/// <summary>
///
/// </summary>
/// <param name="numRows">The number of rows of vertices.</param>
/// <param name="firstVertex"></param>
/// <returns></returns>
public static QuiverWithPotential <int> GetSquareQP(int numRows, int firstVertex = DefaultFirstVertex)
{
if (!SquareParameterIsValid(numRows))
{
throw new ArgumentOutOfRangeException(nameof(numRows));
}
int numVerticesInRow = numRows;
int numVertices = numVerticesInRow * numRows;
if (numRows == 1)
{
var quiver = UsefulQuivers.GetSquareQuiver(numRows, firstVertex);
return(new QuiverWithPotential <int>(quiver, new Potential <int>()));
}
var potential = new Potential <int>();
for (int rowIndex = 0; rowIndex < numRows - 1; rowIndex++)
{
var curRow = GetVerticesInSquareQPRow(numRows, rowIndex, firstVertex).ToList();
var nextRow = GetVerticesInSquareQPRow(numRows, rowIndex + 1, firstVertex).ToList();
for (int indexInRow = 0; indexInRow < numVerticesInRow - 1; indexInRow++)
{
int sign = (rowIndex + indexInRow).Modulo(2) == 0 ? +1 : -1;
var cycleVertices = sign == +1 ?
new int[] { curRow[indexInRow], curRow[indexInRow + 1], nextRow[indexInRow + 1], nextRow[indexInRow], curRow[indexInRow] } :
new int[] { curRow[indexInRow + 1], curRow[indexInRow], nextRow[indexInRow], nextRow[indexInRow + 1], curRow[indexInRow + 1] };
potential = potential.AddCycle(new DetachedCycle <int>(cycleVertices), sign);
}
}
var qp = new QuiverWithPotential <int>(potential);
return(qp);
}
