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##### ordergreatp-sort

sort([123,123,124,11,...

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? ordergreatp;

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? ordergreatp ;

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##### ordergreatp-sort-sqrt

sort([sqrt(2), 0, -sq...

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##### ordergreatp-sort

sort([123,123,124,11,...

Calculate

? ordergreatp;

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? ordergreatp ;

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##### ordergreatp-sort-sqrt

sort([sqrt(2), 0, -sq...

Calculate

### ordergreatp

Run Example
```(%i1)r:15;
(%o1)                                 15
(%i2)  n1:5;
(%o2)                                  5
(%i3)  n2:3;
(%o3)                                  3
(%i4) for i:1 thru n1 do   (a[i,j]:=random(r),    A:genmatrix(a,n2,n2),    p:1, for j:1 thru 3 do   p:p*norm(row(A,j)),  est1:ceiling(float(2/sqrt(3)*p)), print(est1), sum:makelist(0,i,1,n2),  for j:1 thru n2 do     (l:makelist(row(A,j)[1,k],k,1,n2),   l:sort(l,ordergreatp),    for k:1 thru j do       sum[j]:sum[j]+l[k]), est3:sum[1],  for i:2 thru n2 do      est3:est3*sum[i],  print("Permanent:", permanent(A), ", Ots1:", est1, ", Ots3:", est3), kill(a));

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
ceiling(1.154700538379252 norm([ 2.0  12.0  14.0 ]) norm([ 5.0  4.0  1.0 ])
norm([ 14.0  5.0  3.0 ]))
Permanent: 1516 , Ots1: ceiling(1.154700538379252 norm([ 2.0  12.0  14.0 ])
norm([ 5.0  4.0  1.0 ]) norm([ 14.0  5.0  3.0 ])) , Ots3: 2772

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
ceiling(1.154700538379252 norm([ 0.0  6.0  14.0 ]) norm([ 0.0  9.0  4.0 ])
norm([ 13.0  10.0  5.0 ]))
Permanent: 1950 , Ots1: ceiling(1.154700538379252 norm([ 0.0  6.0  14.0 ])
norm([ 0.0  9.0  4.0 ]) norm([ 13.0  10.0  5.0 ])) , Ots3: 3380

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
ceiling(1.154700538379252 norm([ 4.0  8.0  4.0 ]) norm([ 6.0  11.0  1.0 ])
norm([ 7.0  1.0  14.0 ]))
Permanent: 1680 , Ots1: ceiling(1.154700538379252 norm([ 4.0  8.0  4.0 ])
norm([ 6.0  11.0  1.0 ]) norm([ 7.0  1.0  14.0 ])) , Ots3: 3024

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
ceiling(1.154700538379252 norm([ 3.0  10.0  11.0 ]) norm([ 8.0  6.0  10.0 ])
norm([ 12.0  9.0  4.0 ]))
Permanent: 3446 , Ots1: ceiling(1.154700538379252 norm([ 3.0  10.0  11.0 ])
norm([ 8.0  6.0  10.0 ]) norm([ 12.0  9.0  4.0 ])) , Ots3: 5544

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
ceiling(1.154700538379252 norm([ 3.0  9.0  6.0 ]) norm([ 5.0  0.0  2.0 ])
norm([ 13.0  8.0  7.0 ]))
Permanent: 837 , Ots1: ceiling(1.154700538379252 norm([ 3.0  9.0  6.0 ])
norm([ 5.0  0.0  2.0 ]) norm([ 13.0  8.0  7.0 ])) , Ots3: 1365
(%o4)                                done
(%i5) ```
Run Example
```r:15;
(%o1)                                 15
(%i2)  n1:5;
(%o2)                                  5
(%i3)  n2:4;
(%o3)                                  4
