internal static Entity SimplifyChildren(Entity expr)
{
return(expr.Replace(Patterns.InvertNegativePowers)
.Replace(Patterns.InvertNegativeMultipliers).Replace(
Patterns.SortRules(TreeAnalyzer.SortLevel.HIGH_LEVEL)
)
.InnerSimplified.Replace(Patterns.CommonRules).InnerSimplified);
}
/// <summary>Finds all alternative forms of an expression</summary>
internal static IEnumerable <Entity> Alternate(Entity src, int level)
{
if (src is Number or Variable or Entity.Boolean)
{
return new[] { src }
}
;
var stage1 = src.InnerSimplified;
if (stage1 is Number or Variable or Entity.Boolean)
{
return new[] { stage1 }
}
;
// List of criteria for expr's complexity
var history = new SortedDictionary <int, HashSet <Entity> >();
void AddHistory(Entity expr)
{
void __IterAddHistory(Entity expr)
{
static int CountExpressionComplexity(Entity expr) => MathS.Settings.ComplexityCriteria.Value(expr);
var refexpr = expr.Replace(Patterns.SortRules(TreeAnalyzer.SortLevel.HIGH_LEVEL)).InnerSimplified;
var compl1 = CountExpressionComplexity(refexpr);
var compl2 = CountExpressionComplexity(expr);
var n = compl1 > compl2 ? expr : refexpr;
var ncompl = Math.Min(compl2, compl1);
if (history.TryGetValue(ncompl, out var ncomplList))
{
ncomplList.Add(n);
}
else
{
history[ncompl] = new HashSet <Entity> {
n
}
};
}
__IterAddHistory(expr);
__IterAddHistory(expr.Replace(Patterns.InvertNegativePowers));
}
AddHistory(stage1);
var res = stage1;
for (int i = 0; i < Math.Abs(level); i++)
{
res = res.Replace(Patterns.SortRules(i switch
{
1 => TreeAnalyzer.SortLevel.MIDDLE_LEVEL,
2 => TreeAnalyzer.SortLevel.LOW_LEVEL,
_ => TreeAnalyzer.SortLevel.HIGH_LEVEL
})).InnerSimplified;
/// <summary>Finds all alternative forms of an expression</summary>
internal static IEnumerable <Entity> Alternate(Entity src, int level)
{
if (src is FiniteSet ss)
{
return new[] { ss.Apply(ent => ent.Simplify()).InnerSimplified }
}
;
if (src is Number or Variable or Entity.Boolean)
{
return new[] { src }
}
;
var stage1 = src.InnerSimplified;
if (stage1 is Number or Variable or Entity.Boolean)
{
return new[] { stage1 }
}
;
// List of criteria for expr's complexity
var history = new SortedDictionary <double, HashSet <Entity> >();
void AddHistory(Entity expr)
{
void __IterAddHistory(Entity expr)
{
var refexpr = expr.Replace(Patterns.SortRules(TreeAnalyzer.SortLevel.HIGH_LEVEL)).InnerSimplified;
var compl1 = refexpr.SimplifiedRate;
var compl2 = expr.SimplifiedRate;
var n = compl1 > compl2 ? expr : refexpr;
var ncompl = Math.Min(compl2, compl1);
if (history.TryGetValue(ncompl, out var ncomplList))
{
ncomplList.Add(n);
}
else
{
history[ncompl] = new HashSet <Entity> {
n
}
};
}
__IterAddHistory(expr);
__IterAddHistory(expr.Replace(Patterns.InvertNegativePowers));
MultithreadingFunctional.ExitIfCancelled();
}
AddHistory(stage1);
var res = stage1;
for (int i = 0; i < Math.Abs(level); i++)
{
res = res.Replace(Patterns.SortRules(i switch
{
1 => TreeAnalyzer.SortLevel.MIDDLE_LEVEL,
2 => TreeAnalyzer.SortLevel.LOW_LEVEL,
_ => TreeAnalyzer.SortLevel.HIGH_LEVEL
})).InnerSimplified;
if (res.Nodes.Any(child => child is Powf))
{
AddHistory(res = res.Replace(Patterns.PowerRules).InnerSimplified);
}
AddHistory(res = SimplifyChildren(res));
AddHistory(res = res.Replace(Patterns.InvertNegativePowers).Replace(Patterns.DivisionPreparingRules).InnerSimplified);
