When the first-class secondary constraints are added into the Hamiltonian with arbitrary as the first class primary constraints are added to arrive at the total Hamiltonian, then one obtains the "'extended Hamiltonian " '.
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Further, because each of first and last diagonal and reverse diagonals involves only one square on the chessboard, these can be omitted and thus one can reduce the number of secondary constraints to 4 " N " " 6.
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The distinction between primary and secondary constraints is largely an artificial one ( i . e . a constraint for the same system can be primary or secondary depending on the Lagrangian ), so this article does not distinguish between them from here on.
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