internal static Entity TaylorExpansion(Entity expr, Variable exprVariable, Variable polyVariable, Entity point, int termCount)
{
if (termCount < 0)
{
throw new InvalidNumberException($"{nameof(termCount)} is supposed to be at least 0");
}
var terms = new List <Entity>();
foreach (var term in TaylorExpansionTerms(expr, exprVariable, polyVariable, point))
{
if (terms.Count >= termCount)
{
return(TreeAnalyzer.MultiHangBinary(terms, (a, b) => a + b));
}
terms.Add(term);
}
throw new AngouriBugException($"We cannot get here, as {nameof(TaylorExpansionTerms)} is supposed to be endless");
}
/// <summary>
/// Sorts an expression into a polynomial.
/// See more MathS.Utils.TryPolynomial
/// </summary>
/// <param name="expr"></param>
/// <param name="variable"></param>
/// <param name="dst"></param>
/// <returns></returns>
internal static bool TryPolynomial(Entity expr, VariableEntity variable, out Entity dst)
{
dst = null;
var children = TreeAnalyzer.LinearChildren(expr.Expand(), "sumf", "minusf", Const.FuncIfSum);
var monomialsByPower = PolynomialSolver.GatherMonomialInformation <long>(children, variable);
if (monomialsByPower == null)
{
return(false);
}
var newMonomialsByPower = new Dictionary <int, Entity>();
var keys = monomialsByPower.Keys.ToList();
keys.Sort((i, i1) => (i < i1 ? 1 : (i > i1 ? -1 : 0)));
var terms = new List <Entity>();
foreach (var index in keys)
{
var pair = new KeyValuePair <long, Entity>(index, monomialsByPower[index]);
Entity px;
if (pair.Key == 0)
{
terms.Add(pair.Value.Simplify());
continue;
}
if (pair.Key == 1)
{
px = variable;
}
else
{
px = MathS.Pow(variable, pair.Key);
}
if (pair.Value == 1)
{
terms.Add(px);
continue;
}
else
{
terms.Add(pair.Value.Simplify() * px);
}
}
if (terms.Count == 0)
{
return(false);
}
dst = terms[0];
for (int i = 1; i < terms.Count; i++)
{
if (terms[i].Name == "mulf" &&
terms[i].Children[0].entType == Entity.EntType.NUMBER &&
terms[i].Children[0].GetValue().IsReal() && terms[i].Children[0].GetValue().Real < 0)
{
dst -= ((-1) * terms[i].Children[0].GetValue()) * terms[i].Children[1];
}
else
{
dst += terms[i];
}
}
dst = dst.InnerSimplify();
return(true);
}