parameters:
<T> – the type of the field elements
See Also:
FieldElement
Since:
2.0/**
 * Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
 * <p>
 * Classes implementing this interface will often be singletons.
 * </p>
 * @param <T> the type of the field elements
 * @see FieldElement
 * @since 2.0
 */
public interface Field<T> {

    
Get the additive identity of the field.

The additive identity is the element e0 of the field such that
for all elements a of the field, the equalities a + e0 =
e0 + a = a hold.

Returns:
additive identity of the field/** Get the additive identity of the field.
     * <p>
     * The additive identity is the element e<sub>0</sub> of the field such that
     * for all elements a of the field, the equalities a + e<sub>0</sub> =
     * e<sub>0</sub> + a = a hold.
     * </p>
     * @return additive identity of the field
     */
    T getZero();

    
Get the multiplicative identity of the field.

The multiplicative identity is the element e1 of the field such that
for all elements a of the field, the equalities a × e1 =
e1 × a = a hold.

Returns:
multiplicative identity of the field/** Get the multiplicative identity of the field.
     * <p>
     * The multiplicative identity is the element e<sub>1</sub> of the field such that
     * for all elements a of the field, the equalities a &times; e<sub>1</sub> =
     * e<sub>1</sub> &times; a = a hold.
     * </p>
     * @return multiplicative identity of the field
     */
    T getOne();

    
Returns the runtime class of the FieldElement.
Returns:
The Class object that represents the runtime class of this object./**
     * Returns the runtime class of the FieldElement.
     *
     * @return The {@code Class} object that represents the runtime
     *         class of this object.
     */
    Class<? extends FieldElement<T>> getRuntimeClass();

}