public static ComplexMultivariatePolynomial Pow(ComplexMultivariatePolynomial poly, int exponent)
{
if (exponent < 0)
{
throw new NotImplementedException("Raising a polynomial to a negative exponent not supported.");
}
else if (exponent == 0)
{
return(new ComplexMultivariatePolynomial(new Term[] { new Term(1, new Indeterminate[0]) }));
}
else if (exponent == 1)
{
return(poly.Clone());
}
ComplexMultivariatePolynomial result = poly.Clone();
int counter = exponent - 1;
while (counter != 0)
{
result = ComplexMultivariatePolynomial.Multiply(result, poly);
counter -= 1;
}
return(new ComplexMultivariatePolynomial(result.Terms));
}
public static ComplexMultivariatePolynomial GetDerivative(ComplexMultivariatePolynomial poly, char symbol)
{
List <Term> resultTerms = new List <Term>();
foreach (Term term in poly.Terms)
{
if (term.Variables.Any() && term.Variables.Any(indt => indt.Symbol == symbol))
{
Complex newTerm_Coefficient = 0;
List <Indeterminate> newTerm_Variables = new List <Indeterminate>();
foreach (Indeterminate variable in term.Variables)
{
if (variable.Symbol == symbol)
{
newTerm_Coefficient = term.CoEfficient * variable.Exponent;
int newExponent = variable.Exponent - 1;
if (newExponent > 0)
{
newTerm_Variables.Add(new Indeterminate(symbol, newExponent));
}
}
else
{
newTerm_Variables.Add(variable.Clone());
}
}
resultTerms.Add(new Term(newTerm_Coefficient, newTerm_Variables.ToArray()));
}
}
return(new ComplexMultivariatePolynomial(resultTerms.ToArray()));
}
public bool Equals(ComplexMultivariatePolynomial x, ComplexMultivariatePolynomial y)
{
if (x == null)
{
return((y == null) ? true : false);
}
if (!x.Terms.Any())
{
return((!y.Terms.Any()) ? true : false);
}
if (x.Terms.Length != y.Terms.Length)
{
return(false);
}
if (x.Degree != y.Degree)
{
return(false);
}
int index = 0;
foreach (Term term in x.Terms)
{
if (!term.Equals(y.Terms[index++]))
{
return(false);
}
}
return(true);
}
public static ComplexMultivariatePolynomial Divide(ComplexMultivariatePolynomial left, ComplexMultivariatePolynomial right)
{
List <Term> newTermsList = new List <Term>();
List <Term> leftTermsList = CloneHelper <Term> .CloneCollection(left.Terms).ToList();
foreach (Term rightTerm in right.Terms)
{
var matches = leftTermsList.Where(leftTerm => Term.ShareCommonFactor(leftTerm, rightTerm)).ToList();
if (matches.Any())
{
foreach (Term matchTerm in matches)
{
leftTermsList.Remove(matchTerm);
Term result = Term.Divide(matchTerm, rightTerm);
if (result != Term.Empty)
{
if (!newTermsList.Any(lt => lt.Equals(result)))
{
newTermsList.Add(result);
}
}
}
}
else
{
///newTermsList.Add(rightTerm);
}
}
return(new ComplexMultivariatePolynomial(newTermsList.ToArray()));
}
public static ComplexMultivariatePolynomial Multiply(ComplexMultivariatePolynomial left, ComplexMultivariatePolynomial right)
{
List <Term> resultTerms = new List <Term>();
foreach (var leftTerm in left.Terms)
{
foreach (var rightTerm in right.Terms)
{
Term newTerm = Term.Multiply(leftTerm, rightTerm);
// Combine like terms
var likeTerms = resultTerms.Where(trm => Term.AreIdentical(newTerm, trm));
if (likeTerms.Any())
{
resultTerms = resultTerms.Except(likeTerms).ToList();
Term likeTermsSum = likeTerms.Aggregate(Term.Add);
Term sum = Term.Add(newTerm, likeTermsSum);
newTerm = sum;
}
// Add new term to resultTerms
resultTerms.Add(newTerm);
}
}
return(new ComplexMultivariatePolynomial(resultTerms.ToArray()));
}
private static ComplexMultivariatePolynomial OneToOneArithmetic(ComplexMultivariatePolynomial left, ComplexMultivariatePolynomial right, Func <Term, Term, Term> operation)
{
List <Term> leftTermsList = CloneHelper <Term> .CloneCollection(left.Terms).ToList();
foreach (Term rightTerm in right.Terms)
{
var match = leftTermsList.Where(leftTerm => Term.AreIdentical(leftTerm, rightTerm));
if (match.Any())
{
Term matchTerm = match.Single();
leftTermsList.Remove(matchTerm);
Term result = operation.Invoke(matchTerm, rightTerm);
if (result.CoEfficient != 0)
{
if (!leftTermsList.Any(lt => lt.Equals(result)))
{
leftTermsList.Add(result);
}
}
}
else
{
leftTermsList.Add(Term.Negate(rightTerm));
}
}
return(new ComplexMultivariatePolynomial(leftTermsList.ToArray()));
}
public static ComplexMultivariatePolynomial GCD(ComplexMultivariatePolynomial left, ComplexMultivariatePolynomial right)
{
ComplexMultivariatePolynomial minuend = left.Clone();
ComplexMultivariatePolynomial subtrahend = right.Clone();
ComplexMultivariatePolynomial difference;
Complex minuendMaxCoefficient = 0;
Complex subtrahendMaxCoefficient = 0;
Complex differenceMaxCoefficient = 0;
do
{
minuendMaxCoefficient = minuend.MaxCoefficient();
subtrahendMaxCoefficient = subtrahend.MaxCoefficient();
difference = ComplexMultivariatePolynomial.Subtract(minuend, subtrahend).Clone();
differenceMaxCoefficient = difference.MaxCoefficient();
if (Complex.Abs(minuendMaxCoefficient) > Complex.Abs(subtrahendMaxCoefficient) && Complex.Abs(subtrahendMaxCoefficient) > Complex.Abs(differenceMaxCoefficient))
{
minuend = subtrahend.Clone();
subtrahend = difference.Clone();
}
else if (Complex.Abs(differenceMaxCoefficient) > Complex.Abs(subtrahendMaxCoefficient))
{
//minuend = subtrahend.Clone();
subtrahend = difference.Clone();
}
}while (Complex.Abs(minuendMaxCoefficient) > 0 && Complex.Abs(subtrahendMaxCoefficient) > 0 && minuend.HasVariables() && subtrahend.HasVariables());
if (minuend.HasVariables())
{
return(subtrahend.Clone());
}
else
{
return(minuend.Clone());
}
}
public int GetHashCode(ComplexMultivariatePolynomial obj)
{
return(obj.GetHashCode());
}
public bool Equals(ComplexMultivariatePolynomial other)
{
return(this.Equals(this, other));
}
public static ComplexMultivariatePolynomial Subtract(ComplexMultivariatePolynomial left, ComplexMultivariatePolynomial right)
{
return(OneToOneArithmetic(left, right, Term.Subtract));
}
public static ComplexMultivariatePolynomial Add(ComplexMultivariatePolynomial left, ComplexMultivariatePolynomial right)
{
return(OneToOneArithmetic(left, right, Term.Add));
}