public void TryDivide_ByTerm_BySupersetVariables_9x_x()
{
PolynomialTerm x = 'x';
(9 * x).TryDivide(x, out PolynomialTerm r).AssertIsTrue();
r.AssertIsEqualTo(9);
}
public void TryDivide_ByTerm_BySupersetVariables_xy_y()
{
PolynomialTerm x = 'x';
PolynomialTerm y = 'y';
x.TryDivide(x * y, out _).AssertIsFalse();
}
public void Simplify_To_Zero()
{
PolynomialTerm v1 = 2 * Term.a * Term.c.ToPower(3);
PolynomialTerm v2 = -2 * Term.a * Term.c.ToPower(3);
PolynomialTerm.Simplify(new[] { v1, v2 }).AssertIsEmpty();
}
public void TryDivide_ByConstant()
{
PolynomialTerm x = 'x';
(2 * x).TryDivide(2, out PolynomialTerm r).AssertIsTrue();
r.AssertIsEqualTo(x);
}
public void Multiply_Variables()
{
PolynomialTerm v1 = 2 * Term.a * Term.c.ToPower(3);
PolynomialTerm v2 = 3 * Term.a.ToPower(2) * Term.d.ToPower(2);
(v1 * v2).AssertIsEqualTo(6 * Term.a.ToPower(3) * Term.d.ToPower(2) * Term.c.ToPower(3));
}
public void Equality_Zero()
{
PolynomialTerm zero = 0;
(zero / _x).AssertIsEqualTo(0);
(zero / _y).AssertIsEqualTo(zero / _x);
(zero / _y).AssertIsEqualTo(0 * (_x / _y));
}
public void TryDivide_BySubsetTerm()
{
PolynomialTerm x = 'x';
PolynomialTerm y = 'y';
(2 * x.ToPower(3) * y.ToPower(2)).TryDivide(0.5 * x, out PolynomialTerm r).AssertIsTrue();
r.AssertIsEqualTo(4 * x.ToPower(2) * y.ToPower(2));
}
public void Multiply_Inline()
{
PolynomialTerm x = 'x';
(4 * x * x).AssertIsEqualTo(4 * Term.x.ToPower(2));
(4 * x * x).ToString().AssertIsEqualTo("4x²");
(x * x).GetOperation('x').Value(4).AssertIsEqualTo(16);
}
public void Simplify_To_Sum()
{
PolynomialTerm a = 'a';
PolynomialTerm b = 'b';
PolynomialTerm c = 'c';
var expected = new PolynomialTerm[] { a *b *c, a *a, b *b, a *b, a, 2 *b, 3 };
var before = new PolynomialTerm[] { 1, b, 2, b, a, a *b, a *b *c, a *a, b *b };
PolynomialTerm.Simplify(before).AssertSequenceEqualsTo(expected);
}
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 Constructor_Variable()
{
PolynomialTerm v = 'a';
(v == 0).AssertIsFalse();
v.IsConstant.AssertIsFalse();
v.PowerSum.AssertIsEqualTo(1u);
v.GreatestPowerIndeterminate.Variable.AssertIsEqualTo('a');
v.GreatestPowerIndeterminate.Power.AssertIsEqualTo(1);
v.ToString().AssertIsEqualTo("a");
('b' == v).AssertIsFalse();
v.DerivativeBy('a').Single().AssertIsEqualTo(1);
v.DerivativeBy('b').AssertIsEmpty();
(2 * v).AssertIsEqualTo(2 * Term.a);
(v / 2).AssertIsEqualTo(0.5 * Term.a);
v.GetOperation('a').Value(5).AssertIsEqualTo(5);
}
public void Constructor_Default()
{
PolynomialTerm v = default;
(v == 0).AssertIsTrue();
v.IsConstant.AssertIsTrue();
v.ToString().AssertIsEqualTo("0");
v.PowerSum.AssertIsEqualTo(0u);
v.GreatestPowerIndeterminate.Variable.AssertIsEqualTo((char)0);
v.GreatestPowerIndeterminate.Power.AssertIsEqualTo(0);
v.AssertIsEqualTo(0);
(1 == v).AssertIsFalse();
v.DerivativeBy('a').AssertIsEmpty();
(2 * v).AssertIsEqualTo(0);
(v / 2).AssertIsEqualTo(0);
v.GetOperation().Value().AssertIsEqualTo(0);
}
public void Constructor_PolynomialVariable()
{
PolynomialTerm v = 2.1 * Term.a * Term.c.ToPower(3);
(v == 0).AssertIsFalse();
v.IsConstant.AssertIsFalse();
v.ToString().AssertIsEqualTo("2.1ac³");
v.PowerSum.AssertIsEqualTo(4u);
v.GreatestPowerIndeterminate.Variable.AssertIsEqualTo('c');
v.GreatestPowerIndeterminate.Power.AssertIsEqualTo(3);
v.DerivativeBy('a').Single().AssertIsEqualTo(2.1 * Term.c.ToPower(3));
v.DerivativeBy('b').AssertIsEmpty();
v.DerivativeBy('c').Single().AssertIsEqualTo(6.3 * Term.c.ToPower(2) * Term.a.ToPower(1));
v.DerivativeBy('a').DerivativeBy('c').Single().AssertIsEqualTo(6.3 * Term.c.ToPower(2));
(-2 * v).AssertIsEqualTo(-4.2 * Term.a * Term.c.ToPower(3));
v.GetOperation('a', 'c').Value(5, 2).AssertIsEqualTo(2.1 * 5 * 8);
}
public void Power_ByZero()
{
PolynomialTerm x = 'x';
x.ToPower(0).AssertIsEqualTo(1);
}
public void TryDivide_ByTerm_BySupersetPowers()
{
PolynomialTerm x = 'x';
x.TryDivide(x * x, out _).AssertIsFalse();
}
public void Cos_Variable()
{
PolynomialTerm.Cos(Term.a).AssertIsEqualTo(IndeterminateExpression.Cos('a'));
}
public void Sin_Variable()
{
PolynomialTerm.Sin(Term.a).AssertIsEqualTo(IndeterminateExpression.Sin('a'));
}
public static PolynomialTerm Cos(PolynomialTerm term) => IndeterminateExpression.Cos((char)term);
public void Sin_Constant()
{
PolynomialTerm term = Math.PI / 2;
PolynomialTerm.Sin(term).AssertIsEqualTo(1);
}
public void Power_ByOne()
{
PolynomialTerm x = 'x';
x.ToPower(1).AssertIsEqualTo(x);
}
public void Cos_Constant()
{
PolynomialTerm term = 0;
PolynomialTerm.Cos(term).AssertIsEqualTo(1);
}
public void Power_ByTwo()
{
PolynomialTerm x = 'x';
x.ToPower(2).AssertIsEqualTo(x * x);
}
public void TryDivide_ByZero()
{
PolynomialTerm x = 'x';
x.TryDivide(0, out _).AssertIsFalse();
}
public static PolynomialTerm Sin(PolynomialTerm term) => IndeterminateExpression.Sin((char)term);
