//Exp( p ) is
// var t : Tree
// t := P
// while next is a binary operator and prec(binary(next)) >= p
// const op := binary(next)
// consume
// const q := case associativity(op)
// of Right: prec( op )
// Left: 1+prec( op )
// const t1 := Exp( q )
// t := mkNode( op, t, t1)
// return t
private Expression Exp(int p)
{
Expression l = P();
Operator op = new Operator();
while (true)
{
if (IsBinaryOperator(tokens.Tok, ref op) && Precedence(op) >= p)
{
tokens.Consume();
int q = Precedence(op) + (IsLeftAssociative(op) ? 1 : 0);
Expression r = Exp(q);
l = Binary.New(op, l, r);
}
else if (IsUnaryPostOperator(tokens.Tok, ref op) && Precedence(op) >= p)
{
tokens.Consume();
l = Unary.New(op, l);
}
else
{
break;
}
}
return(l);
}
private static Expression Split(Expression P)
{
int child = 0;
if (P is Sum)
{
return(ComputerAlgebra.Sum.New(((ComputerAlgebra.Sum)P).Terms.Select(i => ChildPattern(ref child))));
}
if (P is Product)
{
return(Product.New(((Product)P).Terms.Select(i => ChildPattern(ref child))));
}
if (P is Binary)
{
return(Binary.New(((Binary)P).Operator, ChildPattern(ref child), ChildPattern(ref child)));
}
if (P is Unary)
{
return(Unary.New(((Unary)P).Operator, ChildPattern(ref child)));
}
if (P is Call)
{
return(Call.New(((Call)P).Target, ((Call)P).Arguments.Select(i => ChildPattern(ref child))));
}
return(null);
}
/// <summary>
/// Distribute products across sums, using partial fractions if necessary.
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
public static Expression Expand(this Expression f, Expression x)
{
if (f is Product)
{
return(ExpandMultiply(f, x));
}
else if (f is Sum)
{
return(Sum.New(((Sum)f).Terms.Select(i => i.Expand(x))));
}
else if (f is Power)
{
return(ExpandPower((Power)f, x));
}
else if (f is Binary)
{
return(Binary.New(((Binary)f).Operator, ((Binary)f).Left.Expand(), ((Binary)f).Right.Expand()));
}
else if (f is Unary)
{
return(Unary.New(((Unary)f).Operator, ((Unary)f).Operand.Expand()));
}
return(f);
}
/// <summary>
/// Distribute products across sums, using partial fractions if necessary.
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
public static Expression Expand(this Expression f, Expression x)
{
if (f is Product)
{
return(ExpandMultiply(f, x));
}
else if (f is Sum sum)
{
return(Sum.New(sum.Terms.Select(i => i.Expand(x))));
}
else if (f is Power power)
{
return(ExpandPower(power, x));
}
else if (f is Binary binary)
{
return(Binary.New(binary.Operator, binary.Left.Expand(x), binary.Right.Expand(x)));
}
else if (f is Unary unary)
{
return(Unary.New(unary.Operator, unary.Operand.Expand()));
}
return(f);
}
protected override Expression VisitUnary(Unary U)
{
Expression O = Visit(U.Operand);
if (ReferenceEquals(O, null))
{
return(null);
}
if (ReferenceEquals(O, U.Operand))
{
return(U);
}
else
{
return(Unary.New(U.Operator, O));
}
}
protected override Expression VisitUnary(Unary U)
{
Expression O = Visit(U.Operand);
Real? C = AsReal(O);
switch (U.Operator)
{
case Operator.Not:
if (IsTrue(C))
{
return(Constant.New(false));
}
else if (IsFalse(C))
{
return(Constant.New(true));
}
break;
}
return(Unary.New(U.Operator, O));
}
//P is
// if next is a unary operator
// const op := unary(next)
// consume
// q := prec( op )
// const t := Exp( q )
// return mkNode( op, t )
// else if next = "("
// consume
// const t := Exp( 0 )
// expect ")"
// return t
// else if next is a v
// const t := mkLeaf( next )
// consume
// return t
// else
// error
private Expression P()
{
Operator op = new Operator();
if (tokens.Tok == "+")
{
// Skip unary +.
tokens.Consume();
return(P());
}
else if (IsUnaryPreOperator(tokens.Tok, ref op))
{
// Unary operator.
tokens.Consume();
Expression t = Exp(Precedence(op));
return(Unary.New(op, t));
}
else if (tokens.Tok == "(")
{
// Group.
tokens.Consume();
Expression t = Exp(0);
tokens.Expect(")");
return(t);
}
else if (tokens.Tok == "{")
{
// Set.
tokens.Consume();
return(Set.New(L(",", "}")));
}
else if (tokens.Tok == "[")
{
// Matrix.
tokens.Consume();
List <List <Expression> > entries = new List <List <Expression> >();
while (tokens.Tok == "[")
{
tokens.Consume();
entries.Add(L(",", "]"));
}
tokens.Expect("]");
return(Matrix.New(entries));
}
else
{
string tok = tokens.Consume();
decimal dec = 0;
double dbl = 0.0;
if (decimal.TryParse(tok, NumberStyles.Float, culture, out dec))
{
return(Constant.New(dec));
}
if (double.TryParse(tok, NumberStyles.Float, culture, out dbl))
{
return(Constant.New(dbl));
}
else if (tok == "True")
{
return(Constant.New(true));
}
else if (tok == "False")
{
return(Constant.New(false));
}
else if (tok == "\u221E" || tok == "oo")
{
return(Constant.New(Real.Infinity));
}
else if (tokens.Tok == "[")
{
// Bracket function call.
tokens.Consume();
List <Expression> args = L(",", "]");
return(Call.New(Resolve(tok, args), args));
}
else if (tokens.Tok == "(")
{
// Paren function call.
tokens.Consume();
List <Expression> args = L(",", ")");
return(Call.New(Resolve(tok, args), args));
}
else
{
return(Resolve(tok));
}
}
}