// This is transcribed directly from [Emoto] p. 570
private T2 OptCombine(T2 a, T2 b)
{
U i = _semiring.Add(a.i, _semiring.Mult(a.s, b.i));
U s = _semiring.Mult(a.s, b.s);
return(new T2(i, s));
}
// This is transcribed directly from [Emoto] p. 568
private T4 MitsCombine(T4 a, T4 b)
{
U m = _semiring.Add(_semiring.Add(a.m, _semiring.Mult(a.t, b.i)), b.m);
U i = _semiring.Add(a.i, _semiring.Mult(a.s, b.i));
U t = _semiring.Add(_semiring.Mult(a.t, b.s), b.t);
U s = _semiring.Mult(a.s, b.s);
return(new T4(m, i, t, s));
}
// Lifted multiplication operation
public LiftedSet <γ, Cp> Mult(LiftedSet <γ, Cp> a, LiftedSet <γ, Cp> b)
{
List <γ> coefficients = new List <γ>();
// Sanity check to make sure we have the right number of coefficients
Debug.Assert(a.coefficients.Count() == _p.Symbols().Count);
Debug.Assert(b.coefficients.Count() == _p.Symbols().Count);
foreach (var operandIndices in _multMap)
{
γ k = _semiring.AdditiveIdentity;
foreach (var tuple in operandIndices)
{
var i = tuple.Item1;
var j = tuple.Item2;
var combined = _semiring.Mult(a.coefficients.ElementAt(i),
b.coefficients.ElementAt(j));
// This Add combines two values to one using the underlying semiring
k = _semiring.Add(k, combined);
}
// This is List.Add tacking the next coefficient onto the end of the list
coefficients.Add(k);
}
return(new LiftedSet <γ, Cp> {
coefficients = coefficients
});
}
