Added the Mathematics tools as a prototype (#1162)

app/MindWork AI Studio/Tools/Mathematics/MathVariables.cs

@@ -0,0 +1,32 @@
+using AngouriMath;
+
+namespace AIStudio.Tools.Mathematics;
+
+/// <summary>
+/// The variables of an expression, as the Mathematics tools count them.
+/// </summary>
+/// <remarks>
+/// AngouriMath counts the constants pi and e among the free variables, so ln(0) has the free
+/// variable e, the base of its logarithm. Asked for the variables of an expression, the tools mean
+/// those which have no value, see AngouriMathBehaviorTests.
+/// </remarks>
+public static class MathVariables
+{
+    /// <summary>
+    /// The free variables of an expression without the constants, in the order of their names.
+    /// </summary>
+    /// <param name="expression">The expression.</param>
+    /// <returns>Each variable once.</returns>
+    public static IReadOnlyList<Entity.Variable> FreeIn(Entity expression) => expression.FreeVariables
+        .Where(variable => variable is not Entity.Constant)
+        .Distinct()
+        .OrderBy(variable => variable.Name, StringComparer.Ordinal)
+        .ToList();
+
+    /// <summary>
+    /// Whether an expression has a free variable other than the constants.
+    /// </summary>
+    /// <param name="expression">The expression.</param>
+    /// <returns>True when a variable without a value occurs freely.</returns>
+    public static bool HasAny(Entity expression) => expression.FreeVariables.Any(variable => variable is not Entity.Constant);
+}