public static PermutationMatrix operator *(PermutationMatrix a, PermutationMatrix b)
{
PermutationMatrix ret = new PermutationMatrix(a.Rows, a.Columns);
for (int i = 0; i < ret.Rows; i++)
{
for (int j = 0; j < ret.Columns; j++)
{
for (int k = 0; k < ret.Columns; k++)
{
ret.InternalRep[i, j] += a.InternalRep[i, k] * b.InternalRep[k, j];
}
}
}
StringBuilder sb = new StringBuilder();
sb.Append(a.ToLatex());
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(ret.ToLatex());
ret.FullRep = sb.ToString();
return(ret);
}
public Permutation(int[] TR, int[] BR)
{
TopRow = TR;
BottomRow = BR;
IsIdentity = BR.SequenceEqual(TR);
ElementName = string.Join("", BR);
ElementNameValue = long.Parse(ElementName);
Matrix = new PermutationMatrix(this);
}
public PermutationMatrix Transpose()
{
PermutationMatrix ret = new PermutationMatrix(this.Rows, this.Columns);
for (int i = 0; i < this.Columns; i++)
{
for (int j = 0; j < this.Rows; j++)
{
ret.InternalRep[j, i] = this.InternalRep[i, j];
}
}
return(ret);
}
public PermutationMatrix Inverse()
{
PermutationMatrix ret = this.Transpose();
StringBuilder sb = new StringBuilder();
sb.Append(this.ToLatex() + "^{-1}");
sb.Append(" = ");
sb.Append(ret.ToLatex());
ret.FullRep = sb.ToString();
return(ret);
}