was@sha:~$ sage -------------------------------------------------------- | SAGE Version 1.3.0.3, Build Date: 2006-05-14-2349 | | Distributed under the GNU General Public License V2. | | For help type ? or ??. | -------------------------------------------------------- sage: set_verbose(2) sage: A = MatrixSpace(QQ,10).random_element() sage: A _3 = [-2 -1 2 -1 -1 1 2 2 -1 -2] [ 1 -2 2 1 -2 1 -1 1 -2 -2] [-1 2 1 -1 1 1 -1 1 -2 -1] [-2 -1 2 -1 -1 1 1 -1 1 -2] [ 2 2 -1 -1 -1 1 -1 2 1 2] [-2 1 2 1 1 2 -1 -1 -2 1] [-1 -2 2 2 -1 1 1 1 1 2] [ 1 -2 -1 1 2 -1 -1 -2 -2 -1] [-1 2 1 -2 2 -2 1 -2 2 -2] [ 2 -1 2 2 -1 1 2 -1 -2 -2] sage: E = A.echelon_form() verbose 1 (4072: matrix.py, echelon_form) height_guess=409 6 verbose 1 (4072: matrix.py, echelon_form) p=20011 sage: E = A.echelon_form() verbose 1 (4072: matrix.py, echelon_form) height_guess=409 6 verbose 1 (4072: matrix.py, echelon_form) p=20011 sage: E _6 = [1 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 1] sage: A = MatrixSpace(QQ,10,20).random_element() sage: A _8 = [-1 -2 1 1 -2 -1 2 -1 2 1 1 2 2 -2 -1 1 -2 -1 2 -1] [ 1 1 2 -2 1 -2 1 -2 2 1 1 2 1 1 -1 1 -2 -2 1 -2] [ 2 -2 2 -1 2 -2 -2 2 -1 2 1 1 1 -2 -2 2 2 2 1 -2] [ 1 -1 2 -2 -1 -2 2 2 2 -1 -2 -2 -2 2 -2 -1 2 1 -1 -2] [-1 1 -2 -1 -1 -2 2 -1 -1 -2 1 -2 -1 2 2 1 -2 -1 2 2] [-2 2 1 -2 -2 -2 2 -1 1 -1 -2 -1 1 2 -2 1 1 -2 -1 -1] [-1 2 2 -1 -1 2 -1 -2 2 2 2 -2 -1 2 -2 2 -1 -1 1 2] [-1 -2 -2 -2 -1 -2 -1 2 1 -2 -2 -2 -1 -1 -1 -1 1 2 1 -2] [ 2 -2 2 1 -1 -2 -2 1 -2 -1 -2 1 1 -1 1 2 1 -1 2 1] [-2 2 -1 -1 2 1 1 1 -2 2 -1 -1 1 2 -1 -1 -1 -1 2 1] sage: A _9 = [-1 -2 1 1 -2 -1 2 -1 2 1 1 2 2 -2 -1 1 -2 -1 2 -1] [ 1 1 2 -2 1 -2 1 -2 2 1 1 2 1 1 -1 1 -2 -2 1 -2] [ 2 -2 2 -1 2 -2 -2 2 -1 2 1 1 1 -2 -2 2 2 2 1 -2] [ 1 -1 2 -2 -1 -2 2 2 2 -1 -2 -2 -2 2 -2 -1 2 1 -1 -2] [-1 1 -2 -1 -1 -2 2 -1 -1 -2 1 -2 -1 2 2 1 -2 -1 2 2] [-2 2 1 -2 -2 -2 2 -1 1 -1 -2 -1 1 2 -2 1 1 -2 -1 -1] [-1 2 2 -1 -1 2 -1 -2 2 2 2 -2 -1 2 -2 2 -1 -1 1 2] [-1 -2 -2 -2 -1 -2 -1 2 1 -2 -2 -2 -1 -1 -1 -1 1 2 1 -2] [ 2 -2 2 1 -1 -2 -2 1 -2 -1 -2 1 1 -1 1 2 1 -1 2 1] [-2 2 -1 -1 2 1 1 1 -2 2 -1 -1 1 2 -1 -1 -1 -1 2 1] sage: E = A.echelon_form() verbose 1 (4072: matrix.py, echelon_form) height_guess=4194304 verbose 1 (4072: matrix.py, echelon_form) p=20011 verbose 1 (4072: matrix.py, echelon_form) p=20021 verbose 1 (4072: matrix.py, echelon_form) start rr verbose 2 (4072: matrix.py, echelon_form) (Failed to compute rational reconstruction -- redoing with several more primes verbose 1 (4072: matrix.py, echelon_form) p=20023 verbose 1 (4072: matrix.py, echelon_form) p=20029 verbose 1 (4072: matrix.py, echelon_form) p=20047 verbose 1 (4072: matrix.py, echelon_form) p=20051 verbose 1 (4072: matrix.py, echelon_form) p=20063 verbose 1 (4072: matrix.py, echelon_form) p=20071 verbose 1 (4072: matrix.py, echelon_form) p=20089 verbose 1 (4072: matrix.py, echelon_form) p=20101 verbose 1 (4072: matrix.py, echelon_form) p=20107 verbose 1 (4072: matrix.py, echelon_form) p=20113 verbose 1 (4072: matrix.py, echelon_form) start rr verbose 1 (4072: matrix.py, echelon_form) done (time = 0.01) sage: E _11 = [ 1 0 0 0 0 0 0 0 0 0 19336/4045 -25513/12135 -9596/4045 -2857/4045 -3967/12135 8981/4045 2524/809 48038/12135 -47284/12135 523/4045] [ 0 1 0 0 0 0 0 0 0 0 7487/1618 -2041/1618 -1421/1618 -3949/1618 -3667/1618 4117/1618 5797/809 8831/1618 -14885/1618 -2079/809] [ 0 0 1 0 0 0 0 0 0 0 -39111/8090 43123/24270 13011/8090 14377/8090 18697/24270 -16521/8090 -2900/809 -108923/24270 113029/24270 3071/4045] [ 0 0 0 1 0 0 0 0 0 0 18243/8090 28201/24270 7467/8090 -26631/8090 -36131/24270 9353/8090 4205/809 83389/24270 -172427/24270 -12098/4045] [ 0 0 0 0 1 0 0 0 0 0 -7239/1618 4485/1618 3339/1618 1237/1618 1483/1618 -4533/1618 -2706/809 -6101/1618 5605/1618 -471/809] [ 0 0 0 0 0 1 0 0 0 0 -2508/809 -581/2427 -372/809 2295/809 4306/2427 -1717/809 -4009/809 -9023/2427 14782/2427 2279/809] [ 0 0 0 0 0 0 1 0 0 0 -3169/4045 -668/12135 -741/4045 5113/4045 8773/12135 -3244/4045 -1588/809 -16427/12135 25726/12135 3698/4045] [ 0 0 0 0 0 0 0 1 0 0 9321/4045 -4401/4045 -2856/4045 -7642/4045 -7944/4045 4381/4045 4403/809 17211/4045 -25238/4045 -8887/4045] [ 0 0 0 0 0 0 0 0 1 0 15669/8090 5783/24270 -579/8090 -16803/8090 -39163/24270 