public static RationalSquareMatrix FaddevasMethod(RationalSquareMatrix AIn, out RationalVector CharacteristicEquation)
{
RationalSquareMatrix A = AIn.Clone();
CharacteristicEquation = new RationalVector();
RationalSquareMatrix A_n = A;
Rational b_n = 1;
RationalSquareMatrix B_n = null;
RationalSquareMatrix I = null;
RationalSquareMatrix AInv = null;
int i = 0;
for (i = 1; i < A.Rows; i++)
{
b_n = -A_n.Trace() / (i);
CharacteristicEquation.Add(b_n);
I = RationalSquareMatrix.IdentityMatrix(A.Rows);
B_n = A_n + b_n * I;
A_n = A * B_n;
}
b_n = -A_n.Trace() / (i);
CharacteristicEquation.Add(b_n);
AInv = -1 / b_n * B_n;
AInv.FullRep = A.ToLatex() + "^{-1} = " + AInv.ToLatex();
return(AInv);
}
public static RationalVector operator +(Rational value, RationalVector v)
{
RationalVector vM = new RationalVector();
for (int i = 0; i < v.Count; i++)
{
vM.Add(value + v[i]);
}
return(vM);
}
public static RationalVector operator /(RationalVector v, Rational value)
{
RationalVector vM = new RationalVector();
for (int i = 0; i < v.Count; i++)
{
vM.Add(v[i] / value);
}
return(vM);
}
public static RationalVector operator -(RationalVector v1, RationalVector v2)
{
RationalVector vM = new RationalVector();
for (int i = 0; i < v1.Count; i++)
{
vM.Add(v1[i] - v2[i]);
}
return(vM);
}
public RationalVector this[params string[] exps]
{
get
{
RationalVector rv = new RationalVector();
foreach (string r in exps)
{
rv.Add(Rational.Parse(r));
}
return(rv);
}
}
public RationalVector CramersRule(RationalVector VectorToSolve)
{
RationalVector Deltas = new RationalVector();
RationalSquareMatrix A = this.Clone();
Rational Delta = RationalSquareMatrix.Det(A);
for (int i = 0; i < this.Rows; i++)
{
RationalVector rvSave = A[i];
A[i] = VectorToSolve;
Deltas.Add(RationalSquareMatrix.Det(A) / Delta);
A[i] = rvSave;
}
return(Deltas);
}
public RationalVector this[int Column]
{
get
{
RationalVector ret = new RationalVector();
for (int i = 0; i < this.Rows; i++)
{
ret.Add(this[i, Column]);
}
return(ret);
}
set
{
for (int i = 0; i < this.Rows; i++)
{
this[i, Column] = value[i];
}
}
}
