/// <summary>
/// DUAL.Mul : res = a * b
/// The geometric product.
/// </summary>
public static DUAL operator *(DUAL a, DUAL b)
{
DUAL res = new DUAL();
res[0] = b[0] * a[0];
res[1] = b[1] * a[0] + b[0] * a[1];
return(res);
}
/// <summary>
/// DUAL.Conjugate : res = a.Conjugate()
/// Clifford Conjugation
/// </summary>
public DUAL Conjugate()
{
DUAL res = new DUAL();
res[0] = this[0];
res[1] = -this[1];
return(res);
}
/// <summary>
/// DUAL.Involute : res = a.Involute()
/// Main involution
/// </summary>
public DUAL Involute()
{
DUAL res = new DUAL();
res[0] = this[0];
res[1] = -this[1];
return(res);
}
/// <summary>
/// DUAL.Dual : res = !a
/// Poincare duality operator.
/// </summary>
public static DUAL operator !(DUAL a)
{
DUAL res = new DUAL();
res[0] = a[1];
res[1] = a[0];
return(res);
}
/// <summary>
/// DUAL.adds : res = a + b
/// multivector/scalar addition
/// </summary>
public static DUAL operator +(DUAL a, float b)
{
DUAL res = new DUAL();
res[0] = a[0] + b;
res[1] = a[1];
return(res);
}
/// <summary>
/// DUAL.sadd : res = a + b
/// scalar/multivector addition
/// </summary>
public static DUAL operator +(float a, DUAL b)
{
DUAL res = new DUAL();
res[0] = a + b[0];
res[1] = b[1];
return(res);
}
/// <summary>
/// DUAL.Sub : res = a - b
/// Multivector subtraction
/// </summary>
public static DUAL operator -(DUAL a, DUAL b)
{
DUAL res = new DUAL();
res[0] = a[0] - b[0];
res[1] = a[1] - b[1];
return(res);
}
/// <summary>
/// DUAL.Vee : res = a & b
/// The regressive product. (JOIN)
/// </summary>
public static DUAL operator &(DUAL a, DUAL b)
{
DUAL res = new DUAL();
res[1] = 1 * (a[1] * b[1]);
res[0] = 1 * (a[0] * b[1] + a[1] * b[0]);
return(res);
}