4589/8090 3025/809 72617/24270 -128941/24270 -10854/4045] [ 0 0 0 0 0 0 0 0 0 1 4501/809 -4160/2427 -962/809 -1594/809 -4166/2427 2445/809 3303/809 11275/2427 -11366/2427 -635/809] sage: view(E) sage: A = MatrixSpace(QQ,50,50).random_element() sage: view(A) sage: time E=A.echelon_form(height_guess=2) verbose 1 (4072: matrix.py, echelon_form) height_guess=2 verbose 1 (4072: matrix.py, echelon_form) p=20011 CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 sage: time E=A.echelon_form(height_guess=20000000000000000) verbose 1 (4072: matrix.py, echelon_form) height_guess=20000000000000000 verbose 1 (4072: matrix.py, echelon_form) p=20011 CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 sage: A = MatrixSpace(QQ,50,51).random_element() sage: time E=A.echelon_form(height_guess=2) verbose 1 (4072: matrix.py, echelon_form) height_guess=2 verbose 1 (4072: matrix.py, echelon_form) p=20011 verbose 1 (4072: matrix.py, echelon_form) start rr verbose 2 (4072: matrix.py, echelon_form) (Failed to compute rational reconstruction -- redoing with several more primes verbose 1 (4072: matrix.py, echelon_form) p=20021 verbose 1 (4072: matrix.py, echelon_form) p=20023 verbose 1 (4072: matrix.py, echelon_form) p=20029 verbose 1 (4072: matrix.py, echelon_form) p=20047 verbose 1 (4072: matrix.py, echelon_form) p=20051 verbose 1 (4072: matrix.py, echelon_form) p=20063 verbose 1 (4072: matrix.py, echelon_form) p=20071 verbose 1 (4072: matrix.py, echelon_form) p=20089 verbose 1 (4072: matrix.py, echelon_form) p=20101 verbose 1 (4072: matrix.py, echelon_form) p=20107 verbose 1 (4072: matrix.py, echelon_form) start rr verbose 2 (4072: matrix.py, echelon_form) (Failed to compute rational reconstruction -- redoing with several more primes verbose 1 (4072: matrix.py, echelon_form) p=20113 verbose 1 (4072: matrix.py, echelon_form) p=20117 verbose 1 (4072: matrix.py, echelon_form) p=20123 verbose 1 (4072: matrix.py, echelon_form) p=20129 verbose 1 (4072: matrix.py, echelon_form) p=20143 verbose 1 (4072: matrix.py, echelon_form) p=20147 verbose 1 (4072: matrix.py, echelon_form) p=20149 verbose 1 (4072: matrix.py, echelon_form) p=20161 verbose 1 (4072: matrix.py, echelon_form) p=20173 verbose 1 (4072: matrix.py, echelon_form) p=20177 verbose 1 (4072: matrix.py, echelon_form) start rr verbose 1 (4072: matrix.py, echelon_form) done (time = 0.12) CPU times: user 0.21 s, sys: 0.00 s, total: 0.21 s Wall time: 0.21 sage: E _19 = [ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -586411808768920335439467593172687080031004/44210543959175624206605488399643106112991] [ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -708404508383430095081202980696816113260029/44210543959175624206605488399643106112991] [ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -118039222789596630930807316641505448313820/44210543959175624206605488399643106112991] [ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -308231372354438799657753748558566531603753/14736847986391874735535162799881035370997] [ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 811264936262214376162661748038352690824098/44210543959175624206605488399643106112991] [ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 693405535928011041206724582550570720654756/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 584600750663164978747757929768791865058432/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -66144772139637342263614099449408035824167/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1524566131802902765245589259209179291980615/44210543959175624206605488399643106112991] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 312572096522353878005300652153405065650873/44210543959175624206605488399643106112991] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -210067781412806923927267771209307294969867/44210543959175624206605488399643106112991] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1345093831974751368174841707250379672933383/44210543959175624206605488399643106112991] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 