public void TestModularRing()
{
ModularRing R = new ModularRing(12);
// Ensure addution and multiplication work correctly
for (int i = 0; i < R.Modulus; i++)
{
Assert.AreEqual(R.Add(i, R.AdditiveStructure.Inverse(i)), R.AdditiveIdentity);
Assert.AreEqual(R.Add(i, R.AdditiveIdentity), i);
// While modular rings may have multiplicative inverses, it is only the case if the modulus is prime
// We can't ask for a ring to have this -> included in Field interface
Assert.AreEqual(R.Multiply(i, R.MultiplicativeIdentity), i);
}
}
public void TestModularGroup()
{
// G = Z10
ModularGroup G = new ModularGroup(10);
// Make sure every element has an inverse, and is unchanged by the identity under the operation
for (int i = 0; i < G.Modulus; i++)
{
Assert.AreEqual(G.Identity, G.Operation(i, G.Inverse(i)));
Assert.AreEqual(G.Operation(G.Identity, i), i);
}
ModularMonoid M = G;
ModularRing R = G;
// Ensure casts are working properly
Assert.AreEqual(M, (ModularMonoid)R);
Assert.AreEqual(M, (ModularMonoid)G);
Assert.AreEqual(R, (ModularRing)G);
Assert.AreEqual(R, (ModularRing)M);
Assert.AreEqual(G, (ModularGroup)R);
Assert.AreEqual(G, (ModularGroup)M);
}
