/// <summary>
/// Returns the coefficient u[exponent] of x^exponent in the polynomial <see cref="signal"/>
/// </summary>
/// <returns>
/// Constant UndefinedSymbol if <see cref="signal"/> is not a single-variable polynomial.
/// Constant <see cref="IntegerValue.Zero"/> if there's no summand with the given exponent.
/// Otherwise the sum of all coefficient factors of the term with the given exponent.
/// </returns>
/// <remarks><see cref="signal"/> is assumed to be automatic simplified.</remarks>
public static Signal PolynomialCoefficient(Signal signal, Signal variable, int exponent)
{
ValueStructure vs;
Signal c = MonomialCoefficient(signal, variable, out vs);
if (!(vs is UndefinedSymbol))
{
IntegerValue iv = vs as IntegerValue;
if (iv == null || iv.Value == exponent)
{
return(c);
}
else
{
return(IntegerValue.ConstantZero(signal.Context));
}
}
if (signal.IsDrivenByPortEntity("Add", "Std"))
{
ReadOnlySignalSet inputs = signal.DrivenByPort.InputSignals;
List <Signal> coeffs = new List <Signal>(4);
for (int i = 0; i < inputs.Count; i++)
{
c = MonomialCoefficient(inputs[i], variable, out vs);
IntegerValue iv = vs as IntegerValue;
if (iv != null && iv.Value == exponent)
{
coeffs.Add(c);
}
}
return(signal.Context.Builder.AddSimplified(coeffs));
}
return(UndefinedSymbol.Constant(signal.Context));
}
public static Signal PolynomialLeadingCoefficient(Signal signal, Signal variable)
{
ValueStructure degree = PolynomialDegree(signal, variable);
IntegerValue iv = degree as IntegerValue;
if (iv != null)
{
return(PolynomialCoefficient(signal, variable, (int)iv.Value));
}
if (degree is NegativeInfinitySymbol)
{
return(IntegerValue.ConstantZero(signal.Context));
}
return(UndefinedSymbol.Constant(signal.Context));
}
/// <summary>
/// Returns the coefficient factor in the monomial <see cref="signal"/>
/// </summary>
/// <returns>
/// Constant UndefinedSymbol if <see cref="signal"/> is not a single-variable monomial.
/// Otherwise the coefficient factor of the term.
/// </returns>
/// </returns>
/// <remarks><see cref="signal"/> is assumed to be automatic simplified.</remarks>
public static Signal MonomialCoefficient(Signal signal, Signal variable, out ValueStructure degree)
{
if (signal == null)
{
throw new ArgumentNullException("signal");
}
if (IsConstantAdditiveIdentity(signal))
{
degree = NegativeInfinitySymbol.Instance;
return(signal);
}
if (IsAlwaysRational(signal))
{
degree = IntegerValue.Zero;
return(signal);
}
Signal coeff = IntegerValue.ConstantOne(signal.Context);
if (signal.IsDrivenByPortEntity("Multiply", "Std") && signal.DrivenByPort.InputSignalCount == 2 && IsAlwaysRational(signal.DrivenByPort.InputSignals[0]))
{
coeff = signal.DrivenByPort.InputSignals[0];
signal = signal.DrivenByPort.InputSignals[1];
}
if (signal.Equals(variable))
{
degree = IntegerValue.One;
return(coeff);
}
if (signal.IsDrivenByPortEntity("Power", "Std"))
{
Signal b = signal.DrivenByPort.InputSignals[0];
Signal e = signal.DrivenByPort.InputSignals[1];
if (b.Equals(variable) && Std.IsAlwaysPositiveInteger(e))
{
degree = e.Value;
return(coeff);
}
}
degree = UndefinedSymbol.Instance;
return(UndefinedSymbol.Constant(signal.Context));
}
