public void ComplexDiLogSymmetry()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 12))
{
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(
AdvancedComplexMath.DiLog(z), AdvancedComplexMath.DiLog(-z),
AdvancedComplexMath.DiLog(z * z) / 2.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
-AdvancedComplexMath.DiLog(1.0 / z),
AdvancedComplexMath.DiLog(z) + ComplexMath.Log(-z) * ComplexMath.Log(-z) / 2.0 + Math.PI * Math.PI / 6.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
-AdvancedComplexMath.DiLog(1.0 - z),
AdvancedComplexMath.DiLog(z) + ComplexMath.Log(z) * ComplexMath.Log(1.0 - z) - Math.PI * Math.PI / 6.0
));
}
}
public void ComplexDiLogUnitCircle()
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.DiLog(1.0),
Math.PI * Math.PI / 6.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.DiLog(ComplexMath.I),
new Complex(-Math.PI * Math.PI / 48.0, AdvancedMath.Catalan)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.DiLog(-1.0),
-Math.PI * Math.PI / 12.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.DiLog(-ComplexMath.I),
new Complex(-Math.PI * Math.PI / 48.0, -AdvancedMath.Catalan)
));
}