/// <summary>
/// Considers expr > 0
/// </summary>
internal static Set Solve(Entity expr, Variable x)
{
{
if (MathS.Utils.TryGetPolyLinear(expr, x, out var a, out var b))
{
a = a.InnerSimplified;
b = b.InnerSimplified;
var root = PolynomialSolver.SolveLinear(a, b).First();
if (root is Complex and not Real)
{
return(Empty);
}
if (a is Real {
IsNegative : true
})
internal static void Solve(Entity expr, VariableEntity x, Set dst, bool compensateSolving)
{
if (expr == x)
{
dst.Add(0);
return;
}
// Applies an attempt to downcast roots
void DestinationAddRange(Set toAdd)
{
toAdd.FiniteApply(ent => TryDowncast(expr, x, ent));
dst.AddRange(toAdd);
}
var polyexpr = expr.DeepCopy();
Set res = PolynomialSolver.SolveAsPolynomial(polyexpr, x);
if (res != null)
{
res.FiniteApply(e => e.InnerSimplify());
DestinationAddRange(res);
return;
}
if (expr.entType == Entity.EntType.OPERATOR)
{
switch (expr.Name)
{
case "mulf":
Solve(expr.Children[0], x, dst);
Solve(expr.Children[1], x, dst);
return;
case "divf":
bool IsSetNumeric(Set a)
=> a.Select(piece => piece.LowerBound().Item1).All(MathS.CanBeEvaluated);
var zeroNumerators = new Set();
Solve(expr.Children[0], x, zeroNumerators);
if (!IsSetNumeric(zeroNumerators))
{
dst.AddRange(zeroNumerators);
return;
}
var zeroDenominators = new Set();
Solve(expr.Children[1], x, zeroDenominators);
if (!IsSetNumeric(zeroDenominators))
{
dst.AddRange(zeroNumerators);
return;
}
dst.AddRange((zeroNumerators & !zeroDenominators) as Set);
return;
case "powf":
Solve(expr.Children[0], x, dst);
return;
case "minusf":
if (expr.Children[1].FindSubtree(x) == null && compensateSolving)
{
if (expr.Children[0] == x)
{
dst.Add(expr.Children[1]);
return;
}
var subs = 0;
Entity lastChild = null;
foreach (var child in expr.Children[0].Children)
{
if (child.FindSubtree(x) != null)
{
subs += 1;
lastChild = child;
}
}
if (subs != 1)
{
break;
}
var resInverted = TreeAnalyzer.FindInvertExpression(expr.Children[0], expr.Children[1], lastChild);
foreach (var result in resInverted.FiniteSet())
{
Solve(lastChild - result, x, dst, compensateSolving: true);
}
return;
}
break;
}
}
else if (expr.entType == Entity.EntType.FUNCTION)
{
DestinationAddRange(TreeAnalyzer.InvertFunctionEntity(expr as FunctionEntity, 0, x));
return;
}
// Here we generate a unique variable name
var uniqVars = MathS.Utils.GetUniqueVariables(expr);
uniqVars.Pieces.Sort((a, b) => ((Entity)b).Name.Length.CompareTo(((Entity)a).Name.Length));
VariableEntity newVar = ((Entity)uniqVars.Pieces[0]).Name + "quack";
// // //
// Here we find all possible replacements
var replacements = new List <Tuple <Entity, Entity> >();
replacements.Add(new Tuple <Entity, Entity>(TreeAnalyzer.GetMinimumSubtree(expr, x), expr));
foreach (var alt in expr.Alternate(4).FiniteSet())
{
if ((alt).FindSubtree(x) == null)
{
return; // in this case there is either 0 or +oo solutions
}
replacements.Add(new Tuple <Entity, Entity>(TreeAnalyzer.GetMinimumSubtree(alt, x), alt));
}
// // //
// Here we find one that has at least one solution
foreach (var replacement in replacements)
{
Set solutions = null;
if (replacement.Item1 == x)
{
continue;
}
var newExpr = replacement.Item2.DeepCopy();
TreeAnalyzer.FindAndReplace(ref newExpr, replacement.Item1, newVar);
solutions = newExpr.SolveEquation(newVar);
if (!solutions.IsEmpty())
{
var bestReplacement = replacement.Item1;
// Here we are trying to solve for this replacement
Set newDst = new Set();
foreach (var solution in solutions.FiniteSet())
{
var str = bestReplacement.ToString();
// TODO: make a smarter comparison than just comparison of complexities of two expressions
// The idea is
// similarToPrevious = ((bestReplacement - solution) - expr).Simplify() == 0
// But Simplify costs us too much time
var similarToPrevious = (bestReplacement - solution).Complexity() >= expr.Complexity();
if (!compensateSolving || !similarToPrevious)
{
Solve(bestReplacement - solution, x, newDst, compensateSolving: true);
}
}
DestinationAddRange(newDst);
if (!dst.IsEmpty())
{
break;
}
// // //
}
}
// // //
// if no replacement worked, try trigonometry solver
if (dst.IsEmpty())
{
var trigexpr = expr.DeepCopy();
res = TrigonometricSolver.SolveLinear(trigexpr, x);
if (res != null)
{
DestinationAddRange(res);
return;
}
}
// // //
// if nothing has been found so far
if (dst.IsEmpty() && MathS.Settings.AllowNewton)
{
Set allVars = new Set();
TreeAnalyzer._GetUniqueVariables(expr, allVars);
if (allVars.Count == 1)
{
DestinationAddRange(expr.SolveNt(x));
}
}
}