AddHistory(res = res.Replace(Patterns.PolynomialLongDivision).InnerSimplified);
if (res.Nodes.Any(child => child is TrigonometricFunction))
{
var res1 = res.Replace(Patterns.ExpandTrigonometricRules).InnerSimplified;
AddHistory(res = res.Replace(Patterns.TrigonometricRules).Replace(Patterns.CommonRules).InnerSimplified);
AddHistory(res1);
res = PickSimplest(res, res1);
AddHistory(res = res.Replace(Patterns.CollapseTrigonometricFunctions).Replace(Patterns.TrigonometricRules));
}
if (res.Nodes.Any(child => child is Statement))
{
AddHistory(res = res.Replace(Patterns.BooleanRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is ComparisonSign))
{
AddHistory(res = res.Replace(Patterns.InequalityEqualityRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is Factorialf))
{
AddHistory(res = res.Replace(Patterns.ExpandFactorialDivisions).InnerSimplified);
AddHistory(res = res.Replace(Patterns.FactorizeFactorialMultiplications).InnerSimplified);
}
if (res.Nodes.Any(child => child is Powf or Logf))
{
AddHistory(res = res.Replace(Patterns.PowerRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is Set))
{
AddHistory(res = res.Replace(Patterns.SetOperatorRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is Phif))
{
AddHistory(res = res.Replace(Patterns.PhiFunctionRules).InnerSimplified);
}
Entity?possiblePoly = null;
foreach (var var in res.Vars)
{
if (TryPolynomial(res, var, out var resPoly) &&
(possiblePoly is null || resPoly.Complexity < possiblePoly.Complexity))
{
AddHistory(possiblePoly = resPoly);
}
}
if (possiblePoly is { } && possiblePoly.Complexity < res.Complexity)
/// <summary>Finds all alternative forms of an expression</summary>
internal static IEnumerable <Entity> Alternate(Entity src, int level)
{
if (src is FiniteSet ss)
{
return new[] { ss.Apply(ent => ent.Simplify()).InnerSimplified }
}
;
if (src is Number or Variable or Entity.Boolean)
{
return new[] { src }
}
;
var stage1 = src.InnerSimplified;
#if DEBUG
if (MathS.Diagnostic.CatchOnSimplify.Value(stage1))
{
throw new MathS.Diagnostic.DiagnosticCatchException();
}
#endif
if (stage1 is Number or Variable or Entity.Boolean)
{
return new[] { stage1 }
}
;
// List of criteria for expr's complexity
var history = new SortedDictionary <double, HashSet <Entity> >();
void AddHistory(Entity expr)
{
#if DEBUG
if (MathS.Diagnostic.CatchOnSimplify.Value(expr))
{
throw new MathS.Diagnostic.DiagnosticCatchException();
}
#endif
void __IterAddHistory(Entity expr)
{
var refexpr = expr.Replace(Patterns.SortRules(TreeAnalyzer.SortLevel.HIGH_LEVEL)).InnerSimplified;
var compl1 = refexpr.SimplifiedRate;
var compl2 = expr.SimplifiedRate;
var n = compl1 > compl2 ? expr : refexpr;
var ncompl = Math.Min(compl2, compl1);
if (history.TryGetValue(ncompl, out var ncomplList))
{
ncomplList.Add(n);
}
else
{
history[ncompl] = new HashSet <Entity> {
n
}
};
}
__IterAddHistory(expr);
__IterAddHistory(expr.Replace(Patterns.InvertNegativePowers));
MultithreadingFunctional.ExitIfCancelled();
}
AddHistory(stage1);
var res = stage1;
for (int i = 0; i < Math.Abs(level); i++)
{
var sortLevel = i switch
{
1 => TreeAnalyzer.SortLevel.MIDDLE_LEVEL,
2 => TreeAnalyzer.SortLevel.LOW_LEVEL,
_ => TreeAnalyzer.SortLevel.HIGH_LEVEL
};
