/// <summary>
/// Returns a list of linear children over sum
/// where at most one term doesn't contain x, e. g.
/// x2 + x + a + b + x
/// =>
/// [x2, x, a + b, x]
/// </summary>
internal static List <Entity>?GatherLinearChildrenOverSumAndExpand(Entity expr, Func <Entity, bool> conditionForUniqueTerms)
{
if (expr is not(Sumf or Minusf))
{
return(SmartExpandOver(expr, conditionForUniqueTerms));
}
var res = new List <Entity>();
Entity?freeTerm = null;
foreach (var child in Sumf.LinearChildren(expr))
{
if (conditionForUniqueTerms(child))
{
var expanded = SmartExpandOver(child, conditionForUniqueTerms);
if (expanded is null)
{
return(null);
}
res.AddRange(expanded);
}
else
{
freeTerm = freeTerm is { }
}
}
/// <summary>
/// Finds all monomials with respect to the power of <paramref name="variable"/>
/// </summary>
internal static bool TryGetPolynomial(Entity expr, Variable variable,
[NotNullWhen(true)] out Dictionary <EInteger, Entity>?dst)
{
var children = Sumf.LinearChildren(expr.Expand());
dst = Algebra.AnalyticalSolving.PolynomialSolver.GatherMonomialInformation
<EInteger, PrimitiveInteger>(children, variable);
return(dst is not null);
}
/// <summary>
/// Sorts an expression into a polynomial.
/// See more at <see cref="MathS.TryPolynomial"/>
/// </summary>
internal static bool TryPolynomial(Entity expr, Variable variable,
[System.Diagnostics.CodeAnalysis.NotNullWhen(true)]
out Entity?dst)
{
dst = null;
var children = Sumf.LinearChildren(expr.Expand());
var monomialsByPower = Algebra.AnalyticalSolving.PolynomialSolver.GatherMonomialInformation
<EInteger, TreeAnalyzer.PrimitiveInteger>(children, variable);
if (monomialsByPower == null)
{
return(false);
}
var res = BuildPoly(monomialsByPower, variable);
if (res is null)
{
return(false);
}
dst = res;
return(true);
}
static (Entity poly, Entity remainder) ExtractPolynomialLocally(Entity expr, Variable x)
{
var(powInfo, rem) =
PolynomialSolver.GatherMonomialInformationAllowingBad <EInteger, PrimitiveInteger>(Sumf.LinearChildren(expr), x);
if (
powInfo.TryGetValue(EInteger.Zero, out var info) // if we have something line x^5 + a + a over x then we should get (x^5, a + a) so that we could continute working with the remainder
)
{
rem += info;
powInfo.Remove(EInteger.Zero);
}
return(Simplificator.BuildPoly(powInfo, x) ?? 0, rem);
}
Sinf(Sumf(var any1, var any2)) => new Sinf(any1) * new Cosf(any2) + new Sinf(any2) * new Cosf(any1),