253482467974529732691237548116036497975788/44210543959175624206605488399643106112991] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10382660945269122311568919374204843613954/4019140359925056746055044399967555101181] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -41675546357084855800392499361577628336856/1194879566464206059637986172963327192243] [ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -27873051061625326901996118490888846119263/14736847986391874735535162799881035370997] [ 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278704489819327919274131180972432988764579/44210543959175624206605488399643106112991] [ 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 160223342225066156482440539188764373182816/14736847986391874735535162799881035370997] [ 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 186176660919319802928177948849366146917984/14736847986391874735535162799881035370997] [ 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 771722465596836899453505945461800022180267/44210543959175624206605488399643106112991] [ 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -198989601972148411872979061573958338545201/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 3023831062679230888014452592878993975896/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 -500540359568695947763836733884825563233715/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 545780269768328429570633813070960194808040/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 1265623809896196468985794652690697974052677/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 293399927151689633985835860995938702283/108625415133109641785271470269393381113] [ 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 10313090006388405154894500985207556213330/1194879566464206059637986172963327192243] [ 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 -884688162055490752047387097585661206866308/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 459159019420187237615700543312381822041674/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 -848034360827235709578179898182329491336559/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 265635366861443389127418815578131745497337/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 -7417594840768901386895350311833299806023/1339713453308352248685014799989185033727] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 109634022236834339994876831001510604402740/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 -122029094626170876551209471266182117655370/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -522880917192803369380443168287137729862755/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -50557760888738181064100259418637824721110/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1202562977027662830340791146643349199141960/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -88738802526481386739738622524744899034295/4019140359925056746055044399967555101181] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 22872791966318207973373327274087783294099/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -42353024688363159250574368378309955029591/1339713453308352248685014799989185033727] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1271102522898671994877060442481239364435574/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -702597211982873857025951733116654687356379/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -38202446595190905348007126342360253534308/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 8372236786706967142560651273913179708508/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -106261371463869174548704194493094627924165/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 272537540340554730783035582985354910078648/14736847986391874735535162799881035370997] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 117905221149479953177808116150347040001099/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -594340680420865140619999470985181394128473/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -263089143435892119606568122818183832228001/44210543959175624206605488399643106112991] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 34097314252480390853639510602760460930954/14736847986391874735535162799881035370997] sage: A.transpose()[-1] ------------------------------------------------------------ Traceback (most recent call last): File "", line 1, in ? File "/home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix.py", line 3813, in __getitem__ return self.row(ij) File "/home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix.py", line 1122, in row return V([self[i,j] for j in xrange(self.ncols())]) File "/home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix.py", line 3814, in __getitem__ return self.