public static Polynomial Divide(Polynomial N, Polynomial D, out Polynomial R)
{
if (!Equals(N.Variable, D.Variable))
{
throw new ArgumentException("Polynomials must be of the same variable.", "N/D");
}
DefaultDictionary <int, Expression> q = new DefaultDictionary <int, Expression>(0);
DefaultDictionary <int, Expression> r = new DefaultDictionary <int, Expression>(0);
foreach (KeyValuePair <int, Expression> i in N.Coefficients)
{
r.Add(i.Key, i.Value);
}
while (r.Any() && !r[0].Equals(0) && r.Keys.Max() + 1 >= D.Degree)
{
int rd = r.Keys.Max() + 1;
int dd = D.Degree;
Expression t = r[rd] / D[dd];
int td = rd - dd;
// Compute q += t
q[td] += t;
// Compute r -= d * t
for (int i = 0; i <= dd; ++i)
{
r[i + td] -= -D[i] * t;
}
}
R = new Polynomial(r, N.Variable);
return(new Polynomial(q, N.Variable));
}
private Polynomial(IEnumerable<KeyValuePair<int, Expression>> Coefficients, Expression Variable)
{
coefficients = new DefaultDictionary<int,Expression>(0);
foreach (KeyValuePair<int, Expression> i in Coefficients)
coefficients.Add(i.Key, i.Value);
variable = Variable;
}
private Polynomial(IEnumerable <KeyValuePair <int, Expression> > Coefficients, Expression Variable)
{
coefficients = new DefaultDictionary <int, Expression>(0);
foreach (KeyValuePair <int, Expression> i in Coefficients)
{
coefficients.Add(i.Key, i.Value);
}
variable = Variable;
}
// Combine like terms and multiply constants.
protected override Expression VisitProduct(Product M)
{
// Map terms to exponents.
DefaultDictionary <Expression, Real> terms = new DefaultDictionary <Expression, Real>(0);
// Accumulate constants and sum exponent of each term.
Real C = 1;
foreach (Expression i in M.Terms.SelectMany(i => Product.TermsOf(Visit(i))))
{
if (i is Constant)
{
Real Ci = (Real)i;
// Early exit if 0.
if (Ci.EqualsZero())
{
return(0);
}
C *= Ci;
}
else
{
Power Pi = i as Power;
if (!ReferenceEquals(Pi, null) && Pi.Right is Constant)
{
terms[Pi.Left] += (Real)Pi.Right;
}
else
{
terms[i] += 1;
}
}
}
// Build a new expression with the accumulated terms.
if (!C.EqualsOne())
{
// Find a sum term that has a constant term to distribute into.
KeyValuePair <Expression, Real> A = terms.FirstOrDefault(i => Real.Abs(i.Value).EqualsOne() && i.Key is Sum);
if (!ReferenceEquals(A.Key, null))
{
terms.Remove(A.Key);
terms[ExpandExtension.Distribute(C ^ A.Value, A.Key)] += A.Value;
}
else
{
terms.Add(C, 1);
}
}
return(Product.New(terms
.Where(i => !i.Value.EqualsZero())
.Select(i => !i.Value.EqualsOne() ? Power.New(i.Key, Constant.New(i.Value)) : i.Key)));
}
private void ParseParameters()
{
var parameters = OriginalParametersString
.Split('&')
.Where(p => !string.IsNullOrEmpty(p))
.ToList();
var originalParameters = new DefaultDictionary <string, IList <string> >(StringComparer.OrdinalIgnoreCase);
var newParameters = new DefaultDictionary <string, IList <string> >(StringComparer.OrdinalIgnoreCase);
foreach (var parameter in parameters)
{
string key;
string value = null;
var equalsPos = parameter.IndexOf('=');
if (equalsPos < 0)
{
key = parameter.ToLower();
}
else
{
key = parameter.Substring(0, equalsPos).Trim().ToLower();
value = parameter.Substring(equalsPos + 1).Trim();
}
IList <string> values;
if (originalParameters.TryGetValue(key, out values))
{
values.Add(value);
newParameters[key].Add(value);
}
else
{
originalParameters.Add(key, new List <string> {
value
});
newParameters.Add(key, new List <string> {
value
});
}
}
_originalParameters = originalParameters;
_newParameters = newParameters;
}
public static Expression EvaluateSum(IEnumerable <Expression> Terms)
{
// Map terms to their coefficients.
DefaultDictionary <Expression, Real> terms = new DefaultDictionary <Expression, Real>(0);
// Accumulate constants and sum coefficient of each term.
