/// <summary>
/// Checks whether a signal is a single variable monomial, e.g. '2*x^3'
/// </summary>
/// <remarks><see cref="signal"/> is assumed to be automatic simplified</remarks>
public static bool IsMonomial(Signal signal, Signal variable)
{
if (signal == null)
{
throw new ArgumentNullException("signal");
}
if (Std.IsAlwaysRational(signal))
{
return(true);
}
if (signal.IsDrivenByPortEntity("Multiply", "Std") && signal.DrivenByPort.InputSignalCount == 2 && Std.IsAlwaysRational(signal.DrivenByPort.InputSignals[0]))
{
signal = signal.DrivenByPort.InputSignals[1];
}
if (signal.Equals(variable))
{
return(true);
}
if (signal.IsDrivenByPortEntity("Power", "Std"))
{
Signal b = signal.DrivenByPort.InputSignals[0];
Signal e = signal.DrivenByPort.InputSignals[1];
if (b.Equals(variable) && Std.IsAlwaysPositiveInteger(e))
{
return(true);
}
}
return(false);
}
/// <summary>
/// Evaluates the degree of the single-variable monomial <see cref="signal"/>.
/// </summary>
/// <returns>
/// <see cref="UndefinedSymbol"/> if <see cref="signal"/> is not a single-variable monomial.
/// <see cref="NegativeInfinitySymbol"/> if <see cref="signal"/> is zero.
/// Otherwise an <see cref="IntegerValue"/> representing the asked degree.
/// </returns>
/// <remarks><see cref="signal"/> is assumed to be automatic simplified.</remarks>
public static IValueStructure MonomialDegree(Signal signal, Signal variable)
{
if (signal == null)
{
throw new ArgumentNullException("signal");
}
if (Std.IsConstantAdditiveIdentity(signal))
{
return(NegativeInfinitySymbol.Instance);
}
if (Std.IsAlwaysRational(signal))
{
return(IntegerValue.Zero);
}
if (signal.IsDrivenByPortEntity("Multiply", "Std") && signal.DrivenByPort.InputSignalCount == 2 && Std.IsAlwaysRational(signal.DrivenByPort.InputSignals[0]))
{
signal = signal.DrivenByPort.InputSignals[1];
}
if (signal.Equals(variable))
{
return(IntegerValue.One);
}
if (signal.IsDrivenByPortEntity("Power", "Std"))
{
Signal b = signal.DrivenByPort.InputSignals[0];
Signal e = signal.DrivenByPort.InputSignals[1];
if (b.Equals(variable) && Std.IsAlwaysPositiveInteger(e))
{
return(e.Value);
}
}
return(UndefinedSymbol.Instance);
}
public static Signal[] PolynomialVariables(Signal signal)
{
List <Signal> variables = new List <Signal>();
ISignalSet monomials;
if (signal.IsDrivenByPortEntity("Add", "Std"))
{
monomials = signal.DrivenByPort.InputSignals;
}
else
{
monomials = new SignalSet(signal);
}
for (int i = 0; i < monomials.Count; i++)
{
ISignalSet factors;
if (monomials[i].IsDrivenByPortEntity("Multiply", "Std"))
{
factors = monomials[i].DrivenByPort.InputSignals;
}
else
{
factors = new SignalSet(monomials[i]);
}
for (int j = 0; j < factors.Count; j++)
{
if (Std.IsAlwaysRational(factors[j]))
{
continue;
}
if (factors[j].IsDrivenByPortEntity("Power", "Std"))
{
Signal b = factors[j].DrivenByPort.InputSignals[0];
if (Std.IsAlwaysPositiveInteger(factors[j].DrivenByPort.InputSignals[1]))
{
if (!variables.Contains(b))
{
variables.Add(b);
}
}
else
{
if (!variables.Contains(signal))
{
variables.Add(signal);
}
}
}
else
if (!variables.Contains(factors[j]))
{
variables.Add(factors[j]);
}
}
}
return(variables.ToArray());
}
/// <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 IValueStructure degree)
{
if (signal == null)
{
throw new ArgumentNullException("signal");
}
if (Std.IsConstantAdditiveIdentity(signal))
{
degree = NegativeInfinitySymbol.Instance;
return(signal);
}
if (Std.IsAlwaysRational(signal))
{
degree = IntegerValue.Zero;
return(signal);
}
Signal coeff = IntegerValue.ConstantOne;
if (signal.IsDrivenByPortEntity("Multiply", "Std") && signal.DrivenByPort.InputSignalCount == 2 && Std.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);
}
private static bool IsMonomialFactor(Signal signal, Signal[] generalizedVariables)
{
if (Array.Exists <Signal>(generalizedVariables, signal.Equals))
{
return(true);
}
if (!Array.Exists <Signal>(generalizedVariables, signal.DependsOn))
{
return(true);
}
if (signal.IsDrivenByPortEntity("Power", "Std"))
{
Signal b = signal.DrivenByPort.InputSignals[0];
Signal e = signal.DrivenByPort.InputSignals[1];
if (Array.Exists <Signal>(generalizedVariables, b.Equals) && Std.IsAlwaysPositiveInteger(e))
{
return(true);
}
}
return(false);
}