/// <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)
{
IValueStructure 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);
}
}
if (signal.IsDrivenByPortEntity("Add", "Std"))
{
ISignalSet 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(Std.Add(coeffs));
}
return(UndefinedSymbol.Constant);
}
public static Signal ConstructPolynomial <TCoeff>(Signal variable, params TCoeff[] coefficients)
where TCoeff : IAlgebraicRingWithUnity <TCoeff>, IValueStructure
{
Signal zero = null;
Signal[] summands = new Signal[coefficients.Length];
for (int i = 0; i < summands.Length; i++)
{
TCoeff c = coefficients[i];
if (c.IsAdditiveIdentity)
{
if (zero == null)
{
zero = Std.DefineConstant(c);
}
summands[i] = zero;
continue;
}
Signal coeff = Std.DefineConstant(c);
if (i == 0)
{
summands[0] = coeff;
}
else if (i == 1)
{
if (c.IsMultiplicativeIdentity)
{
summands[1] = variable;
}
else
{
summands[1] = StdBuilder.Multiply(coeff, variable);
}
}
else
{
if (c.IsMultiplicativeIdentity)
{
summands[i] = StdBuilder.Power(variable, IntegerValue.Constant(i));
}
else
{
summands[i] = StdBuilder.Multiply(coeff, StdBuilder.Power(variable, IntegerValue.Constant(i)));
}
}
}
return(Std.Add(summands));
}
public static Signal ConstructPolynomial(Signal variable, params Signal[] coefficients)
{
Signal[] summands = new Signal[coefficients.Length];
for (int i = 0; i < summands.Length; i++)
{
Signal coeff = coefficients[i];
if (Std.IsConstantAdditiveIdentity(coeff))
{
summands[i] = coeff;
continue;
}
if (i == 0)
{
summands[0] = coeff;
}
else if (i == 1)
{
if (Std.IsConstantMultiplicativeIdentity(coeff))
{
summands[1] = variable;
}
else
{
summands[1] = StdBuilder.Multiply(coeff, variable);
}
}
else
{
if (Std.IsConstantMultiplicativeIdentity(coeff))
{
summands[i] = StdBuilder.Power(variable, IntegerValue.Constant(i));
}
else
{
summands[i] = StdBuilder.Multiply(coeff, StdBuilder.Power(variable, IntegerValue.Constant(i)));
}
}
}
return(Std.Add(summands));
}
/// <summary>
/// Extracts all coefficients of the polynomial <see cref="signal"/>.
/// </summary>
/// <returns>A signal array [c0,c1,c2,..] where ci ist the coefficient of x^i.</returns>
public static Signal[] PolynomialCoefficients(Signal signal, Signal variable)
{
IValueStructure vs;
SortedList <long, Signal> polynom = new SortedList <long, Signal>();
Signal c = MonomialCoefficient(signal, variable, out vs);
if (!(vs is UndefinedSymbol))
{
IntegerValue iv = vs as IntegerValue;
if (iv != null)
{
polynom.Add(iv.Value, c);
}
else
{
return new Signal[] { IntegerValue.ConstantZero }
};
}
else if (signal.IsDrivenByPortEntity("Add", "Std"))
{
ISignalSet inputs = signal.DrivenByPort.InputSignals;
for (int i = 0; i < inputs.Count; i++)
{
c = MonomialCoefficient(inputs[i], variable, out vs);
IntegerValue iv = vs as IntegerValue;
if (iv != null)
{
if (!polynom.ContainsKey(iv.Value))
{
polynom.Add(iv.Value, c);
}
else
{
polynom[iv.Value] = Std.Add(polynom[iv.Value], c);
}
}
}
}
if (polynom.Keys.Count == 0)
{
return new Signal[] { }
}
;
long deg = polynom.Keys[polynom.Keys.Count - 1];
Signal[] ret = new Signal[deg + 1];
Signal zero = IntegerValue.ConstantZero;
for (int i = 0; i < ret.Length; i++)
{
if (polynom.ContainsKey(i))
{
ret[i] = polynom[i];
}
else
{
ret[i] = zero;
}
}
return(ret);
}