__matrix[ij] File "dense_matrix_pyx.pyx", line 708, in dense_matrix_pyx.Matrix_rational.__getitem__ IndexError: Invalid index. sage: A.transpose()[50] _21 = (2, -1, 1, -2, -1, -1, -2, 2, 1, 2, 1, -2, 1, -1, 1, 2, 2, 2, -2, -1, -2, 1, -2, -2, -1, -2, 1, 2, 1, 2, -1, -2, -1, -1, 1, -1, -2, 1, 2, -1, -1, 2, -1, -2, -1, 2, 2, -2, 1, 1) sage: A.transpose()[51] ------------------------------------------------------------ Traceback (most recent call last): File "", line 1, in ? File "/home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix.py", line 3813, in __getitem__ return self.row(ij) File "/home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix.py", line 1122, in row return V([self[i,j] for j in xrange(self.ncols())]) File "/home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix.py", line 3814, in __getitem__ return self.__matrix[ij] File "dense_matrix_pyx.pyx", line 708, in dense_matrix_pyx.Matrix_rational.__getitem__ IndexError: Invalid index. sage: A.transpose()[50] _23 = (2, -1, 1, -2, -1, -1, -2, 2, 1, 2, 1, -2, 1, -1, 1, 2, 2, 2, -2, -1, -2, 1, -2, -2, -1, -2, 1, 2, 1, 2, -1, -2, -1, -1, 1, -1, -2, 1, 2, -1, -1, 2, -1, -2, -1, 2, 2, -2, 1, 1) sage: E.transpose()[50] _24 = (-586411808768920335439467593172687080031004/44210543959175624206605488399643106112991, -708404508383430095081202980696816113260029/44210543959175624206605488399643106112991, -118039222789596630930807316641505448313820/44210543959175624206605488399643106112991, -308231372354438799657753748558566531603753/14736847986391874735535162799881035370997, 811264936262214376162661748038352690824098/44210543959175624206605488399643106112991, 693405535928011041206724582550570720654756/44210543959175624206605488399643106112991, 584600750663164978747757929768791865058432/44210543959175624206605488399643106112991, -66144772139637342263614099449408035824167/14736847986391874735535162799881035370997, -1524566131802902765245589259209179291980615/44210543959175624206605488399643106112991, 312572096522353878005300652153405065650873/44210543959175624206605488399643106112991, -210067781412806923927267771209307294969867/44210543959175624206605488399643106112991, -1345093831974751368174841707250379672933383/44210543959175624206605488399643106112991, 253482467974529732691237548116036497975788/44210543959175624206605488399643106112991, 10382660945269122311568919374204843613954/4019140359925056746055044399967555101181, -41675546357084855800392499361577628336856/1194879566464206059637986172963327192243, -27873051061625326901996118490888846119263/14736847986391874735535162799881035370997, 278704489819327919274131180972432988764579/44210543959175624206605488399643106112991, 160223342225066156482440539188764373182816/14736847986391874735535162799881035370997, 186176660919319802928177948849366146917984/14736847986391874735535162799881035370997, 771722465596836899453505945461800022180267/44210543959175624206605488399643106112991, -198989601972148411872979061573958338545201/44210543959175624206605488399643106112991, 3023831062679230888014452592878993975896/14736847986391874735535162799881035370997, -500540359568695947763836733884825563233715/44210543959175624206605488399643106112991, 545780269768328429570633813070960194808040/44210543959175624206605488399643106112991, 1265623809896196468985794652690697974052677/44210543959175624206605488399643106112991, 293399927151689633985835860995938702283/108625415133109641785271470269393381113, 10313090006388405154894500985207556213330/1194879566464206059637986172963327192243, -884688162055490752047387097585661206866308/44210543959175624206605488399643106112991, 459159019420187237615700543312381822041674/44210543959175624206605488399643106112991, -848034360827235709578179898182329491336559/44210543959175624206605488399643106112991, 