/// <summary> /// Returns true iff <paramref name="x"/> is strictly not equal to <paramref name="y"/> in the total order <paramref name="order"/>. /// </summary> /// <typeparam name="T">The type of the elements in the relation.</typeparam> /// <param name="order">The total order.</param> /// <param name="x">The first element to compare.</param> /// <param name="y">The second element to compare.</param> public static bool Neq <T>(this ITotalOrder <T> order, T x, T y) => order.Compare(x, y) != 0;
/// <summary> /// Returns true iff <paramref name="x"/> is strictly greater than <paramref name="y"/> in the total order <paramref name="order"/>. /// </summary> /// <typeparam name="T">The type of the elements in the relation.</typeparam> /// <param name="order">The total order.</param> /// <param name="x">The first element to compare.</param> /// <param name="y">The second element to compare.</param> public static bool Ge <T>(this ITotalOrder <T> order, T x, T y) => order.Compare(x, y) > 0;
/// <summary>
/// Returns the sign (-1 for negative values, 0 for 0, 1 for positive values) of an element <paramref name="x"/>.
/// </summary>
/// <typeparam name="TStructure">The type of the algebraic structure to use.</typeparam>
/// <typeparam name="T">The type of the elements.</typeparam>
/// <param name="st">The algebraic structure to use</param>
/// <param name="order">The total order.</param>
/// <param name="x">The element whose sign to get.</param>
public static int Signum <TStructure, T>(this TStructure st, ITotalOrder <T> order, T x)
where TStructure : INeutralElement <T>
=> order.Compare(x, st.Neutral);