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# * #laplace_expansion(row_or_column: num)

# * #cofactor_expansion(row_or_column: num)

# * #cofact_exp(row_or_column: num)

#

# Returns the laplace_expansion along +num+ -th +row_or_column+

#

# Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0)

# => Vector[3, -2]

#

# Matrix[[7,6], [3,9]].laplace_expansion(column: 1)

# => 45

#

def laplace_expansion(row: nil, column: nil)

Matrix.Raise ErrDimensionMismatch unless square?

raise RuntimeError, "laplace_expansion of empty matrix is not defined" if empty?

num = row || column

if !num || (row && column)

raise ArgumentError, "should be hash which has either :row or :column as key"

end

unless 0 <= num && num < row_count

raise ArgumentError, "invalid num (#{num.inspect} for 0..#{row_count - 1})"

end

send(row ? :row : :column, num).map.with_index { |e, k|

e * cofactor(*(row ? [num, k] : [k,num]))

}.inject(:+)

end

alias_method :cofactor_expansion, :laplace_expansion

alias_method :cofact_exp, :laplace_expansion