i1 : h={1,4,6,5,1}
o1 = {1, 4, 6, 5, 1}
o1 : List
|
i2 : r={1,3,3,4}
o2 = {1, 3, 3, 4}
o2 : List
|
i3 : C=randomChainComplex(h,r)
2 8 12 12 5
o3 = ZZ <-- ZZ <-- ZZ <-- ZZ <-- ZZ
0 1 2 3 4
o3 : ChainComplex
|
i4 : prune HH C
1
o4 = 0 : ZZ
4
1 : ZZ
6
2 : ZZ
5
3 : ZZ
1
4 : ZZ
o4 : GradedModule
|
i5 : for i from 0 to 4 list rank HH_i C
o5 = {1, 4, 6, 5, 1}
o5 : List
|
i6 : for i from 1 to 4 list rank(C.dd_i)
o6 = {1, 3, 3, 4}
o6 : List
|
The optional argument Height chooses the maximum sizes of the random numbers used. The actual numbers are somewhat larger (twice as many bits), as matrices are multiplied together.
i7 : h={1,4,0,5,1}
o7 = {1, 4, 0, 5, 1}
o7 : List
|
i8 : r={2,3,3,4}
o8 = {2, 3, 3, 4}
o8 : List
|
i9 : C=randomChainComplex(h,r, Height=>1000)
3 9 6 12 5
o9 = ZZ <-- ZZ <-- ZZ <-- ZZ <-- ZZ
0 1 2 3 4
o9 : ChainComplex
|
i10 : C.dd
3 9
o10 = 0 : ZZ <---------------------------------------------------------------------- ZZ : 1
| 44424 -8775 -2160 -53262 -62508 -10437 -6822 -62838 1011 |
| 90516 14087 19368 -141214 -90936 2397 -10686 -117210 24977 |
| 138645 31572 37098 -226521 -127899 11070 -15363 -176148 45423 |
9 6
1 : ZZ <--------------------------------------------------------- ZZ : 2
| 330985 16445 756805 1698 330472 348418 |
| 713026 -154053 -42697 1538759 531828 793108 |
| 1313518 -554313 -1321367 952247 994858 2800 |
| 1504309 -561736 -934444 734919 1193028 74986 |
| -566001 95813 3887 -1731404 -398918 -893718 |
| -940456 315736 168999 191100 -803825 96554 |
| -505191 256413 438512 888174 -448781 587460 |
| -380977 341680 1286800 724845 -281448 878246 |
| 1910440 -687155 -752920 2107 1588083 -178598 |
6 12
2 : ZZ <-------------------------------------------------------------------------------------------------------------------------------- ZZ : 3
| 41388167 -95238274 5488161 12322184 -52314315 -15854513 50425642 -29862626 -100716183 -78673592 -64535295 57729071 |
| 9777314 29735878 8710464 42894623 -632054 -31139424 6643135 83313808 -38773955 -56265921 3886477 -86494233 |
| 21143227 -17020460 17282979 975209 12792629 -27787635 -357149 9785294 -29488934 -28260935 -29357422 16504066 |
| 20760737 -1043822 21170415 7109264 22491307 -36115359 -6466526 30843814 -27310181 -32178816 -24665021 -4404699 |
| -40854113 120671920 421659 2171879 64292129 1029525 -57179939 69499514 98152576 65571655 71827928 -98294804 |
| -47055725 11588622 -43668471 -17943160 -39150723 76088519 6825892 -62888800 68596487 76741536 56882559 6646445 |
12 5
3 : ZZ <---------------------------------------------------- ZZ : 4
| -2098931 -882197 -1197770 192505 -821100 |
| -540649 1132991 -2558060 653635 -1393888 |
| -1333740 3364752 -3624762 -4878996 2320266 |
| -1425716 -2621421 1862275 564680 -64468 |
| 1352058 -1470320 3544570 -96870 1495604 |
| -121418 1868293 -1472318 -1881704 649512 |
| -37268 -77123 -385029 440508 -259828 |
| -469251 -460737 -885687 1959819 -1865142 |
| -1299118 659729 -1037071 -1031938 -476574 |
| 28821 -1464654 -120682 2377619 -941278 |
| -857790 -1893725 2246803 -1115706 1519562 |
| -1160441 -1211038 -190488 1500701 -1537374 |
o10 : ChainComplexMap
|
i11 : C.dd^2 == 0 o11 = true |
i12 : prune HH C
o12 = 0 : cokernel | 3 |
| 0 |
4
1 : ZZ
2 : cokernel | 64931150 |
3 : cokernel | 6 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
1
4 : ZZ
o12 : GradedModule
|
i13 : for i from 0 to 4 list rank HH_i C
o13 = {1, 4, 0, 5, 1}
o13 : List
|
i14 : for i from 1 to 4 list rank(C.dd_i)
o14 = {2, 3, 3, 4}
o14 : List
|
This returns a chain complex over the integers. Notice that if one gives h to be a list of zeros, then that doesn’t mean that the complex is exact, just that the ranks are as expected.