// 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
});
}
// Lifted addition operation
public LiftedSet <γ, Cp> Add(LiftedSet <γ, Cp> a, LiftedSet <γ, Cp> b)
{
return(new LiftedSet <γ, Cp>
{
// zip the coefficient vectors with the underlying semiring's addition
coefficients = a.coefficients.Zip <γ, γ, γ>(b.coefficients, _semiring.Add)
});
}
