316.sagews

a = matrix(QQ,15,[4,8,3,1,0,4,8,1,5,6,2,3,8,6,7,1,3,9,4,2,1,5,5,8,6,7,5,5,1,6,4,0,6,0,6,4,3,3,4,3,9,0,5,6,7,2,0,8,0,7,1,7,1,8,3,5,5,1,3,4,1,8,4,1,1,6,6,1,4,7,1,8,2,8,0,7,4,2,4,3,6,9,1,5,8,3,0,2,0,5,5,8,9,0,2,9,3,6,7,6,8,0,5,2,0,7,6,2,6,5,8,7,1,9,2,5,1,5,0,0,6,9,5,6,7,5,8,4,3,6,2,1,5,3,7,3,3,3,4,1,2,5,3,4,6,8,8,5,7,1,6,0,1,2,0,7,3,5,6,7,9,1,8,1,3,4,6,8,1,3,5,4,8,1,9,5,6,7,6,7,7,4,6,7,1,8,9,9,4,9,2,8,5,7,2,5,3,3,3,3,7,2,8,5,0,5,4,1,6,6,5,9,1,4,7,5,4,0,8,3,1,9,3,4,2]); a

[4 8 3 1 0 4 8 1 5 6 2 3 8 6 7] [1 3 9 4 2 1 5 5 8 6 7 5 5 1 6] [4 0 6 0 6 4 3 3 4 3 9 0 5 6 7] [2 0 8 0 7 1 7 1 8 3 5 5 1 3 4] [1 8 4 1 1 6 6 1 4 7 1 8 2 8 0] [7 4 2 4 3 6 9 1 5 8 3 0 2 0 5] [5 8 9 0 2 9 3 6 7 6 8 0 5 2 0] [7 6 2 6 5 8 7 1 9 2 5 1 5 0 0] [6 9 5 6 7 5 8 4 3 6 2 1 5 3 7] [3 3 3 4 1 2 5 3 4 6 8 8 5 7 1] [6 0 1 2 0 7 3 5 6 7 9 1 8 1 3] [4 6 8 1 3 5 4 8 1 9 5 6 7 6 7] [7 4 6 7 1 8 9 9 4 9 2 8 5 7 2] [5 3 3 3 3 7 2 8 5 0 5 4 1 6 6] [5 9 1 4 7 5 4 0 8 3 1 9 3 4 2]

a.rank()

