/// <summary>
/// Like the Evaluate method, except it replaces indeterminates with Polynomials instead of integers,
/// and returns the resulting (usually large) Polynomial
/// </summary>
public MultivariatePolynomial FunctionalComposition(List <Tuple <char, MultivariatePolynomial> > indeterminateValues)
{
List <Term> terms = this.Terms.ToList();
List <MultivariatePolynomial> composedTerms = new List <MultivariatePolynomial>();
foreach (Term trm in terms)
{
MultivariatePolynomial constant = MultivariatePolynomial.Parse(trm.CoEfficient.ToString());
List <MultivariatePolynomial> toCompose = new List <MultivariatePolynomial>();
toCompose.Add(constant.Clone());
foreach (Indeterminate variable in trm.Variables)
{
int exp = variable.Exponent;
MultivariatePolynomial valueOfIndeterminate = indeterminateValues.Where(tup => tup.Item1 == variable.Symbol).Select(tup => tup.Item2).FirstOrDefault();
if (valueOfIndeterminate == null)
{
MultivariatePolynomial thisVariableAsPoly = new MultivariatePolynomial(new Term[] { new Term(BigInteger.One, new Indeterminate[] { variable }) });
toCompose.Add(thisVariableAsPoly);
}
else if (exp == 0)
{
continue;
}
else if (exp == 1)
{
toCompose.Add(valueOfIndeterminate);
}
else
{
MultivariatePolynomial toMultiply = MultivariatePolynomial.Pow(valueOfIndeterminate, exp);
toCompose.Add(toMultiply);
}
}
MultivariatePolynomial composed = MultivariatePolynomial.Product(toCompose);
composedTerms.Add(composed);
}
MultivariatePolynomial result = MultivariatePolynomial.Sum(composedTerms);
return(result);
}
