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);
}
// solves equation f(sin(x), cos(x), tan(x), cot(x)) for x
internal static bool TrySolveLinear(Entity expr, Variable variable, out Set res)
{
res = Empty;
var replacement = Variable.CreateTemp(expr.Vars);
expr = expr.Replace(Patterns.NormalTrigonometricForm);
expr = expr.Replace(Patterns.TrigonometricToExponentialRules(variable, replacement));
MultithreadingFunctional.ExitIfCancelled();
// if there is still original variable after replacements,
// equation is not in a form f(sin(x), cos(x), tan(x), cot(x))
if (expr.ContainsNode(variable))
{
return(false);
}
if (AnalyticalEquationSolver.Solve(expr, replacement) is FiniteSet els)
{
MultithreadingFunctional.ExitIfCancelled();
res = (Set)els.Select(sol => MathS.Pow(MathS.e, MathS.i * variable).Invert(sol, variable).ToSet()).Unite().InnerSimplified;
return(true);
}
else
{
return(false);
}
}
/// <summary>Solves one equation</summary>
internal static Set Solve(Entity equation, Variable x)
{
using var _ = MathS.Settings.PrecisionErrorZeroRange.Set(1e-12m);
using var __ = MathS.Settings.FloatToRationalIterCount.Set(0);
using var ___ = MathS.Settings.MaxExpansionTermCount.Set(50);
var solutions = AnalyticalEquationSolver.Solve(equation, x);
/// <summary>Solves one equation</summary>
internal static Set Solve(Entity equation, Variable x)
{
var solutions = MathS.Settings.PrecisionErrorZeroRange.As(1e-12m, () =>
MathS.Settings.FloatToRationalIterCount.As(0, () =>
AnalyticalEquationSolver.Solve(equation, x)
));