public void Constructor_Polynomial()
{
Polynomial constant = 1;
PolynomialDivision v = _x / constant;
v.IsPolynomial.AssertIsTrue();
v.IsConstant.AssertIsFalse();
v.ToString().AssertIsEqualTo("x");
}
public void Constructor_PolynomialDivision()
{
PolynomialDivision v = _x / _y;
(v == 0).AssertIsFalse();
v.IsPolynomial.AssertIsFalse();
v.IsConstant.AssertIsFalse();
v.GetOperation('x', 'y').Value(10, 2).AssertIsEqualTo(5);
}
public void TryDivideBy_Polynomial()
{
PolynomialDivision numerator = (_x - 1) * (_x + 2);
// test
PolynomialDivision result;
numerator.TryDivideBy(_x - 1, out result).AssertIsTrue();
result.AssertIsEqualTo(_x + 2);
}
private static void EqualityAfterTransformation(PolynomialDivision polynomial)
{
var cartesianPoint = new Number[] { Term.x, Term.y, Term.z };
var sphericalPoint = new HypersphericalCoordinate(Term.r, new Number[] { Term.θ, Term.φ });
PolynomialDivision sphericalPolynomial = polynomial.ToSpherical(cartesianPoint, sphericalPoint);
double sqrt2 = Math.Sqrt(2);
double sqrt3 = Math.Sqrt(3);
Number polynomialResult = polynomial.GetOperation(Term.x, Term.y, Term.z).Value(sqrt2, sqrt2, 2 * sqrt3);
double sphericalResult = sphericalPolynomial.GetOperation(Term.r, Term.θ, Term.φ).Value(4, Math.PI / 4, Math.PI / 3);
polynomialResult.AssertIsEqualTo(sphericalResult);
}
public void GeneralizationForSum()
{
PolynomialDivision last = default;
for (uint i = 2; i <= 5; ++i)
{
PolynomialDivision current = GetSum(i);
if (last != default)
{
last.AssertIsEqualTo(current.Composition(Number.GreekTerm(i - 2), 0));
}
last = current;
}
}
public void Constructor_Default()
{
PolynomialDivision v = default;
v.AssertIsEqualTo(0);
(v == 0).AssertIsTrue();
v.IsPolynomial.AssertIsTrue();
v.IsConstant.AssertIsTrue();
v.ToString().AssertIsEqualTo("0");
v.DerivativeBy('a').AssertIsEqualTo(0);
(2 * v).AssertIsEqualTo(0);
(v / 2).AssertIsEqualTo(0);
v.GetOperation().Value().AssertIsEqualTo(0);
}
public void Constructor_Variable()
{
PolynomialDivision v = 'a';
(v == 0).AssertIsFalse();
v.IsConstant.AssertIsFalse();
v.IsPolynomial.AssertIsTrue();
v.ToString().AssertIsEqualTo("a");
((PolynomialTerm)v).AssertIsEqualTo('a');
v.DerivativeBy('a').AssertIsEqualTo(1);
v.DerivativeBy('b').AssertIsEqualTo(0);
(2 * v).AssertIsEqualTo(2 * Term.a);
(v / 2).AssertIsEqualTo(0.5 * Term.a);
v.GetOperation('a').Value(5).AssertIsEqualTo(5);
}
public void Constructor_Constant()
{
PolynomialDivision v = 2;
(v == 0).AssertIsFalse();
v.IsPolynomial.AssertIsTrue();
v.IsConstant.AssertIsTrue();
v.ToString().AssertIsEqualTo("2");
v.AssertIsEqualTo(2);
(1 == v).AssertIsFalse();
(0 == v).AssertIsFalse();
v.DerivativeBy('a').AssertIsEqualTo(0);
(2 * v).AssertIsEqualTo(4);
(v / 2).AssertIsEqualTo(1);
v.GetOperation().Value().AssertIsEqualTo(2);
}
public void GetCartesianAxisViewsRatiosDerivativesByAngle()
{
var sphericalPoint = new HypersphericalCoordinate(r, new Number[] { α, β, γ, δ });
Span <Number> cartesianActual = new Number[5];
sphericalPoint.ToCartesian(in cartesianActual);
for (ushort anglePos = 0; anglePos < sphericalPoint.Angles.Length; ++anglePos)
{
PolynomialTerm angleTerm = (PolynomialTerm)sphericalPoint.Angles.Span[anglePos];
var derivatives = new HypersphericalCoordinateOnAxisViewForAngleDerivatives(sphericalPoint, anglePos: anglePos).DerivativesCartesianVector;
derivatives.Length.AssertIsEqualTo(sphericalPoint.DimensionsCount);
for (ushort coordinatePos = 0; coordinatePos < cartesianActual.Length; ++coordinatePos)
{
PolynomialDivision coordinate = (PolynomialDivision)cartesianActual[coordinatePos];
PolynomialDivision expected = coordinate.DerivativeBy(angleTerm);
derivatives[coordinatePos].AssertIsEqualTo(expected);
}
}
}
public void Composition_Division()
{
PolynomialDivision entry = _x / (_x + 1);
entry.Composition(_x, _y / _x).AssertIsEqualTo(_y / (_x + _y));
}
public void Composition_Square()
{
PolynomialDivision entry = (_x + 1) / (_x - 1);
entry.Composition((char)_x, _y + 1).AssertIsEqualTo((_y + 2) / _y);
}
