/// <summary>
/// 分数を簡単にする
/// </summary>
private void Reduction()
{
var factor = Factorizations.GCD((long)Numerator, (long)Denominator);
Numerator = Numerator / (ulong)factor;
Denominator = Denominator / (ulong)factor;
}
/// <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;
}
}
}
}
/// <summary>
/// ある文字で式を整理する(x =の形にする)
/// </summary>
/// <param name="LeftSide">左辺</param>
/// <param name="RightSide">右辺</param>
/// <param name="target">文字</param>
/// <returns></returns>
public async static Task <List <Formula> > SolveAboutX(Formula LeftSide, Formula RightSide, char target)
{
//分母部分を無くす
var L = LeftSide.GetNumerator() * RightSide.GetDenominator();
var R = RightSide.GetNumerator() * LeftSide.GetDenominator();
//単項式の分母部分をなくす
var LcommonFactor = Factorizations.FactorOut(L);
var RcommonFactor = Factorizations.FactorOut(R);
L = LcommonFactor.Item2 * LcommonFactor.Item1.GetNumerator() * RcommonFactor.Item1.GetDenominator();
R = RcommonFactor.Item2 * RcommonFactor.Item1.GetNumerator() * LcommonFactor.Item1.GetDenominator();
//xを含む単項式と含まないものに分け、左辺に含むものを集める
var Lx = L.NumMonof.Where(x => x.GetCharDics().ContainsKey(target));
var Lexceptx = L.NumMonof.Where(x => !x.GetCharDics().ContainsKey(target));
var Rx = R.NumMonof.Where(x => x.GetCharDics().ContainsKey(target));
var Rexceptx = R.NumMonof.Where(x => !x.GetCharDics().ContainsKey(target));
L = new Formula(Lx.Concat(Rx.Select(x => - x)).ToList());
R = new Formula(Lexceptx.Select(x => - x).Concat(Rexceptx).ToList());
//Xがどのようなものなのかを調べる
var XInfo = L.GetTargetCharInfo(target);
var XTypes = XInfo.NumMonof.Select(x =>
{
if (x.NthRoots.Count() > 0)
{
return(x, -Factorizations.LCM(x.NthRoots.Keys.ToList()));
}
else
{
return(x, x.Character[target]);
}
}).GroupBy(x => x.Item2).ToDictionary(x => x.Key, x => x.Select(y => y.Item1).ToList());
bool IsRightZero = R.IsZero();
if (XInfo.NumMonof.Any(x => x.NumFuncs.Count() != 0 || x.DenFuncs.Count() != 0))//関数部に文字列がある場合
{
throw new Exception(AppResources.VariablesInFunction);
}
else if (XTypes.Count() > 4 || (IsRightZero && XTypes.Count() >= 3))//三次方程式以上の場合は解けない
{
throw new Exception(AppResources.TooComplicatedX);
}
else if (XTypes.Count() == 1)//xの種類が1の場合
{
if (IsRightZero && XTypes.All(x => x.Key > 0))
{
return new List <Formula> {
(Formula)0
}
}
;
if (!XTypes.Any(x => x.Key < 0))
{
R = R / L * new Monomial(1.0, new Dictionary <char, int> {
{ target, XTypes.Keys.First() }
});
return(new List <Formula> {
Formula.CalcRoot(R, XTypes.First().Key)
});
}
else
{
if (XTypes.First().Value.Count() >= 3)//3つ以上
{
throw new Exception(AppResources.TooComplicatedX);
}
else if (XTypes.First().Value.Count() == 1)//1つ
{
if (XTypes.First().Key > 0)
{
L = Formula.CalcRoot(L, Math.Abs(XTypes.First().Key));
R = Formula.CalcRoot(R, Math.Abs(XTypes.First().Key));
}
else
{
L = L ^ Math.Abs(XTypes.First().Key);
R = R ^ Math.Abs(XTypes.First().Key);
}
return(await SolveAboutX(L, R, target));
}