15

b=a^(-1);b

[ 72892257431/865114825368 -34557680387/576743216912 149241711479/1730229650736 -35375081743/576743216912 -228949614743/865114825368 68037568265/432557412684 51447452479/432557412684 -27308977257/576743216912 -169382583965/865114825368 133968984403/1730229650736 -26951289961/144185804228 6519495227/216278706342 202962209759/1730229650736 -25406609823/576743216912 85756788747/576743216912] [ 7416375091/288371608456 -13461113741/576743216912 -52243486149/576743216912 2328457127/576743216912 -3410201315/288371608456 -388898545/144185804228 8766352179/144185804228 -15882593871/576743216912 20607309523/288371608456 39416546647/576743216912 -2375222151/144185804228 -59528533/72092902114 -43093871885/576743216912 22098994775/576743216912 -691432291/576743216912] [ 3596188879/432557412684 26553065373/288371608456 138027471943/865114825368 -32681880911/288371608456 -27821723383/432557412684 19017025705/216278706342 5032118915/216278706342 34102301831/288371608456 -95053223269/432557412684 -41057532277/865114825368 -16607806879/72092902114 12027632287/108139353171 72792131503/865114825368 -21244100047/288371608456 8382294611/288371608456] [-148870756015/2595344476104 237221892155/1730229650736 740802336353/5190688952208 -294925162537/1730229650736 58358528047/2595344476104 39489122195/1297672238052 -58143453431/1297672238052 75477768833/1730229650736 -56827932515/2595344476104 -76100013611/5190688952208 -36153729415/432557412684 -41019318937/648836119026 382139387465/5190688952208 -69406382089/1730229650736 55540494733/1730229650736] [ -49572613603/648836119026 -28894826023/432557412684 -44773348711/1297672238052 47561115131/432557412684 35550995341/648836119026 -70422882335/648836119026 -5196981188/324418059513 -27529355299/432557412684 63665909237/324418059513 -30379484183/1297672238052 15404813822/108139353171 -16648681976/324418059513 -38027484547/1297672238052 -7314001405/432557412684 4677193213/432557412684] [ -23115443302/324418059513 4776948199/108139353171 46159073987/648836119026 -19154169067/216278706342 50936284921/324418059513 31916586161/648836119026 -41694210013/324418059513 54552053135/216278706342 -105041104345/648836119026 -84546685607/648836119026 -5529289676/108139353171 63458931629/324418059513 -30569325649/648836119026 5177379995/216278706342 -17052991679/216278706342] [ 20027780045/648836119026 -42205802545/432557412684 -236420998987/1297672238052 72854029235/432557412684 30605267569/648836119026 -11175470824/324418059513 -20299373525/324418059513 50604559337/432557412684 49279376263/648836119026 77108773765/1297672238052 4670565395/108139353171 25800521293/324418059513 -111525369667/1297672238052 28121308859/432557412684 -76197371375/432557412684] [ -472197395/144185804228 -25833662799/288371608456 -61581825195/288371608456 51691415001/288371608456 -9831601/144185804228 -5764066018/36046451057 4198516261/72092902114 -49885572353/288371608456 39491320071/144185804228 9330572081/288371608456 15918069343/72092902114 -4594934828/36046451057 -4112759499/288371608456 26949844009/288371608456 -16450291237/288371608456] [ 12856076075/288371608456 22715605931/576743216912 -970656925/576743216912 28836233903/576743216912 -1346229371/288371608456 -10701038653/144185804228 13139836291/144185804228 -128432463207/576743216912 35252165195/288371608456 -26065754417/576743216912 20433989301/144185804228 -19961073247/72092902114 39608952587/576743216912 235853855/576743216912 56853189445/576743216912] [ -62706964103/1297672238052 18902520631/865114825368 79980777733/2595344476104 -8475935549/865114825368 59253368531/1297672238052 9657338989/648836119026 37184561327/648836119026 -194992163555/865114825368 161822232869/1297672238052 -50654109343/2595344476104 28315482217/216278706342 -52080936431/324418059513 122446848589/2595344476104 -60317235653/865114825368 68247600473/865114825368] [ -16938958361/432557412684 -4759626903/288371608456 -39849458261/865114825368 1134468549/288371608456 5781070361/432557412684 11257871287/216278706342 -3782920525/216278706342 28411864971/288371608456 -13289511757/432557412684 105280384247/865114825368 -2261615491/72092902114 10872696331/108139353171 -107680103957/865114825368 15409100101/288371608456 -24281631601/288371608456] [ -24222542669/1297672238052 6896399725/865114825368 -108161169413/2595344476104 -7853642531/865114825368 -16971420847/1297672238052 21515781944/324418059513 -60405616915/648836119026 157918175851/865114825368 -254094339811/1297672238052 44009712599/2595344476104 -22263906107/216278706342 79906126801/324418059513 -129121372757/2595344476104 17312524021/865114825368 -1265517049/865114825368] [ 15087762358/324418059513 -383507974/108139353171 5324773505/324418059513 303498737/108139353171 -2984213404/324418059513 -37729447036/324418059513 -15655342562/324418059513 9357562073/108139353171 1350455408/324418059513 -15418231628/324418059513 5745026498/108139353171 17991244489/324418059513 7534757981/324418059513 -7363009660/108139353171 -865600898/108139353171] [ 50527500181/1297672238052 -14347319645/865114825368 295054646689/2595344476104 -19886822369/865114825368 19944772595/1297672238052 -40164210593/648836119026 44107855709/648836119026 -161245318055/865114825368 129355450613/1297672238052 49240678085/2595344476104 7393085215/216278706342 -74124435581/324418059513 254095617145/2595344476104 -13936724729/865114825368 49113408917/865114825368] [ 23479901645/1297672238052 63705317387/865114825368 137930861621/2595344476104 -62446928989/865114825368 11418401455/1297672238052 28615382497/324418059513 -49847812937/648836119026 47784997181/865114825368 -126667432901/1297672238052 -137456414975/2595344476104 -14222391685/216278706342 30553343876/324418059513 -114471254827/2595344476104 38588366195/865114825368 888865681/865114825368]

a*b;

[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]