private LutFunction(string Name, IEnumerable <Arrow> Points) : base(Name)
{
parameters = new List <Variable>()
{
Variable.New("x1")
};
foreach (Arrow i in Points)
{
points.Add((double)i.Left, (double)i.Right);
}
}
// Expand N(x)/D(x) using partial fractions.
private static Expression ExpandPartialFractions(Expression N, Expression D, Expression x)
{
List <Expression> terms = new List <Expression>();
List <Variable> unknowns = new List <Variable>();
List <Expression> basis = new List <Expression>();
foreach (Expression i in Product.TermsOf(D))
{
// Get the multiplicity of this basis term.
Expression e = i;
int n = Power.IntegralExponentOf(e);
if (n != 1)
{
e = ((Power)i).Left;
}
// Convert to a polynomial.
Polynomial Pi = Polynomial.New(e, x);
// Add new terms for each multiplicity n.
for (int j = 1; j <= n; ++j)
{
// Expression for the unknown numerator of this term.
Expression unknown = 0;
for (int k = 0; k < Pi.Degree; ++k)
{
Variable Ai = Variable.New("_A" + unknowns.Count.ToString());
unknown += Ai * (x ^ k);
unknowns.Add(Ai);
}
terms.Add(Product.New(unknown, Power.New(e, -j)));
}
basis.Add(i);
}
// Equate the original expression with the decomposed expressions.
D = Sum.New(terms.Select(j => (Expression)(D * j))).Expand();
Polynomial l = Polynomial.New(N, x);
Polynomial r = Polynomial.New(D, x);
// Equate terms of equal degree and solve for the unknowns.
int degree = Math.Max(l.Degree, r.Degree);
List <Equal> eqs = new List <Equal>(degree + 1);
for (int i = 0; i <= degree; ++i)
{
eqs.Add(Equal.New(l[i], r[i]));
}
List <Arrow> A = eqs.Solve(unknowns);
// Substitute the now knowns.
return(Sum.New(terms.Select(i => i.Evaluate(A))));
}
private Expression Resolve(string Token)
{
Expression resolve = context.LookupName(Token).SingleOrDefault();
if (!ReferenceEquals(resolve, null))
{
return(resolve);
}
else
{
return(Variable.New(Token));
}
}
protected override string VisitSet(Set S)
{
IEnumerable <Expression> members = S.Members;
// If there are more than 100 elements in the set, truncate all but 5 elements and append '...'.
if (members.Skip(100).Any())
{
members = members.Take(5).Append(Variable.New("..."));
}
string s = "{" + Join(members, ", ") + "}";
return(s);
}
public static UnknownFunction New(string Name, int ParamCount)
{
return(New(Name, Enumerable.Range(0, ParamCount).Select(i => Variable.New("_" + i.ToString()))));
}
private static Expression ChildPattern(ref int unique)
{
unique++;
return(Variable.New("_" + unique.ToString()));
}