res = res.Replace(Patterns.SortRules(sortLevel)).InnerSimplified;
if (res.Nodes.Any(child => child is Powf))
{
AddHistory(res = res.Replace(Patterns.PowerRules).InnerSimplified);
}
AddHistory(res = SimplifyChildren(res));
AddHistory(res = res.Replace(Patterns.InvertNegativePowers).Replace(Patterns.DivisionPreparingRules).InnerSimplified);
AddHistory(res = res.Replace(Patterns.PolynomialLongDivision).InnerSimplified);
AddHistory(res = res.Replace(Patterns.NormalTrigonometricForm).InnerSimplified);
AddHistory(res = res.Replace(Patterns.CollapseMultipleFractions).InnerSimplified);
AddHistory(res = res.Replace(e => Patterns.FractionCommonDenominatorRules(e, sortLevel)).InnerSimplified);
AddHistory(res = res.Replace(Patterns.InvertNegativePowers).Replace(Patterns.DivisionPreparingRules).InnerSimplified);
AddHistory(res = res.Replace(Patterns.PowerRules).InnerSimplified);
AddHistory(res = res.Replace(Patterns.TrigonometricRules).InnerSimplified);
AddHistory(res = res.Replace(Patterns.CollapseTrigonometricFunctions).InnerSimplified);
if (res.Nodes.Any(child => child is TrigonometricFunction))
{
var res1 = res.Replace(Patterns.ExpandTrigonometricRules).InnerSimplified;
AddHistory(res = res.Replace(Patterns.TrigonometricRules).Replace(Patterns.CommonRules).InnerSimplified);
AddHistory(res1);
res = PickSimplest(res, res1);
AddHistory(res = res.Replace(Patterns.CollapseTrigonometricFunctions).Replace(Patterns.TrigonometricRules));
}
if (res.Nodes.Any(child => child is Statement))
{
AddHistory(res = res.Replace(Patterns.BooleanRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is ComparisonSign))
{
AddHistory(res = res.Replace(Patterns.InequalityEqualityRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is Factorialf))
{
AddHistory(res = res.Replace(Patterns.ExpandFactorialDivisions).InnerSimplified);
AddHistory(res = res.Replace(Patterns.FactorizeFactorialMultiplications).InnerSimplified);
}
if (res.Nodes.Any(child => child is Powf or Logf))
{
AddHistory(res = res.Replace(Patterns.PowerRules).InnerSimplified);
}
if (res.Nodes.Any(child => child is Set))
{
var replaced = res.Replace(Patterns.SetOperatorRules);
AddHistory(res = replaced.InnerSimplified);
}
if (res.Nodes.Any(child => child is Phif))
{
AddHistory(res = res.Replace(Patterns.PhiFunctionRules).InnerSimplified);
}
Entity?possiblePoly = null;
foreach (var var in res.Vars)
{
if (TryPolynomial(res, var, out var resPoly) &&
(possiblePoly is null || resPoly.Complexity < possiblePoly.Complexity))
{
AddHistory(possiblePoly = resPoly);
}
}
if (possiblePoly is { } && possiblePoly.Complexity < res.Complexity)
{
res = possiblePoly;
}
AddHistory(res = res.Replace(Patterns.CommonRules));
AddHistory(res = res.Replace(Patterns.NumericNeatRules));
/*
* This was intended to simplify expressions as polynomials over nodes, some kind of
* greatest common node and simplifying over it. However, the current algorithm does
* not solve this issue completely and yet too slow to be accepted.
*
* AddHistory(res = TreeAnalyzer.Factorize(res));
*/
res = history[history.Keys.Min()].First();
}
if (level > 0) // if level < 0 we don't check whether expanded version is better
{
AddHistory(res.Expand().Simplify(-level));
AddHistory(res.Factorize().Simplify(-level));
}
return(history.Values.SelectMany(x => x));
}
