/// <summary>
/// MINK.Mul : res = a * b
/// The geometric product.
/// </summary>
public static MINK operator *(MINK a, MINK b)
{
MINK res = new MINK();
res[0] = b[0] * a[0] + b[1] * a[1] - b[2] * a[2] + b[3] * a[3];
res[1] = b[1] * a[0] + b[0] * a[1] + b[3] * a[2] - b[2] * a[3];
res[2] = b[2] * a[0] + b[3] * a[1] + b[0] * a[2] - b[1] * a[3];
res[3] = b[3] * a[0] + b[2] * a[1] - b[1] * a[2] + b[0] * a[3];
return(res);
}
/// <summary>
/// MINK.Conjugate : res = a.Conjugate()
/// Clifford Conjugation
/// </summary>
public MINK Conjugate()
{
MINK res = new MINK();
res[0] = this[0];
res[1] = -this[1];
res[2] = -this[2];
res[3] = -this[3];
return(res);
}
/// <summary>
/// MINK.Involute : res = a.Involute()
/// Main involution
/// </summary>
public MINK Involute()
{
MINK res = new MINK();
res[0] = this[0];
res[1] = -this[1];
res[2] = -this[2];
res[3] = this[3];
return(res);
}
/// <summary>
/// MINK.Dual : res = !a
/// Poincare duality operator.
/// </summary>
public static MINK operator !(MINK a)
{
MINK res = new MINK();
res[0] = a[3];
res[1] = -a[2];
res[2] = -a[1];
res[3] = a[0];
return(res);
}
/// <summary>
/// MINK.subs : res = a - b
/// multivector/scalar subtraction
/// </summary>
public static MINK operator -(MINK a, float b)
{
MINK res = new MINK();
res[0] = a[0] - b;
res[1] = a[1];
res[2] = a[2];
res[3] = a[3];
return(res);
}
/// <summary>
/// MINK.ssub : res = a - b
/// scalar/multivector subtraction
/// </summary>
public static MINK operator -(float a, MINK b)
{
MINK res = new MINK();
res[0] = a - b[0];
res[1] = -b[1];
res[2] = -b[2];
res[3] = -b[3];
return(res);
}
/// <summary>
/// MINK.Sub : res = a - b
/// Multivector subtraction
/// </summary>
public static MINK operator -(MINK a, MINK b)
{
MINK res = new MINK();
res[0] = a[0] - b[0];
res[1] = a[1] - b[1];
res[2] = a[2] - b[2];
res[3] = a[3] - b[3];
return(res);
}
/// <summary>
/// MINK.Vee : res = a & b
/// The regressive product. (JOIN)
/// </summary>
public static MINK operator &(MINK a, MINK b)
{
MINK res = new MINK();
res[3] = 1 * (a[3] * b[3]);
res[2] = -1 * (a[2] * -1 * b[3] + a[3] * b[2] * -1);
res[1] = 1 * (a[1] * b[3] + a[3] * b[1]);
res[0] = 1 * (a[0] * b[3] + a[1] * b[2] * -1 - a[2] * -1 * b[1] + a[3] * b[0]);
return(res);
}
