require 'matrix'
class Matrix
 def det_b
  abort '!error: not square!' unless square?
  n=row_size
  a=to_a
  (0...n).inject(1) do |det,k|
   i=a.transpose[k].slice(k...n).index{|e| e!=0}
   return 0 if i.nil? #not full ranked
   if i!=0 then
    a[k],a[k+i]=a[k+i],a[k]
    det*=-1
   end
   for i in (k+1)...n
    for j in (k...n).to_a.reverse
     a[i][j]=a[k][k]*a[i][j]-a[i][k]*a[k][j]
     a[i][j]/=a[k-1][k-1] if k!=0
    end
   end
   det/=a[k-1][k-1] if k!=0
   det*a[k][k]
  end
 end
end

n=44
require 'mathn'
10.times do
 a=Matrix.unit(n).map{|_| rand(10)-5}
 #a=Matrix.unit(n).map{|_| 10.0*rand-5.0}
 puts '@@@@@@@@@@@@@@@@@@@@@@@@@'
 puts 'det:   ' << a.det.to_s
 puts 'det_e: ' << a.det_e.to_s
 puts 'det_b: ' << a.det_b.to_s
end