// a * b * c / (b * c * d)
// =>
// a * (b / b) * (c / c) * 1/d
private static IEnumerable <Entity> PairwiseGrouping(Entity num, Entity den, TreeAnalyzer.SortLevel level)
{
var numFactors = Mulf.LinearChildren(num);
var denFactors = Mulf.LinearChildren(den);
var factors = new Dictionary <string, Entity>();
foreach (var numFactor in numFactors)
{
var sorted = numFactor.SortHash(level);
if (!factors.ContainsKey(sorted))
{
factors[sorted] = 1;
}
factors[sorted] = (factors[sorted] * numFactor).InnerSimplified;
}
foreach (var denFactor in denFactors)
{
var sorted = denFactor.SortHash(level);
if (!factors.ContainsKey(sorted))
{
factors[sorted] = 1;
}
factors[sorted] = (factors[sorted] / denFactor).InnerSimplified;
}
return(factors.Values);
}
internal static bool TrySolve(Entity expr, Variable x, out Set dst)
{
dst = Set.Empty;
var children = TreeAnalyzer.GatherLinearChildrenOverSumAndExpand(
expr, entity => entity.ContainsNode(x)
);
if (children is null)
{
return(false);
}
Entity normalPolynom = 0;
var fractioned = new List <(Entity multiplier, List <(Entity main, Integer pow)> fracs)>();
// Use PowerRules to replace sqrt(f(x))^2 => f(x)
foreach (var child in children.Select(c => c.InnerSimplified.Replace(Patterns.PowerRules)))
{
(Entity multiplier, List <(Entity main, Integer pow)> fracs)potentialFraction;
potentialFraction.multiplier = 1;
potentialFraction.fracs = new List <(Entity main, Integer pow)>();
foreach (var mpChild in Mulf.LinearChildren(child))
{
if (!(mpChild is Powf(var @base, Number num and not Integer))) // (x + 3) ^ 3
{
potentialFraction.multiplier *= mpChild;
continue;
}
if (num is not Rational fracNum)
{
return(false); // (x + 1)^0.2348728
}
var newChild = MathS.Pow(@base, fracNum.ERational.Numerator).InnerSimplified;
var den = fracNum.ERational.Denominator;
potentialFraction.fracs.Add((newChild, den));
MultithreadingFunctional.ExitIfCancelled();
}
if (potentialFraction.fracs.Count > 0)
{
fractioned.Add(potentialFraction);
}
else
{
normalPolynom += child;
}
}
if (fractioned.Count == 0)
{
return(false); // means that one can either be solved polynomially or unsolvable at all
}