Field.cs

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//
//      http://www.apache.org/licenses/LICENSE-2.0
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using System;

namespace Math3
{
   /// <summary>
   /// Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
   /// <para>
   /// Classes implementing this interface will often be singletons.
   /// </para>
   /// </summary>
   /// <remarks>See <see cref="FieldElement"/></remarks>
   /// <typeparam name="T">the type of the field elements</typeparam>
    public interface Field<T>
    {
        /// <summary>
        /// Get the additive identity of the field.
        /// <para>
        /// The additive identity is the element e_0 of the field such that
        /// for all elements a of the field, the equalities a + e<sub>0</sub> =
        /// e_0 + a = a hold.
        /// </para>
        /// </summary>
        /// <returns>additive identity of the field</returns>
        T getZero();

        /// <summary>
        /// Get the multiplicative identity of the field.
        /// <para>
        /// 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_1 =
        /// e_1 &times; a = a hold.
        /// </para>
        /// </summary>
        /// <returns>multiplicative identity of the field</returns>
        T getOne();

        /// <summary>
        /// Returns the runtime type of the FieldElement.
        /// </summary>
        /// <returns>The <c>Type</c> object that represents the runtime
        /// Type of this object.</returns>
        Type getRuntimeClass();
    }
}