public static void CheckFieldInverses <ElementType>(
IAlgebraFieldFinite <ElementType> field)
{
FiniteFieldElement <ElementType>[] elements = field.GetElements();
// check + inverse
for (int index_0 = 1; index_0 < elements.Length; index_0++)
{
for (int index_1 = 1; index_1 < elements.Length; index_1++)
{
Assert.AreEqual(elements[index_0], (elements[index_0] + elements[index_1]) - elements[index_1], elements[index_0] + " +- " + elements[index_1] + " should yield " + elements[index_0] + " but yielded " + ((elements[index_0] + elements[index_1]) - elements[index_1]));
Assert.AreEqual(elements[index_0], (elements[index_0] - elements[index_1]) + elements[index_1], elements[index_0] + " -+ " + elements[index_1] + " should yield " + elements[index_0] + " but yielded " + ((elements[index_0] - elements[index_1]) + elements[index_1]));
}
}
// check * inverse
for (int index_0 = 2; index_0 < elements.Length; index_0++)
{
for (int index_1 = 2; index_1 < elements.Length; index_1++)
{
Assert.AreEqual(elements[index_0], (elements[index_0] * elements[index_1]) / elements[index_1]);
Assert.AreEqual(elements[index_0], (elements[index_0] / elements[index_1]) * elements[index_1]);
}
}
}
public static string [,] GetDivisionTable <ElementType>(
IAlgebraFieldFinite <ElementType> field)
{
FiniteFieldElement <ElementType> [] elements = field.GetElements();
string[,] table = new string[elements.Length, elements.Length];
for (int index_0 = 0; index_0 < elements.Length; index_0++)
{
for (int index_1 = 0; index_1 < elements.Length; index_1++)
{
table[index_0, index_1] = field.Divide(elements[index_0], elements[index_1]).ToString();
}
}
return(table);
}
public static void CheckFieldDistributivity <ElementType>(
IAlgebraFieldFinite <ElementType> field)
{
FiniteFieldElement <ElementType>[] elements = field.GetElements();
// check distributivity a X (b + c) = (a X b) + (a X c).
for (int index_0 = 0; index_0 < elements.Length; index_0++)
{
for (int index_1 = 0; index_1 < elements.Length; index_1++)
{
for (int index_2 = 0; index_2 < elements.Length; index_2++)
{
FiniteFieldElement <ElementType> result_0 = (elements[index_0] + elements[index_1]) * elements[index_2];
FiniteFieldElement <ElementType> result_1 = (elements[index_0] * elements[index_2]) + (elements[index_1] * elements[index_2]);
Assert.AreEqual(result_0, result_1);
}
}
}
}
public static void CheckFieldIdentities <ElementType>(
IAlgebraFieldFinite <ElementType> field)
{
FiniteFieldElement <ElementType>[] elements = field.GetElements();
FiniteFieldElement <ElementType> add_identity = field.AddIdentity;
FiniteFieldElement <ElementType> multiply_identity = field.MultiplyIdentity;
Assert.AreNotEqual(add_identity, multiply_identity, "add_identiy should be different from multiply_identity");
// check identity elements
for (int index_0 = 0; index_0 < elements.Length; index_0++)
{
Assert.AreEqual(elements[index_0], elements[index_0] + add_identity, elements[index_0] + " + " + add_identity + " should yield " + elements[index_0] + " but yielded " + (elements[index_0] + add_identity));
Assert.AreEqual(elements[index_0], add_identity + elements[index_0], add_identity + " + " + elements[index_0] + " should yield " + elements[index_0] + " but yielded " + (add_identity + elements[index_0]));
Assert.AreEqual(elements[index_0], elements[index_0] * multiply_identity, elements[index_0] + " * " + multiply_identity + " should yield " + elements[index_0] + " but yielded " + (elements[index_0] * multiply_identity));
Assert.AreEqual(elements[index_0], multiply_identity * elements[index_0], multiply_identity + " * " + elements[index_0] + " should yield " + elements[index_0] + " but yielded " + (multiply_identity * elements[index_0]));
}
}