/// <summary>
/// 多項式が整理できる場合は整理する
/// ・分母分子ごとに同類項をまとめる
/// ・共通因数があれば求める
/// ・共通因数を掛けて約分し、それを分母分子に分けて掛ける
/// </summary>
private void Initialise()
{
if (NumMonof.IsZero())
{
DenMonof = new List <Monomial> {
1
};
return;
}
if (NumMonof.IsOne() && DenMonof.IsOne())
{
return;
}
//0の項を削除
NumMonof = NumMonof.Where(x => !x.IsZero()).ToList();
DenMonof = DenMonof.Where(x => !x.IsZero()).ToList();
//同類項をまとめる
var SortedNumerator = NumMonof.Grouping(IsNumberKey: false).Select(x =>
{
var res = x[0];
res.Number = x.Select(y => y.Number).Aggregate((now, next) => now + next);
return(res);
}).ToList();
var SortedDenominator = DenMonof.Grouping(IsNumberKey: false).Select(x =>
{
var res = x[0];
res.Number = x.Select(y => y.Number).Aggregate((now, next) => now + next);
return(res);
}).ToList();
if (SortedNumerator.IsOne() || SortedDenominator.IsOne())
{
NumMonof = SortedNumerator;
DenMonof = SortedDenominator;
return;
}
var NumFactor = Factorizations.FactorOut(SortedNumerator);
var DenFactor = Factorizations.FactorOut(SortedDenominator);
Monomial Factor = NumFactor.Item1 / DenFactor.Item1;
NumMonof = NumFactor.Item2.Select(x => x * Factor.GetNumerator()).ToList();
DenMonof = DenFactor.Item2.Select(x => x * Factor.GetDenominator()).ToList();
Reduction();
Trace.WriteLine("Formula Initialized:" + this.GetString());
}
/// <summary>
/// 約分する
/// </summary>
private void Reduction()
{
var factors = Factorizations.FactorOut(this);
NumMonof = (factors.Item1.GetNumerator() * factors.Item2.GetNumerator()).NumMonof;
DenMonof = (factors.Item1.GetDenominator() * factors.Item2.GetDenominator()).NumMonof;
if (DenMonof.Count() == 1)//分母が一つだけであれば数字は上につける
{
NumMonof = NumMonof.Select(x => x / DenMonof[0].Number.ToDouble()).ToList();
DenMonof[0].Number = 1;
return;
}
else//上下の式がどちらかの因数である場合は、割り切る
{
var chars = this.GetCharDics().Keys.ToList();
char target = '0';
if (chars.Count() == 0)
{
return;
}
if (chars.Count() == 1)
{
target = chars[0];
}
else
{
var chardic = chars.ToDictionary(x => x, x => NumMonof.Concat(DenMonof).Max(y => y.Character.ContainsKey(x) ? y.Character[x] : 0));
target = chardic.First().Key;
foreach (var dic in chardic)
{
if (dic.Key != target)
{
if (dic.Value > chardic[target])
{
target = dic.Key;
}
else if (dic.Value == chardic[target])
{
if (dic.Key.CompareTo(target) < 0)
{
target = dic.Key;
}
}
}
}
}
var IsNumBigger = NumMonof.Max(x => x.Character.ContainsKey(target) ? x.Character[target] : 0)
> DenMonof.Max(x => x.Character.ContainsKey(target) ? x.Character[target] : 0);
var Bigger = new Dictionary <int, List <Monomial> > {
};
var Smaller = new Dictionary <int, List <Monomial> > {
};
var BiggerF = new List <Monomial> {
};
var SmallerF = new List <Monomial> {
};
if (IsNumBigger)
{
BiggerF = NumMonof;
SmallerF = DenMonof;
Bigger = NumMonof.GroupBy(x => x.Character.ContainsKey(target) ? x.Character[target] : 0).ToDictionary(x => x.Key, x => x.Select(y => y).ToList());
Smaller = DenMonof.GroupBy(x => x.Character.ContainsKey(target) ? x.Character[target] : 0).ToDictionary(x => x.Key, x => x.Select(y => y).ToList());
}
else
{
BiggerF = DenMonof;
SmallerF = NumMonof;
Bigger = DenMonof.GroupBy(x => x.Character.ContainsKey(target) ? x.Character[target] : 0).ToDictionary(x => x.Key, x => x.Select(y => y).ToList());
Smaller = NumMonof.GroupBy(x => x.Character.ContainsKey(target) ? x.Character[target] : 0).ToDictionary(x => x.Key, x => x.Select(y => y).ToList());
}
if (Smaller.Any(x => x.Value.Count() != 1))
{
return;
}
var SUMfactor = new List <Monomial> {
};
var BiggerMax = Bigger.Keys.Max();
var SmallerMax = Smaller.Keys.Max();
while (true)
{
var factor = Bigger[BiggerMax].Select(x => x / Smaller[SmallerMax][0]).ToList();
SUMfactor = SUMfactor.Concat(factor).ToList();
BiggerF = (new Formula(BiggerF) - new Formula(SmallerF) * new Formula(factor)).NumMonof;
Bigger = BiggerF.GroupBy(x => x.Character.ContainsKey(target) ? x.Character[target] : 0).ToDictionary(x => x.Key, x => x.Select(y => y).ToList());
BiggerMax = Bigger.Keys.Max();
if (BiggerF.Count() == 0)
{
var res = new Formula(SUMfactor);
NumMonof = res.NumMonof;
DenMonof = res.DenMonof;
return;
}
else if (BiggerMax < SmallerMax)
{
return;
}
}
}
}
