Пример #1
0
        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);
            }
Пример #2
0
        // 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);
            }
        }
Пример #3
0
 /// <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);
Пример #4
0
 /// <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)
                                                                                                          ));