public static PolynomialMonomial operator +(PolynomialMonomial f, PolynomialMonomial g)
{
if (f is null || g is null)
{
throw new ArgumentNullException();
}
if (!f.VariableName.Equals(g.VariableName))
{
throw new PolynomialMonomialVariableNameException(f, g);
}
var result = new RationalMonomialsNumber[Math.Max(f.Degree, g.Degree) + 1];
var minDegree = Math.Min(f.Degree, g.Degree);
for (var d = 0; d <= minDegree; ++d)
{
result[d] = f[d] + g[d];
}
for (var d = minDegree + 1; d <= f.Degree; ++d)
{
result[d] = f[d];
}
for (var d = minDegree + 1; d <= g.Degree; ++d)
{
result[d] = g[d];
}
return(new PolynomialMonomial(result, f.VariableName));
}
private static (PolynomialMonomial, PolynomialMonomial) DivisionWithRemainder(PolynomialMonomial f,
PolynomialMonomial g)
{
var resultLength = Math.Max(f.Degree - g.Degree + 1, 0);
var result = new RationalMonomialsNumber[resultLength];
var fCoefficients = (RationalMonomialsNumber[])f._coefficients.Clone();
var leadingG = g[g.Degree];
for (var d1 = f.Degree; d1 >= g.Degree; --d1)
{
if (fCoefficients[d1].IsZero)
{
continue;
}
var newCoefficient = fCoefficients[d1] / leadingG;
var monomDegree = d1 - g.Degree;
result[monomDegree] = newCoefficient;
for (var d2 = 0; d2 <= g.Degree; ++d2)
{
fCoefficients[monomDegree + d2] -= newCoefficient * g[d2];
}
}
var q = new PolynomialMonomial(result, f.VariableName);
var r = new PolynomialMonomial(fCoefficients, f.VariableName);
return(q, r);
}
public PolynomialMonomial SetSigns(List <Sign> signs)
{
if (signs.Count > _coefficients.Length)
{
throw new ArgumentException();
}
var newCoef = new RationalMonomialsNumber[_coefficients.Length + 1];
var degree = Degree;
foreach (var s in signs)
{
newCoef[degree] = _coefficients[degree].SetSign(s);
degree--;
}
while (degree >= 0)
{
newCoef[degree] = _coefficients[degree];
degree--;
}
return(new PolynomialMonomial(newCoef, VariableName));
}
public PolynomialMonomial GetDerivative()
{
if (IsZero)
{
return(this);
}
var result = new RationalMonomialsNumber[Degree];
for (var d = 1; d <= Degree; d++)
{
result[d - 1] = this[d] * d;
}
return(new PolynomialMonomial(result, VariableName));
}
public static PolynomialMonomial operator *(PolynomialMonomial f, PolynomialMonomial g)
{
if (f is null || g is null)
{
throw new ArgumentNullException();
}
if (!f.VariableName.Equals(g.VariableName))
{
throw new PolynomialMonomialVariableNameException(f, g);
}
if (f.IsZero)
{
return(f);
}
if (g.IsZero)
{
return(g);
}
var result = new RationalMonomialsNumber[f.Degree + g.Degree + 1];
for (var i = 0; i < result.Length; ++i)
{
result[i] = new RationalMonomialsNumber(0, 1);
}
for (var d1 = 0; d1 <= f.Degree; ++d1)
{
for (var d2 = 0; d2 <= g.Degree; ++d2)
{
result[d1 + d2] += f[d1] * g[d2];
}
}
return(new PolynomialMonomial(result, f.VariableName));
}
public RationalMonomialsNumber Pow(int degree)
{
if (degree < 0)
{
throw new ArgumentOutOfRangeException();
}
RationalMonomialsNumber res = 1;
var cur = this;
while (degree != 0)
{
if (degree % 2 == 1)
{
res *= cur;
}
degree /= 2;
cur *= cur;
}
return(res);
}
public Hypothesis(RationalMonomialsNumber number, Sign sign)
{
Number = number;
Sign = sign;
}
public static RationalMonomialsNumber Inverse(RationalMonomialsNumber number)
{
return(number.Inverse());
}
public bool Equals(RationalMonomialsNumber other)
{
return(_numerator.Equals(other._numerator) && _denominator.Equals(other._denominator));
}