(%i4) for i:1 thru n1 do   (int:makelist(i,i,1,n2), sprm:permutations(int),  a[i,j]:=random(r),    A:genmatrix(a,n2,n2),    est3:10^10, for i:1 thru n2! do   (sum:makelist(0,i,1,n2),  p:first(sprm),   sprm:rest(sprm),    for j:1 thru n2 do      (l:makelist(row(A,p[j])[1,k],k,1,n2),    l:sort(l,ordergreatp),     for k:1 thru j do       sum[j]:sum[j]+l[k]    ),   est:sum[1],    for i:2 thru n2 do      est:est*sum[i],  est3:min(est3,est)  ), print("Permanent:", permanent(A), ", Otsenka3:", est3),   kill(a) );
Permanent: 18530 , Otsenka3: 148120
Permanent: 46746 , Otsenka3: 104832
Permanent: 20116 , Otsenka3: 50400
Permanent: 28386 , Otsenka3: 95472
Permanent: 55598 , Otsenka3: 146692
(%o4)                                done
(%i5) ```
Run Example
```r:15;
(%o1)                                 15
(%i2)  n1:5;
(%o2)                                  5
(%i3)  n2:3;
(%o3)                                  3
(%i4) for i:1 thru n1 do   (a[i,j]:=random(r),    A:genmatrix(a,n2,n2),    /* первая оценка */ p:1, for j:1 thru 3 do   p:p*norm(row(A,j)),  est1:ceiling(float(2/sqrt(3)*p)),  /* третья оценка */ sum:makelist(0,i,1,n2),  for j:1 thru n2 do     (l:makelist(row(A,j)[1,k],k,1,n2),   l:sort(l,ordergreatp),    for k:1 thru j do       sum[j]:sum[j]+l[k]), est3:sum[1],  for i:2 thru n2 do      est3:est3*sum[i],  print(A, "Permanent:", permanent(A), ", Ots1:", est1, ", Ots3:", est3), kill(a));

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
[ 2   12  14 ]
[            ]
[ 5   4   1  ] Permanent: 1516 , Ots1:
[            ]
[ 14  5   3  ]
ceiling(1.154700538379252 norm([ 2.0  12.0  14.0 ]) norm([ 5.0  4.0  1.0 ])
norm([ 14.0  5.0  3.0 ])) , Ots3: 2772

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
[ 13  10  5  ]
[            ]
[ 0   6   14 ] Permanent: 1950 , Ots1:
[            ]
[ 0   9   4  ]
ceiling(1.154700538379252 norm([ 0.0  6.0  14.0 ]) norm([ 0.0  9.0  4.0 ])
norm([ 13.0  10.0  5.0 ])) , Ots3: 3380

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 14.0 by 14/1 = 14.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
[ 7  1   14 ]
[           ]
[ 4  8   4  ] Permanent: 1680 , Ots1: ceiling(1.154700538379252
[           ]
[ 6  11  1  ]
norm([ 4.0  8.0  4.0 ]) norm([ 6.0  11.0  1.0 ]) norm([ 7.0  1.0  14.0 ]))
, Ots3: 3024

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 12.0 by 12/1 = 12.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 4.0 by 4/1 = 4.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 11.0 by 11/1 = 11.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
[ 3   10  11 ]
[            ]
[ 12  9   4  ] Permanent: 3446 , Ots1:
[            ]
[ 8   6   10 ]
ceiling(1.154700538379252 norm([ 3.0  10.0  11.0 ]) norm([ 8.0  6.0  10.0 ])
norm([ 12.0  9.0  4.0 ])) , Ots3: 5544

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839

rat: replaced 13.0 by 13/1 = 13.0

rat: replaced 8.0 by 8/1 = 8.0

rat: replaced 7.0 by 7/1 = 7.0

rat: replaced 5.0 by 5/1 = 5.0

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 2.0 by 2/1 = 2.0

rat: replaced 3.0 by 3/1 = 3.0

rat: replaced 9.0 by 9/1 = 9.0

rat: replaced 6.0 by 6/1 = 6.0

rat: replaced -1.15470053837925 by -2911/2521 = -1.15470051566839
[ 13  8  7 ]
[          ]
[ 3   9  6 ] Permanent: 837 , Ots1: ceiling(1.154700538379252
[          ]
[ 5   0  2 ]
norm([ 3.0  9.0  6.0 ]) norm([ 5.0  0.0  2.0 ]) norm([ 13.0  8.0  7.0 ]))
, Ots3: 1365
(%o4)                                done
(%i5) ```

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