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