public static void moebius_test()
//****************************************************************************80
//
// Purpose:
//
// MOEBIUS_TEST tests MOEBIUS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 June 2007
//
// Author:
//
// John Burkardt
//
{
int c = 0;
int n = 0;
Console.WriteLine("");
Console.WriteLine("MOEBIUS_TEST");
Console.WriteLine(" MOEBIUS computes the Moebius function.");
Console.WriteLine("");
Console.WriteLine(" N Exact MOEBIUS(N)");
Console.WriteLine("");
int n_data = 0;
for (;;)
{
Burkardt.Values.Moebius.moebius_values(ref n_data, ref n, ref c);
if (n_data == 0)
{
break;
}
Console.WriteLine(" "
+ n.ToString().PadLeft(8) + " "
+ c.ToString().PadLeft(10) + " "
+ Moebius.moebius(n).ToString().PadLeft(10) + "");
}
}
public void Update()
{
if (this.oculusTouch.GetButton(this.button1) || this.oculusTouch.GetButton(this.button2))
{
//this.intersectionManager.Update();
if (!this.HaveInterSections()) //this.intersectionManager.HaveInterSections())
{
Moebius moebius = new Moebius(newCurves);
if (this.oculusTouch.GetButton(this.button1))
{
moebius.Flow();
}
else if (this.oculusTouch.GetButton(this.button2))
{
moebius.MomentumFlow();
}
foreach (Curve curve in this.newCurves)
{
while (true)
{
Elasticity elasticity = new Elasticity(curve.points, curve.momentum, curve.segment);
if (elasticity.MaxError() < curve.segment * 0.2f)
{
break;
}
elasticity.Flow();
}
}
}
}
if (this.oculusTouch.GetButtonUp(this.button2))
{
foreach (Curve curve in this.newCurves)
{
curve.MomentumInitialize();
}
}
foreach (Curve curve in this.newCurves)
{
curve.MeshUpdate();
Graphics.DrawMesh(curve.mesh, Vector3.zero, Quaternion.identity, MakeMesh.SelectedCurveMaterial, 0);
}
}
public static void moebius_values_test()
//****************************************************************************80
//
// Purpose:
//
// MOEBIUS_VALUES_TEST tests MOEBIUS_VALUES.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 June 2007
//
// Author:
//
// John Burkardt
//
{
int fn = 0;
int n = 0;
Console.WriteLine("");
Console.WriteLine("MOEBIUS_VALUES_TEST:");
Console.WriteLine(" MOEBIUS_VALUES returns values of");
Console.WriteLine(" the Moebius function.");
Console.WriteLine("");
Console.WriteLine(" N MU(N)");
Console.WriteLine("");
int n_data = 0;
for (;;)
{
Moebius.moebius_values(ref n_data, ref n, ref fn);
if (n_data == 0)
{
break;
}
Console.WriteLine(" "
+ n.ToString().PadLeft(8) + " "
+ fn.ToString().PadLeft(12) + "");
}
}
public static int mertens(int n)
//****************************************************************************80
//
// Purpose:
//
// MERTENS evaluates the Mertens function.
//
// Discussion:
//
// The Mertens function M(N) is the sum from 1 to N of the Moebius
// function MU. That is,
//
// M(N) = sum ( 1 <= I <= N ) MU(I)
//
// N M(N)
// -- ----
// 1 1
// 2 0
// 3 -1
// 4 -1
// 5 -2
// 6 -1
// 7 -2
// 8 -2
// 9 -2
// 10 -1
// 11 -2
// 12 -2
// 100 1
// 1000 2
// 10000 -23
// 100000 -48
//
// The determinant of the Redheffer matrix of order N is equal
// to the Mertens function M(N).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 16 October 2007
//
// Author:
//
// John Burkardt
//
// Reference:
//
// M Deleglise, J Rivat,
// Computing the Summation of the Moebius Function,
// Experimental Mathematics,
// Volume 5, 1996, pages 291-295.
//
// Eric Weisstein,
// CRC Concise Encyclopedia of Mathematics,
// CRC Press, 2002,
// Second edition,
// ISBN: 1584883472,
// LC: QA5.W45
//
// Parameters:
//
// Input, int N, the argument.
//
// Output, int MERTENS, the value.
//
{
int i;
int value = 0;
for (i = 1; i <= n; i++)
{
value += Moebius.moebius(i);
}
return(value);
}