Real C = 0;
foreach (Expression i in Terms)
{
if (i is Constant)
{
C += (Real)i;
}
else
{
// Find constant term.
Constant coeff = Product.TermsOf(i).OfType <Constant>().FirstOrDefault();
if (!ReferenceEquals(coeff, null))
{
terms[Product.New(Product.TermsOf(i).ExceptUnique(coeff, Expression.RefComparer))] += (Real)coeff;
}
else
{
terms[i] += 1;
}
}
}
// Build a new expression with the accumulated terms.
if (!C.EqualsZero())
{
terms.Add(Constant.New(C), (Real)1);
}
return(Sum.New(terms
.Where(i => !i.Value.EqualsZero())
.Select(i => !i.Value.EqualsOne() ? Product.New(i.Key, Constant.New(i.Value)) : i.Key)));
}
public static Polynomial Divide(Polynomial N, Polynomial D, out Polynomial R)
{
if (!Equals(N.Variable, D.Variable))
throw new ArgumentException("Polynomials must be of the same variable.", "N/D");
DefaultDictionary<int, Expression> q = new DefaultDictionary<int, Expression>(0);
DefaultDictionary<int, Expression> r = new DefaultDictionary<int, Expression>(0);
foreach (KeyValuePair<int, Expression> i in N.Coefficients)
r.Add(i.Key, i.Value);
while (r.Any() && !r[0].Equals(0) && r.Keys.Max() + 1 >= D.Degree)
{
int rd = r.Keys.Max() + 1;
int dd = D.Degree;
Expression t = r[rd] / D[dd];
int td = rd - dd;
// Compute q += t
q[td] += t;
// Compute r -= d * t
for (int i = 0; i <= dd; ++i)
r[i + td] -= -D[i] * t;
}
R = new Polynomial(r, N.Variable);
return new Polynomial(q, N.Variable);
}
// Combine like terms and multiply constants.
protected override Expression VisitProduct(Product M)
{
// Map terms to exponents.
DefaultDictionary<Expression, Real> terms = new DefaultDictionary<Expression, Real>(0);
// Accumulate constants and sum exponent of each term.
Real C = 1;
foreach (Expression i in M.Terms.SelectMany(i => Product.TermsOf(Visit(i))))
{
if (i is Constant)
{
Real Ci = (Real)i;
// Early exit if 0.
if (Ci.EqualsZero())
return 0;
C *= Ci;
}
else
{
Power Pi = i as Power;
if (!ReferenceEquals(Pi, null) && Pi.Right is Constant)
terms[Pi.Left] += (Real)Pi.Right;
else
terms[i] += 1;
}
}
// Build a new expression with the accumulated terms.
if (!C.EqualsOne())
{
// Find a sum term that has a constant term to distribute into.
KeyValuePair<Expression, Real> A = terms.FirstOrDefault(i => Real.Abs(i.Value).EqualsOne() && i.Key is Sum);
if (!ReferenceEquals(A.Key, null))
{
terms.Remove(A.Key);
terms[ExpandExtension.Distribute(C ^ A.Value, A.Key)] += A.Value;
}
else
{
terms.Add(C, 1);
}
}
return Product.New(terms
.Where(i => !i.Value.EqualsZero())
.Select(i => !i.Value.EqualsOne() ? Power.New(i.Key, Constant.New(i.Value)) : i.Key));
}
public static Expression EvaluateSum(IEnumerable<Expression> Terms)
{
// Map terms to their coefficients.
DefaultDictionary<Expression, Real> terms = new DefaultDictionary<Expression, Real>(0);
// Accumulate constants and sum coefficient of each term.
Real C = 0;
foreach (Expression i in Terms)
{
if (i is Constant)
{
C += (Real)i;
}
else
{
// Find constant term.
Constant coeff = Product.TermsOf(i).OfType<Constant>().FirstOrDefault();
if (!ReferenceEquals(coeff, null))
terms[Product.New(Product.TermsOf(i).ExceptUnique(coeff, Expression.RefComparer))] += (Real)coeff;
else
terms[i] += 1;
}
}
// Build a new expression with the accumulated terms.
if (!C.EqualsZero())
terms.Add(Constant.New(C), (Real)1);
return Sum.New(terms
.Where(i => !i.Value.EqualsZero())
.Select(i => !i.Value.EqualsOne() ? Product.New(i.Key, Constant.New(i.Value)) : i.Key));
}