// Evaluate x*A, distributing x if A is Add.
public static Expression Distribute(Expression x, Expression A)
{
if (A is Sum || x is Sum)
{
return(EvaluateVisitor.EvaluateSum(Sum.TermsOf(A).SelectMany(i => Sum.TermsOf(Distribute(i, x)))));
}
else
{
return(Product.New(A, x).Evaluate());
}
}
/// <summary>
/// Create a new linear combination expression equal to x.
/// </summary>
/// <param name="B">Basis terms for the linear combination.</param>
/// <param name="x"></param>
/// <returns></returns>
public static LinearCombination New(IEnumerable <Expression> B, Expression x)
{
B = B.Buffer();
LinearCombination ret = new LinearCombination();
foreach (Expression t in Sum.TermsOf(x.Expand()))
{
ret.AddTerm(B, t);
}
return(ret);
}
public Equation(Equal Eq, IEnumerable <Expression> Terms)
: base(0)
{
Terms = Terms.AsList();
Expression f = Eq.Left - Eq.Right;
foreach (Expression i in Sum.TermsOf(f.Expand()))
{
AddTerm(Terms, i);
}
}
/// <summary>
/// Construct a polynomial of x from f(x).
/// </summary>
/// <param name="f"></param>
/// <param name="x"></param>
/// <returns></returns>
public static Polynomial New(Expression f, Expression x)
{
// Match each term to A*x^N where A is constant with respect to x, and N is an integer.
Variable A = PatternVariable.New("A", i => !i.DependsOn(x));
Variable N = PatternVariable.New("N", i => i.IsInteger());
Expression TermPattern = Product.New(A, Power.New(x, N));
DefaultDictionary <int, Expression> P = new DefaultDictionary <int, Expression>(0);
foreach (Expression i in Sum.TermsOf(f))
{
MatchContext Matched = TermPattern.Matches(i, Arrow.New(x, x));
if (Matched == null)
{
throw new ArgumentException("f is not a polynomial of x.");
}
int n = (int)Matched[N];
P[n] += Matched[A];
}
return(new Polynomial(P, x));
}
protected override Expression VisitSum(Sum A)
{
return(EvaluateSum(A.Terms.SelectMany(i => Sum.TermsOf(Visit(i)))));
}