265635366861443389127418815578131745497337/14736847986391874735535162799881035370997, -7417594840768901386895350311833299806023/1339713453308352248685014799989185033727, 109634022236834339994876831001510604402740/14736847986391874735535162799881035370997, -122029094626170876551209471266182117655370/14736847986391874735535162799881035370997, -522880917192803369380443168287137729862755/44210543959175624206605488399643106112991, -50557760888738181064100259418637824721110/14736847986391874735535162799881035370997, 1202562977027662830340791146643349199141960/44210543959175624206605488399643106112991, -88738802526481386739738622524744899034295/4019140359925056746055044399967555101181, 22872791966318207973373327274087783294099/14736847986391874735535162799881035370997, -42353024688363159250574368378309955029591/1339713453308352248685014799989185033727, 1271102522898671994877060442481239364435574/44210543959175624206605488399643106112991, -702597211982873857025951733116654687356379/44210543959175624206605488399643106112991, -38202446595190905348007126342360253534308/44210543959175624206605488399643106112991, 8372236786706967142560651273913179708508/14736847986391874735535162799881035370997, -106261371463869174548704194493094627924165/44210543959175624206605488399643106112991, 272537540340554730783035582985354910078648/14736847986391874735535162799881035370997, 117905221149479953177808116150347040001099/44210543959175624206605488399643106112991, -594340680420865140619999470985181394128473/44210543959175624206605488399643106112991, -263089143435892119606568122818183832228001/44210543959175624206605488399643106112991, 34097314252480390853639510602760460930954/14736847986391874735535162799881035370997) sage: view(E.transpose()[50]) sage: A = MatrixSpace(QQ,200,200).random_element() sage: E = A.echelon_form() verbose 1 (4072: matrix.py, echelon_form) height_guess=6427752177035961102167848369364650410088811975131171341205504 verbose 1 (4072: matrix.py, echelon_form) p=20011 sage: A = MatrixSpace(QQ,50,50, sparse=True).random_element() sage: A _29 = [ 2 1 -2 -1 -1 -1 1 -1 1 1 -1 -1 1 2 2 1 -1 2 -1 2 2 -2 2 -2 -1 -1 -1 -1 -2 2 1 1 -2 1 -2 1 -1 1 2 -1 2 -2 -1 -1 -1 -1 -1 1 -1 -2] [ 1 1 2 -2 1 1 -1 -2 -1 -2 1 -2 2 -2 -1 2 -1 -2 1 -2 -2 -2 -2 -1 -2 -1 1 -2 -2 -2 -1 2 2 1 1 2 2 2 2 -1 -2 1 2 -2 -1 1 -1 -2 1 1] [-2 -2 -2 -1 -1 2 -2 -1 -1 -1 2 -2 -2 2 2 1 2 2 1 2 1 2 -1 -2 -1 1 -2 2 1 2 1 2 -1 2 2 1 1 -1 -1 -1 -1 2 -1 -2 2 -2 1 -2 2 2] [ 1 -1 -2 2 -1 -1 -2 -2 1 -1 2 -1 2 1 -2 -1 -1 2 2 1 2 2 2 -1 -2 -1 2 1 -1 -1 2 2 1 1 -1 1 -2 -1 -1 -2 2 2 -2 -1 -1 -2 -1 1 1 -2] [ 2 1 1 2 1 2 1 -1 -2 -2 -1 1 2 2 2 -2 2 1 -1 2 1 -1 -1 1 1 1 -1 2 -1 2 1 -1 -1 -1 1 2 1 2 2 2 -2 1 1 -1 1 2 1 2 -2 1] [ 1 2 -2 -1 -2 2 1 2 -1 2 1 -1 2 -2 1 -2 1 -1 2 1 2 1 -2 -2 1 2 2 2 1 -2 1 2 1 -2 -1 2 -1 -2 2 1 1 1 1 1 -2 -2 -1 2 1 2] [ 2 2 1 1 -1 2 -1 1 1 1 1 1 1 -1 -2 1 1 -2 -1 1 -1 1 2 1 -1 -2 -1 -1 -2 -2 -2 -2 2 2 -1 -1 2 -1 1 2 -2 -2 1 -1 1 -1 -2 2 -2 -2] [ 2 2 -2 1 -1 1 -2 2 2 2 1 -1 -2 -2 -2 -1 1 1 -2 1 -1 2 2 2 2 2 2 -1 -1 -2 -1 -2 1 2 1 -2 -2 -1 -2 1 -1 2 1 2 -1 -1 2 -2 -1 1] [-1 2 -2 -1 2 -1 -1 2 2 1 -1 -2 2 -2 1 2 1 1 2 2 -2 -1 -2 2 -2 -2 2 1 1 1 -2 -2 2 1 -1 2 1 -1 2 -1 2 1 1 -2 -2 1 1 1 1 -2] [ 2 -1 1 2 -1 2 -1 -1 2 -2 1 1 1 2 -2 2 1 -1 2 1 -2 2 -2 1 1 -1 -1 2 -1 1 -2 1 -1 -2 1 -1 2 -2 -1 1 2 -1 2 -1 -2 -1 1 2 2 -1] [-2 2 2 1 2 1 1 -2 -1 1 2 1 -2 -2 -2 2 -2 2 -1 -1 -2 2 -1 1 -2 1 1 2 2 1 2 2 2 -1 -2 -2 2 -2 2 -2 -1 -2 1 2 -2 1 1 2 1 -2] [ 2 -2 -2 2 2 -1 -1 -2 -1 1 2 1 2 1 -2 -1 -1 -2 1 1 -2 -1 -2 -2 2 2 -1 -2 1 -1 2 -1 -1 -1 1 -2 -2 2 -1 -1 2 1 -1 1 1 1 -2 1 2 -1] [-2 -1 2 -1 1 -2 1 -2 2 2 -1 -2 2 2 -2 -2 2 2 -2 1 -2 2 1 -1 -1 -2 -1 1 1 1 -1 -2 -1 1 -1 -2 -1 2 1 1 -1 2 1 2 1 1 2 -1 2 -1] [-1 1 1 2 1 2 -2 -2 -2 1 1 -2 -2 1 1 2 2 -2 -2 -1 -2 1 1 -1 1 1 1 2 2 -1 -1 -1 1 1 -1 -2 -1 -1 -1 -2 2 -1 -2 2 2 -1 1 1 -1 1] [-1 -2 2 -2 1 -2 1 -2 -2 1 2 2 -1 -2 -1 -1 1 2 -2 -2 -2 -2 2 -2 2 -2 -1 2 -2 1 1 -2 -2 -1 1 -2 2 2 -1 2 -2 -1 2 -1 -1 2 1 -1 2 -2] [-2 2 -1 1 1 1 1 2 -2 -2 -2 2 -1 1 1 -1 2 -1 1 -2 1 1 -1 2 1 -2 -1 -1 -1 1 2 1 -2 -2 -1 -2 -2 -2 -2 2 2 -1 1 1 -2 2 1 2 -2 -2] [-1 -1 1 -2 1 2 2 -2 1 -1 -2 1 1 -2 1 -1 -2 1 -2 2 -2 1 -2 -1 1 2 2 -1 2 -2 -2 -2 1 -2 -1 -1 1 -2 -1 -1 1 -2 2 -2 -1 2 2 -1 2 2] [ 1 -2 2 -1 2 2 2 2 -2 -1 1 -2 -2 1 1 2 -2 -1 -1 1 -2 -1 1 2 1 2 -1 -1 -2 -2 2 2 1 1 -2 -2 -1 -2 2 1 -2 -1 1 1 -2 2 -1 -2 1 -2] [-1 -1 2 -1 2 -1 -1 -1 -2 -2 -1 1 1 2 -2 1 -2 1 -2 -2 1 -1 2 2 -1 1 2 2 -2 -1 2 -2 1 1 -2 -2 -2 -1 -1 -2 -2 -1 2 1 -2 -1 2 1 -2 1] [-2 2 -2 -2 2 1 1 2 -2 -1 1 1 1 -2 -2 -2 1 1 2 2 2 -1 -2 -2 -2 -1 1 -2 1 1 -2 1 1 -2 2 -1 2 1 -2 -2 -2 -1 2 -1 -2 2 -2 -1 -2 2] [ 2 1 -2 -1 2 1 -1 1 1 -1 -1 1 -2 1 2 -2 2 1 -1 1 -2 2 -2 -1 2 2 -2 1 1 2 1 -2 -2 -2 2 -1 -1 -1 2 2 -2 -2 -1 -2 1 1 2 -2 2 -1] [-2 2 2 1 2 1 -2 -1 2 2 -2 2 1 -2 2 -2 2 -1 1 -2 1 -1 1 -2 -2 -2 2 1 -1 -1 2 -1 2 1 1 -2 2 -1 2 2 -1 2 1 2 1 -2 -1 -1 -1 2] [-1 2 2 -1 2 1 2 -2 2 -2 1 2 -1 -1 1 -2 2 1 1 -2 2 1 -2 1 1 -2 1 -2 -1 -2 -1 -2 -2 -2 1 1 -2 2 2 2 2 1 -2 -2 -1 1 -2 -2 -1 -2] [-2 -2 2 1 -1 1 -2 2 -1 -2 1 1 -1 -1 1 2 -1 -2 2 2 -2 2 2 -1 1 -1 1 2 -1 1 2 -2 -2 1 -1 -2 1 2 -1 1 -1 2 -1 1 1 1 2 2 -2 -2] [-2 2 1 -1 1 -1 1 2 2 -1 -1 2 2 2 -1 -1 -2 -1 2 2 2 -2 -1 2 2 -2 2 -2 1 -2 2 -2 1 -2 1 1 2 1 2 -1 2 -2 -1 2 1 1 -1 -2 2 2] [ 2 1 2 2 1 1 -1 2 1 2 -1 -2 -1 -2 1 -2 -1 -1 -2 2 -1 1 -2 -1 2 -2 2 -1 -1 -1 -2 1 2 2 -1 -2 2 -2 1 2 2 -1 2 1 2 1 -2 2 -1 2] [ 1 1 -2 -1 1 2 2 1 1 1 -2 1 -1 -2 1 -1 -1 1 -1 1 1 -1 2 2 1 -1 -1 -2 2 -1 1 2 1 -2 2 -2 2 -1 2 -2 -2 -2 -1 -1 -2 -2 -2 1 -1 1] [-1 -2 -2 -2 2 2 -2 2 -2 -2 -2 -2 2 2 -1 -2 1 -1 -1 -2 -2 2 -1 -2 2 -2 -1 -1 -1 -1 2 -1 -1 2 1 2 -1 1 1 1 -1 -1 -2 -2 -1 1 -1 -1 -1 2] [-1 2 -1 2 -2 2 -2 1 1 2 2 -1 2 -2 1 -1 1 2 1 -2 -2 -1 -2 1 1 1 2 2 1 2 2 1 -2 1 1 2 -2 2 -2 -1 -2 -2 -2 2 2 -1 -2 2 1 -1] [-2 1 -2 1 -2 -1 -1 1 -1 1 -2 2 2 1 1 1 1 1 2 -2 1 1 1 1 -2 2 1 -1 1 1 -1 -2 2 1 -1 -2 2 1 -1 2 -2 1 1 1 -2 2 1 -2 -2 2] [-2 -1 2 1 1 2 -1 -2 1 1 -1 -1 -2 2 2 1 2 1 1 2 1 -1 1 -2 2 2 -1 -2 -1 1 -1 -2 -1 2 1 2 -2 -2 1 -1 -1 1 -1 1 2 -2 -2 -2 -1 2] [ 1 -1 -2 2 1 1 1 -2 1 1 -2 2 -2 2 -2 2 -2 2 2 2 1 2 1 2 1 -1 1 -2 2 1 2 -1 -1 -2 2 -2 -2 2 1 2 -2 1 2 2 1 2 1 2 -2 2] [ 2 2 2 2 -2 -2 -2 -1 2 -2 2 -2 -1 1 -1 1 1 1 1 -2 1 -1 2 2 -1 -1 -2 2 -2 -1 -2 -1 -2 2 -2 -1 -2 -1 -1 -2 1 -2 -1 1 -1 -2 1 2 -1 1] [-1 -2 -2 1 -2 1 2 -2 -1 1 1 2 1 1 -2 -2 -2 -2 2 2 2 -2 -2 1 2 2 2 -2 1 2 -1 2 -1 -2 -2 -1 -2 -1 -1 -2 -1 -1 1 1 -1 -2 2 1 -1 -1] [-2 1 1 1 -2 -1 -2 -2 -2 -1 -1 -2 -2 2 -2 2 -1 1 -1 -2 -1 1 -1 1 2 1 2 -2 -1 2 2 -2 2 2 2 2 2 2 -2 -1 2 2 -1 1 1 -1 2 2 1 1] [ 1 -1 1 2 -2 -2 -1 -1 -1 -1 1 2 2 2 -1 2 2 -2 1 -2 -2 1 -1 -1 -1 1 2 2 -1 -1 -1 -1 2 1 1 -1 1 1 -2 -2 2 2 2 2 -1 1 -1 -1 2 2] [-1 -2 2 -1 1 -1 1 -1 -1 -2 -1 2 -1 2 2 -1 -1 -1 1 -1 2 1 2 -1 -2 2 -1 2 -1 2 1 1 -1 1 2 2 -2 1 1 1 1 1 1 1 2 2 1 -2 -2 -1] [ 2 1 -2 2 2 2 2 1 1 2 -1 -2 2 -2 -2 1 2 -2 -2 1 1 -2 -2 2 2 -1 -2 1 1 -1 1 -1 1 1 -2 2 2 1 -1 -2 2 2 -2 -1 1 2 -2 -2 2 2] [ 2 2 -2 2 -2 1 1 -1 1 2 1 1 1 2 -2 -2 -1 2 -2 1 -1 -2 -1 1 -1 -2 -2 -2 -1 1 2 -2 -1 -2 1 2 2 -1 -1 1 1 -2 -1 -1 -1 2 2 2 2 -1] [ 2 -1 1 -2 2 -2 2 2 -2 2 -2 2 2 1 1 -2 -1 -2 -2 1 -2 1 -2 -1 -2 -2 -1 -1 2 2 2 1 2 -1 -2 1 1 2 1 1 2 2 2 2 1 -1 -2 1 -2 2] [ 1 -2 2 1 -2 2 -1 2 -1 -1 2 1 -1 1 -1 2 2 1 -2 -2 -1 2 1 2 -1 -1 -1 -1 1 2 1 1 -2 -1 2 -1 1 1 -2 -2 -2 2 -1 1 -1 1 1 1 1 -1] [-2 1 2 -2 -2 -2 1 -1 1 -1 1 -2 2 -1 1 1 1 1 -1 -1 -2 2 2 -2 1 -2 1 1 -2 -2 -1 -1 1 1 1 2 1 2 1 1 -2 2 -1 -1 -1 -2 -2 1 2 2] [-1 2 -1 -1 1 2 1 2 2 -2 2 -1 -2 -1 -1 -1 -2 -2 2 1 2 2 -1 -2 -1 2 1 1 -2 -1 -1 -2 1 1 2 2 1 1 -1 -2 -2 -2 2 2 -2 2 2 -1 -1 -2] [-2 -2 1 1 2 1 2 1 -2 2 1 -2 1 -2 2 -2 -1 -2 -2 2 2 -2 2 -2 1 -2 -2 1 -2 -2 -2 1 2 -2 1 -2 -1 -1 1 -2 -2 -1 1 2 -1 2 -2 -1 1 1] [-2 -2 -2 2 1 -1 1 2 -2 2 -1 1 -1 1 -1 -1 1 2 2 -1 -2 -1 2 -2 -2 -1 -2 -1 2 -2 1 1 1 2 -2 1 2 -1 2 1 -1 -1 2 -1 -1 -1 1 1 -1 2] [ 2 2 1 2 -2 2 2 1 -1 -2 2 -1 -1 1 1 2 2 1 -1 -1 -1 1 -1 -2 -2 1 1 -1 -2 1 2 2 -2 -1 -1 2 -2 -1 -2 -2 -2 1 -2 2 -2 1 1 -2 1 -1] [-1 1 1 1 1 1 2 -1 -2 -2 -1 -2 -1 1 2 2 -2 2 -2 -2 1 -1 1 -1 2 -1 -2 -1 1 1 2 1 -2 2 1 -1 -1 1 -2 1 2 1 2 -1 2 -1 -2 -1 -1 1] [ 2 2 -1 -1 -2 1 -1 -1 -1 2 -2 2 2 1 2 -2 -1 -1 2 2 2 -2 1 -2 2 -1 1 2 -1 -1 -2 2 -2 -2 2 2 2 -2 -2 -1 2 1 1 -2 -2 -1 2 2 2 1] [ 2 2 1 1 1 -2 1 1 -1 1 -2 2 -2 -2 1 2 1 1 -2 -1 2 1 -2 2 -2 -1 2 -1 2 2 1 -2 2 -1 -2 -1 1 -1 -2 1 -2 2 -1 2 1 -1 -1 1 -1 2] [-2 -1 -2 -1 2 2 -2 -1 -1 -1 1 1 -2 2 1 -2 1 2 1 1 2 -1 -2 -1 2 1 2 1 -2 -1 2 -1 1 -1 2 1 -1 -1 2 1 -2 2 -2 -1 1 1 1 2 2 -2] sage: M = MatrixSpace(QQ,50,50, sparse=True) sage: M _31 = Full MatrixSpace of 50 by 50 sparse matrices over Rational Field sage: M.random_element? Type: instancemethod Base Class: String Form: Namespace: Interactive File: /home/was/s/local/lib/python2.4/site-packages/sage/matrix/matrix_space.py Definition: M.random_element(self, X=[-2, -1, 1, 2], prob=1.0, coerce=True) Docstring: Returns a random element of self. sage: A = M.random_element(prob=0.1) sage: A[0] _34 = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) sage: E = A.echelon_form() verbose 2 (4195: matrix.py, echelon_form) height_guess = 1600000 verbose 2 (4195: matrix.py, echelon_form) echelon modulo p=20011 (11.11% done) verbose 2 (4195: matrix.py, echelon_form) time to reduce matrix mod p: (time = 0.0) verbose 1 (4195: matrix.py, sparse_matrix_pyx matrix_modint echelon) verbose 2 (4195: matrix.py, echelon_form) time to put reduced matrix in echelon form: (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) time for pivot compare (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) echelon modulo p=20021 (55.56% done) verbose 2 (4195: matrix.py, echelon_form) time to reduce matrix mod p: (time = 0.0) verbose 1 (4195: matrix.py, sparse_matrix_pyx matrix_modint echelon) verbose 2 (4195: matrix.py, echelon_form) time to put reduced matrix in echelon form: (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) time for pivot compare (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) start crt and rr verbose 2 (4195: matrix.py, echelon_form) crt and rr time is (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) total time (time = 0.01) sage: M = MatrixSpace(QQ,500,300, sparse=True) sage: A = M.random_element(prob=0.01) sage: time E=A.echelon_form(height_guess=2) verbose 2 (4195: matrix.py, echelon_form) height_guess = 2 verbose 2 (4195: matrix.py, echelon_form) echelon modulo p=20011 (25.00% done) verbose 2 (4195: matrix.py, echelon_form) time to reduce matrix mod p: (time = 0.0) verbose 1 (4195: matrix.py, sparse_matrix_pyx matrix_modint echelon) verbose 2 (4195: matrix.py, echelon_form) time to put reduced matrix in echelon form: (time = 0.01) verbose 2 (4195: matrix.py, echelon_form) time for pivot compare (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) start crt and rr verbose 2 (4195: matrix.py, echelon_form) crt and rr time is (time = 0.01) verbose 2 (4195: matrix.py, echelon_form) total time (time = 0.02) CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s Wall time: 0.03 sage: ModularSymbols(389) verbose 1 (59: relation_matrix.py, modS_relations) verbose 1 (59: relation_matrix.py, modS_relations) finished creating S relations (time = 0.01) verbose 1 (322: relation_matrix.py, sparse_2term_quotient) verbose 1 (322: relation_matrix.py, sparse_2term_quotient) finished (time = 0.02) verbose 1 (136: relation_matrix.py, T_relation_matrix_wtk_g0) verbose 1 (136: relation_matrix.py, T_relation_matrix_wtk_g0) finished (number of rows=130) (time = 0.05) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) verbose 2 (4195: matrix.py, echelon_form) height_guess = 1 verbose 2 (4195: matrix.py, echelon_form) echelon modulo p=20011 (33.33% done) verbose 2 (4195: matrix.py, echelon_form) time to reduce matrix mod p: (time = 0.0) verbose 1 (4195: matrix.py, sparse_matrix_pyx matrix_modint echelon) verbose 2 (4195: matrix.py, echelon_form) time to put reduced matrix in echelon form: (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) time for pivot compare (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) start crt and rr verbose 2 (4195: matrix.py, echelon_form) crt and rr time is (time = 0.01) verbose 2 (4195: matrix.py, echelon_form) total time (time = 0.01) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) echelon done, now creating gens --> basis mapping (time = 0.02) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) done doing setup (time = 0.02) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) done making quotient matrix (time = 0.01) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) now filling in the rest of the matrix verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) set 194 rows verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) time