internal static Set?SolveLinear(Entity expr, Entity.Variable x)
{
var replacement = Variable.CreateTemp(expr.Vars);
Func <Entity, Entity> preparator = e => e switch
{
Powf(var @base, var arg) when
TreeAnalyzer.TryGetPolyLinear(arg, x, out var a, out var b) =>
MathS.Pow(@base, b) * MathS.Pow(MathS.Pow(MathS.e, x), MathS.Ln(@base) * a),
_ => e,
};
Func <Entity, Entity> replacer = e => e switch
{
Powf(var @base, var arg)
when @base == MathS.e && arg == x
=> replacement,
_ => e,
};
expr = expr.Replace(preparator);
expr = expr.Replace(replacer);
if (expr.ContainsNode(x))
{
return(null); // cannot be solved, not a pure exponential
}
expr = expr.InnerSimplified;
if (AnalyticalEquationSolver.Solve(expr, replacement) is FiniteSet els && els.Any())
{
return((Set)els.Select(sol => MathS.Pow(MathS.e, x).Invert(sol, x).ToSet()).Unite().InnerSimplified);
}
public void TestComplex()
{
var expr = MathS.FromString("ln(x) + sqrt(x) + tan(x) + sec(x) + cosec(x) + cotan(x)");
var expected = MathS.Ln(x) + MathS.Sqrt(x) +
MathS.Tan(x) + MathS.Sec(x) + MathS.Cosec(x) +
MathS.Cotan(x);
Assert.IsTrue(expr == expected);
}
public DerivationTest()
{
IterCount = 10000;
tests = new List <Func <object> > {
() => x.Derive(x),
() => (MathS.Cos(x) * MathS.Sin(x)).Derive(x),
() => (MathS.Sqr(MathS.Sin(x + 2 * y)) + MathS.Sqr(MathS.Cos(x + 2 * y))).Derive(x),
() => (x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))).Derive(x)
};
}
public SubsTest()
{
IterCount = 10000;
tests = new List <Func <object> > {
() => (x * MathS.Sin(x)).Substitute(x, 3).Eval(),
() => (MathS.Cos(x) * MathS.Sin(x)).Substitute(x, 3).Eval(),
() => (MathS.Sqr(MathS.Sin(x + 2 * x)) + MathS.Sqr(MathS.Cos(x + 2 * x))).Substitute(x, 3).Eval(),
() => (x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))).Substitute(x, 3).Eval()
};
}
public SimplificationTest()
{
IterCount = 1500;
tests = new List <Func <object> > {
() => (x * MathS.Sin(x)).Simplify(),
() => (MathS.Cos(x) * MathS.Sin(x)).Simplify(),
() => (MathS.Sqr(MathS.Sin(x + 2 * y)) + MathS.Sqr(MathS.Cos(x + 2 * y))).Simplify(),
() => (x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))
* x * MathS.Cos(x) / MathS.Sin(MathS.Sqrt(x / MathS.Ln(x)))).Simplify()
};
}
[Fact] public void Test31() => TestLimit("ln(ln((e^2*x + t) / (x + 1)))", Real.PositiveInfinity, ApproachFrom.Left, MathS.Ln(2));
[Fact] public void Test25() => TestLimit("ln((x - 1) / (2x + 1))", Real.PositiveInfinity, ApproachFrom.Right, MathS.Ln(0.5));
[TestMethod] public void Ln() => Test(@"\ln\left(10\right)", MathS.Ln(10));
public void Test6() => Assert.IsTrue(Measure(() => (x * MathS.Pow(MathS.e, x) * MathS.Ln(x) - MathS.Sqrt(x / (x * x - 1))).Derive(x).Substitute(x, 3).Eval()) < 50);
public void Test5() => Assert.IsTrue(Measure(() => (x * MathS.Pow(MathS.e, x) * MathS.Ln(x) - MathS.Sqrt(x / (x * x - 1))).Derive(x)) < 30);
[Fact] public void Ln() => Test(@"\ln\left(10\right)", MathS.Ln(10));
TreeAnalyzer.TryGetPolyLinear(arg, x, out var a, out _) => MathS.Ln(MathS.Sin(arg)) / a,