public void TestInteger()
{
var actual = Rational.Create(3);
Assert.IsType <Integer>(actual);
Assert.Equal(Integer.Create(3), actual);
}
public void TestRationalDowncasting()
{
var frac21_10 = Rational.Create(21, 10);
Assert.IsType <Rational>(frac21_10);
Assert.Equal(frac21_10, frac21_10.EvalNumerical());
Assert.Equal(frac21_10, frac21_10.Simplify().EvalNumerical());
var squared = Entity.Number.Pow(frac21_10, 2);
Assert.IsType <Rational>(squared);
Assert.Equal(Rational.Create(441, 100), squared);
Assert.Equal(squared, squared.EvalNumerical());
Assert.Equal(squared, squared.Simplify().EvalNumerical());
var cubed = Entity.Number.Pow(squared, Rational.Create(3, 2));
Assert.IsType <Rational>(cubed);
Assert.Equal(Rational.Create(9261, 1000), cubed);
Assert.Equal(cubed, cubed.EvalNumerical());
Assert.Equal(cubed, cubed.Simplify().EvalNumerical());
var ten = cubed + Rational.Create(739, 1000);
Assert.IsType <Integer>(ten);
Assert.Equal(Integer.Create(10), ten);
Assert.Equal(ten, ten.EvalNumerical());
Assert.Equal(ten, ten.Simplify().EvalNumerical());
}
/// <summary>Solves ax^3 + bx^2 + cx + d</summary>
/// <param name="a">Coefficient of x^3</param>
/// <param name="b">Coefficient of x^2</param>
/// <param name="c">Coefficient of x</param>
/// <param name="d">Free coefficient</param>
/// <returns>Set of roots</returns>
internal static IEnumerable <Entity> SolveCubic(Entity a, Entity b, Entity c, Entity d)
{
// en: https://en.wikipedia.org/wiki/Cubic_equation
// ru: https://ru.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0_%D0%9A%D0%B0%D1%80%D0%B4%D0%B0%D0%BD%D0%BE
if (TreeAnalyzer.IsZero(d))
{
return(SolveQuadratic(a, b, c).Append(0));
}
if (TreeAnalyzer.IsZero(a))
{
return(SolveQuadratic(b, c, d));
}
var coeff = MathS.i * MathS.Sqrt(3) / 2;
var u1 = Integer.Create(1);
var u2 = Rational.Create(-1, 2) + coeff;
var u3 = Rational.Create(-1, 2) - coeff;
var D0 = MathS.Sqr(b) - 3 * a * c;
var D1 = (2 * MathS.Pow(b, 3) - 9 * a * b * c + 27 * MathS.Sqr(a) * d).InnerSimplified;
var C = MathS.Pow((D1 + MathS.Sqrt(MathS.Sqr(D1) - 4 * MathS.Pow(D0, 3))) / 2, Rational.Create(1, 3));
return(new[] { u1, u2, u3 }.Select(uk =>
C.Evaled == 0 && D0.Evaled == 0 ? -(b + uk * C) / 3 / a : -(b + uk * C + D0 / C / uk) / 3 / a));
}
public void TestWithUndefined8()
{
var x = Rational.Create(-1, 2);
Assert.IsType <Rational>(x);
Assert.Equal(Real.NaN, x / 0);
}
public void TestWithUndefined9()
{
var x = Rational.Create(-1, 2);
var result = x / Real.PositiveInfinity;
Assert.IsType <Integer>(result);
Assert.Equal(0, result);
}
public void TestWithUndefined6()
{
var a = Real.Create(4);
var b = Rational.Create(0, 6);
Assert.IsType <Integer>(b);
Assert.Equal(Real.NaN, a / b);
}
/// <summary>Solves ax^4 + bx^3 + cx^2 + dx + e</summary>
/// <param name="a">Coefficient of x^4</param>
/// <param name="b">Coefficient of x^3</param>
/// <param name="c">Coefficient of x^2</param>
/// <param name="d">Coefficient of x</param>
/// <param name="e">Free coefficient</param>
/// <returns>Set of roots</returns>
internal static IEnumerable <Entity> SolveQuartic(Entity a, Entity b, Entity c, Entity d, Entity e)
{
// en: https://en.wikipedia.org/wiki/Quartic_function
// ru: https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%A4%D0%B5%D1%80%D1%80%D0%B0%D1%80%D0%B8
if (TreeAnalyzer.IsZero(e))
{
return(SolveCubic(a, b, c, d).Append(0));
}
if (TreeAnalyzer.IsZero(a))
{
return(SolveCubic(b, c, d, e));
}
var alpha = (-3 * MathS.Sqr(b) / (8 * MathS.Sqr(a)) + c / a)
.InnerSimplified;
var beta = (MathS.Pow(b, 3) / (8 * MathS.Pow(a, 3)) - (b * c) / (2 * MathS.Sqr(a)) + d / a)
.InnerSimplified;
var gamma = (-3 * MathS.Pow(b, 4) / (256 * MathS.Pow(a, 4)) + MathS.Sqr(b) * c / (16 * MathS.Pow(a, 3)) - (b * d) / (4 * MathS.Sqr(a)) + e / a)
.InnerSimplified;
if (beta.Evaled == 0)
{
return(sqrtsOf1.SelectMany(_ => sqrtsOf1,
(s, t) => - b / 4 * a + s * MathS.Sqrt((-alpha + t * MathS.Sqrt(MathS.Sqr(alpha) - 4 * gamma)) / 2)));
}
var oneThird = Rational.Create(1, 3);
var P = (-MathS.Sqr(alpha) / 12 - gamma)
.InnerSimplified;
var Q = (-MathS.Pow(alpha, 3) / 108 + alpha * gamma / 3 - MathS.Sqr(beta) / 8)
.InnerSimplified;
var R = -Q / 2 + MathS.Sqrt(MathS.Sqr(Q) / 4 + MathS.Pow(P, 3) / 27);
var U = MathS.Pow(R, oneThird)
.InnerSimplified;
var y = (Rational.Create(-5, 6) * alpha + U + (U.Evaled == 0 ? -MathS.Pow(Q, oneThird) : -P / (3 * U)))
.InnerSimplified;
var W = MathS.Sqrt(alpha + 2 * y)
.InnerSimplified;
// Now we need to permutate all four combinations
return(sqrtsOf1.SelectMany(_ => sqrtsOf1,
(s, t) => - b / (4 * a) + (s * W + t * MathS.Sqrt(-(3 * alpha + 2 * y + s * 2 * beta / W))) / 2));
}
private static GraceObject mNumeric(EvaluationContext ctx,
MethodRequest req,
CodepointObject self)
{
// By convention, return -1 for non-numeric codepoints.
if (self.parts[7] == "")
{
return(GraceNumber.Create(-1));
}
int val;
if (int.TryParse(self.parts[7], out val))
{
return(GraceNumber.Create(val));
}
// At this point, it must be a fraction n/m.
var bits = self.parts[7].Split('/');
var rat = Rational.Create(int.Parse(bits[0]), int.Parse(bits[1]));
return(GraceNumber.Create(rat));
}
public void TestRational3() =>
Assert.Equal(Rational.Create(15, 4),
Rational.Create(7, 4) + Rational.Create(8, 4));
public void TestRational2() => Assert.Equal(Rational.Create(7, 4), Rational.Create(3, 4) + 1);
public void TestRational1() =>
Assert.Equal(Rational.Create(19, 12),
Rational.Create(3, 4) + Rational.Create(5, 6));
private GraceNumber(double val)
: base(createSharedMethods())
{
Value = Rational.Create(val);
}