else if (XTypes.Keys.First() <= -3)//3√以上かつ2つ
{
throw new Exception(AppResources.TooComplicatedX);
}
else//2√かつ2つ
{
L = L ^ 2;
R = R ^ 2;
return(await SolveAboutX(L, R, target));
}
}
}
else if (!XTypes.Any(x => x.Key < 0))//ルートがない場合
{
var LXMin = XTypes.Keys.Min();
if (IsRightZero)
{
if (XTypes.Count() == 3)
{
var factoredx = XTypes.Keys.Select(x => x - LXMin).ToList();
var max = factoredx.Max();
factoredx.Remove(0);
var min = factoredx.Min();
if (max == min * 2)
{
var ordered = L.NumMonof.GroupBy(x => x.Character[target])
.ToDictionary(
x => x.Key,
x => new Formula(x.Select(y =>
{
var z = y;
z.Character.Remove(target);
return(z);
}).ToList()));
return((await SolveEquations.SolveEquation(ordered[max + LXMin], ordered[min + LXMin], ordered[LXMin]))
.Concat(new List <Formula> {
(Formula)0
}).ToList());
}
else
{
throw new Exception(AppResources.TooComplicatedX);
}
}
else
{
var factoredx = XTypes.Keys.Select(x => x - LXMin).ToList();
var max = factoredx.Max();
var ordered = L.NumMonof.GroupBy(x => x.Character[target])
.ToDictionary(
x => x.Key,
x => new Formula(x.Select(y =>
{
var z = y;
z.Character.Remove(target);
return(z);
})
.ToList()));
return(new List <Formula>
{
(Formula)0,
Formula.CalcRoot((Formula)(-1) * ordered[LXMin] / ordered[max + LXMin], max)
});
}
}
else
{
if (XTypes.Keys.Max() == LXMin * 2)
{
var ordered = L.NumMonof.GroupBy(x => x.Character[target])
.ToDictionary(
x => x.Key,
x => new Formula(x.Select(y =>
{
var z = y;
z.Character.Remove(target);
return(z);
}).ToList()));
return((await SolveEquations.SolveEquation(ordered[XTypes.Keys.Max()], ordered[LXMin], -R)).ToList());
}
else
{
throw new Exception(AppResources.TooComplicatedX);
}
}
}
else if (XTypes.Count(x => x.Key < 0) == 1 && XTypes.Keys.Min() == -2)
{
var RootX = new Formula(XTypes[-2]);
R = R - L + RootX;
return(await SolveAboutX(RootX ^ 2, R ^ 2, target));
}
else if (XTypes.Count(x => x.Key < 0) == 1 && XTypes.Where(x => x.Key < 0).First().Value.Count() == 1)
{
var RootX = new Formula(XTypes[XTypes.Keys.Min()]);
R = R - L + RootX;
return(await SolveAboutX(RootX ^ XTypes.Keys.Min(), R ^ XTypes.Keys.Min(), target));
}
else if (XTypes.Count(x => x.Key < 0) == 2 && !XTypes.Any(x => x.Key > 0) && XTypes.Keys.Max() * 2 == XTypes.Keys.Min())
{
var max = XTypes.Keys.Max();
var min = XTypes.Keys.Min();
var MaxXs = XTypes[max].Select(x => x.GetTargetCharInfo(target) ^ max);
var MinXs = XTypes[min].Select(x => x.GetTargetCharInfo(target) ^ min);
if (MaxXs.Concat(MinXs).Distinct().Count() == 1)
{
var formX = MaxXs.First();
var MaxExceptX = XTypes[max].Select(x => x.RemoveX(target)).ToList();
var MinExceptX = XTypes[min].Select(x => x.RemoveX(target)).ToList();
return(await SolveAboutX((Formula)formX, (await SolveEquations.SolveEquation(new Formula(MaxExceptX), new Formula(MinExceptX), R))[0], target));
}
else
{
throw new Exception(AppResources.TooComplicatedX);
}
}
else
{
throw new Exception(AppResources.TooComplicatedX);
}
}
}