-- -*- M2-comint -*- {* hash: -1727830538 *}
i1 : m1 = map(ZZ^10, ZZ^10, (j,i) -> (i+1)^3 * (j+1)^2 + i + j + 2)
o1 = | 3 11 31 69 131 223 351 521 739 1011 |
| 7 36 113 262 507 872 1381 2058 2927 4012 |
| 13 77 249 583 1133 1953 3097 4619 6573 9013 |
| 21 134 439 1032 2009 3466 5499 8204 11677 16014 |
| 31 207 683 1609 3135 5411 8587 12813 18239 25015 |
| 43 296 981 2314 4511 7788 12361 18446 26259 36016 |
| 57 401 1333 3147 6137 10597 16821 25103 35737 49017 |
| 73 522 1739 4108 8013 13838 21967 32784 46673 64018 |
| 91 659 2199 5197 10139 17511 27799 41489 59067 81019 |
| 111 812 2713 6414 12515 21616 34317 51218 72919 100020 |
10 10
o1 : Matrix ZZ <--- ZZ
i2 : m = syz m1
o2 = | -3 -15216643 -26282293 -41725081 -62274530 -88660163 -121611503 |
| 8 40577716 70086119 111266892 166065430 236427128 324297381 |
| -7 -35505504 -61325361 -97358544 -145307274 -206873772 -283760259 |
| 2 10144432 17521536 27816734 41516375 59106808 81074382 |
| 0 -1 0 0 0 0 0 |
| 0 0 -1 0 0 0 0 |
| 0 0 0 -1 0 0 0 |
| 0 0 0 0 -1 0 0 |
| 0 0 0 0 0 -1 0 |
| 0 0 0 0 0 0 -1 |
10 7
o2 : Matrix ZZ <--- ZZ
i3 : LLL m
o3 = | 1 0 1 0 1 1 1 |
| -1 1 0 1 0 -1 -2 |
| -1 -1 -1 -2 -2 0 1 |
| 0 -1 -1 0 1 -1 1 |
| 2 1 -1 1 -1 1 -2 |
| -1 -1 2 1 1 0 0 |
| 0 2 0 0 -1 0 2 |
| 0 -1 1 -2 1 -1 -1 |
| 0 0 -1 1 1 2 0 |
| 0 0 0 0 -1 -1 0 |
10 7
o3 : Matrix ZZ <--- ZZ
i4 : (n,c) = LLL(m, Strategy => NTL, ChangeMatrix=>true)
o4 = (| 1 0 1 0 1 1 1 |, | 1383664 3369994 3654103 1870013 -445414
| -1 1 0 1 0 -1 -2 | | -2 -1 1 -1 1
| -1 -1 -1 -2 -2 0 1 | | 1 1 -2 -1 -1
| 0 -1 -1 0 1 -1 1 | | 0 -2 0 0 1
| 2 1 -1 1 -1 1 -2 | | 0 1 -1 2 -1
| -1 -1 2 1 1 0 0 | | 0 0 1 -1 -1
| 0 2 0 0 -1 0 2 | | 0 0 0 0 1
| 0 -1 1 -2 1 -1 -1 |
| 0 0 -1 1 1 2 0 |
| 0 0 0 0 -1 -1 0 |
------------------------------------------------------------------------
2883645 -3085885 |)
-1 2 |
0 0 |
0 -2 |
1 1 |
-2 0 |
1 0 |
o4 : Sequence
i5 : m * c == n
o5 = true
i6 :