to fill in rest of matrix (time = 0.02) _39 = Full Modular Symbols space for Gamma_0(389) of weight 2 with sign 0 and dimension 65 over Rational Field sage: time ModularSymbols(2006) verbose 1 (59: relation_matrix.py, modS_relations) verbose 1 (59: relation_matrix.py, modS_relations) finished creating S relations (time = 0.12) verbose 1 (322: relation_matrix.py, sparse_2term_quotient) verbose 1 (322: relation_matrix.py, sparse_2term_quotient) finished (time = 0.14) verbose 1 (136: relation_matrix.py, T_relation_matrix_wtk_g0) verbose 1 (136: relation_matrix.py, T_relation_matrix_wtk_g0) finished (number of rows=1080) (time = 0.47) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) verbose 2 (4195: matrix.py, echelon_form) height_guess = 1 verbose 2 (4195: matrix.py, echelon_form) echelon modulo p=20011 (25.00% done) verbose 2 (4195: matrix.py, echelon_form) time to reduce matrix mod p: (time = 0.0) verbose 1 (4195: matrix.py, sparse_matrix_pyx matrix_modint echelon) verbose 2 (4195: matrix.py, echelon_form) time to put reduced matrix in echelon form: (time = 0.17) verbose 2 (4195: matrix.py, echelon_form) time for pivot compare (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) start crt and rr verbose 2 (4195: matrix.py, echelon_form) crt and rr time is (time = 0.13) verbose 2 (4195: matrix.py, echelon_form) total time (time = 0.3) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) echelon done, now creating gens --> basis mapping (time = 0.32) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) done doing setup (time = 0.11) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) done making quotient matrix (time = 0.49) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) now filling in the rest of the matrix verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) set 1620 rows verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) time to fill in rest of matrix (time = 0.06) CPU times: user 1.71 s, sys: 0.11 s, total: 1.82 s Wall time: 1.82 _40 = Full Modular Symbols space for Gamma_0(2006) of weight 2 with sign 0 and dimension 541 over Rational Field sage: time ModularSymbols(10007) verbose 1 (59: relation_matrix.py, modS_relations) verbose 1 (59: relation_matrix.py, modS_relations) finished creating S relations (time = 0.25) verbose 1 (322: relation_matrix.py, sparse_2term_quotient) verbose 1 (322: relation_matrix.py, sparse_2term_quotient) finished (time = 0.44) verbose 1 (136: relation_matrix.py, T_relation_matrix_wtk_g0) verbose 1 (136: relation_matrix.py, T_relation_matrix_wtk_g0) finished (number of rows=3336) (time = 1.2) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) verbose 2 (4195: matrix.py, echelon_form) height_guess = 1 verbose 2 (4195: matrix.py, echelon_form) echelon modulo p=20011 (20.00% done) verbose 2 (4195: matrix.py, echelon_form) time to reduce matrix mod p: (time = 0.0) verbose 1 (4195: matrix.py, sparse_matrix_pyx matrix_modint echelon) verbose 2 (4195: matrix.py, echelon_form) time to put reduced matrix in echelon form: (time = 0.86) verbose 2 (4195: matrix.py, echelon_form) time for pivot compare (time = 0.0) verbose 2 (4195: matrix.py, echelon_form) start crt and rr verbose 2 (4195: matrix.py, echelon_form) crt and rr time is (time = 0.26) verbose 2 (4195: matrix.py, echelon_form) total time (time = 1.13) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) echelon done, now creating gens --> basis mapping (time = 1.16) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) done doing setup (time = 0.19) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) done making quotient matrix (time = 4.24) verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) now filling in the rest of the matrix verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) set 5004 rows verbose 1 (181: relation_matrix.py, gens_to_basis_matrix) time to fill in rest of matrix (time = 0.22) CPU times: user 7.54 s, sys: 0.27 s, total: 7.81 s Wall time: 7.82 _41 = Full Modular Symbols space for Gamma_0(10007) of weight 2 with sign 0 and dimension 1669 over Rational Field sage: sage: sage: sage: Do you really want to exit ([y]/n)? Exiting SAGE (CPU time 0m12.26s, Wall time 15m14.40s). was@sha:~$ was@sha:~$