outputForSingular -- get a string for a matrix over a finite field

Synopsis

Usage:
ouputForSingular(g,n)
Inputs:
- g, an integer, the even (!) genus
- n, an integer, the torsion level
- k, an integer, if present the exponent 2 ≤k ≤n-1 of L^k in the Torsion conjecture
Outputs:
- a string, a string which defines a matrix over a finite field

Description

Produces the string for a matrix over a finite field, whose rank can decides about the truth of the Prym-Green Conjecture for the spezific value (g,n) or the torsion bundle conjecture for the spezific value (g,n,k)

i1 : (p,Mentries)=outputForSingular(6,3,2)

o1 = (10303, {{5142, 2601, 4179, 3504, -1955, -683, -1960, -4240, -3867,
     ------------------------------------------------------------------------
     2248, 0, 0, 0, 0, 0}, {1132, 3528, 2417, 3972, 3253, 0, 0, 0, 0, 0,
     ------------------------------------------------------------------------
     -683, -1960, -4240, -3867, 2248}, {0, 0, 0, 0, 0, 1132, 3528, 2417,
     ------------------------------------------------------------------------
     3972, 3253, -5142, -2601, -4179, -3504, 1955}, {-4368, 3532, -1648,
     ------------------------------------------------------------------------
     1259, -5073, -4042, -525, -4800, 3677, 2967, 0, 0, 0, 0, 0}, {2014,
     ------------------------------------------------------------------------
     4304, 2640, -5042, -3984, 0, 0, 0, 0, 0, -4042, -525, -4800, 3677,
     ------------------------------------------------------------------------
     2967}, {0, 0, 0, 0, 0, 2014, 4304, 2640, -5042, -3984, 4368, -3532,
     ------------------------------------------------------------------------
     1648, -1259, 5073}, {-1365, 545, 5085, 3316, 2664, -760, -1201, -1718,
     ------------------------------------------------------------------------
     -724, 4022, 0, 0, 0, 0, 0}, {2983, -220, -2563, 2682, 4406, 0, 0, 0, 0,
     ------------------------------------------------------------------------
     0, -760, -1201, -1718, -724, 4022}, {0, 0, 0, 0, 0, 2983, -220, -2563,
     ------------------------------------------------------------------------
     2682, 4406, 1365, -545, -5085, -3316, -2664}, {-3152, 2986, 3172, -3954,
     ------------------------------------------------------------------------
     -1620, 3954, -3594, -697, 3305, 4511, 0, 0, 0, 0, 0}, {1487, -2958,
     ------------------------------------------------------------------------
     3650, 3164, -4263, 0, 0, 0, 0, 0, 3954, -3594, -697, 3305, 4511}, {0, 0,
     ------------------------------------------------------------------------
     0, 0, 0, 1487, -2958, 3650, 3164, -4263, 3152, -2986, -3172, 3954,
     ------------------------------------------------------------------------
     1620}, {1694, 631, -467, 1921, -4823, 3447, -4710, -3925, 3567, -2080,
     ------------------------------------------------------------------------
     0, 0, 0, 0, 0}, {763, 2217, -4751, -516, 3568, 0, 0, 0, 0, 0, 3447,
     ------------------------------------------------------------------------
     -4710, -3925, 3567, -2080}, {0, 0, 0, 0, 0, 763, 2217, -4751, -516,
     ------------------------------------------------------------------------
     3568, -1694, -631, 467, -1921, 4823}})

o1 : Sequence

i2 : kk=ZZ/p

o2 = kk

o2 : QuotientRing

i3 : M=matrix Mentries;

              15        15
o3 : Matrix kk   <--- kk

i4 : time betti syz M
     -- used 0.000779 seconds

             0 1
o4 = total: 15 1
        -1:  . 1
         0: 15 .

o4 : BettiTally

i5 : (p,Mentries)=outputForSingular(8,2)

o5 = (12451, {{2002, -4748, 0, 0, 0, -451, -3677, 0, 0, 0, 1679, -4062, 0, 0,
     ------------------------------------------------------------------------
     0, -2710, -6039, 0, 0, 0, -2679, 2705, 0, 0, 0, -4192, 4328, 0, 0, 0,
     ------------------------------------------------------------------------
     5193, 3033, 0, 0, 0, -410, 5528, 0, 0, 0}, {5817, 0, -4748, 0, 0, 194,
     ------------------------------------------------------------------------
     0, -3677, 0, 0, -1527, 0, -4062, 0, 0, -4915, 0, -6039, 0, 0, 2503, 0,
     ------------------------------------------------------------------------
     2705, 0, 0, -2802, 0, 4328, 0, 0, 4574, 0, 3033, 0, 0, 1930, 0, 5528, 0,
     ------------------------------------------------------------------------
     0}, {5598, 0, 0, -4748, 0, 6020, 0, 0, -3677, 0, 1743, 0, 0, -4062, 0,
     ------------------------------------------------------------------------
     -3341, 0, 0, -6039, 0, -5346, 0, 0, 2705, 0, -94, 0, 0, 4328, 0, 3857,
     ------------------------------------------------------------------------
     0, 0, 3033, 0, 4539, 0, 0, 5528, 0}, {-1587, 0, 0, 0, -4748, -4794, 0,
     ------------------------------------------------------------------------
     0, 0, -3677, 2053, 0, 0, 0, -4062, -43, 0, 0, 0, -6039, 5113, 0, 0, 0,
     ------------------------------------------------------------------------
     2705, 2007, 0, 0, 0, 4328, -5938, 0, 0, 0, 3033, 1297, 0, 0, 0, 5528},
     ------------------------------------------------------------------------
     {0, 5817, -2002, 0, 0, 0, 194, 451, 0, 0, 0, -1527, -1679, 0, 0, 0,
     ------------------------------------------------------------------------
     -4915, 2710, 0, 0, 0, 2503, 2679, 0, 0, 0, -2802, 4192, 0, 0, 0, 4574,
     ------------------------------------------------------------------------
     -5193, 0, 0, 0, 1930, 410, 0, 0}, {0, 5598, 0, -2002, 0, 0, 6020, 0,
     ------------------------------------------------------------------------
     451, 0, 0, 1743, 0, -1679, 0, 0, -3341, 0, 2710, 0, 0, -5346, 0, 2679,
     ------------------------------------------------------------------------
     0, 0, -94, 0, 4192, 0, 0, 3857, 0, -5193, 0, 0, 4539, 0, 410, 0}, {0,
     ------------------------------------------------------------------------
     -1587, 0, 0, -2002, 0, -4794, 0, 0, 451, 0, 2053, 0, 0, -1679, 0, -43,
     ------------------------------------------------------------------------
     0, 0, 2710, 0, 5113, 0, 0, 2679, 0, 2007, 0, 0, 4192, 0, -5938, 0, 0,
     ------------------------------------------------------------------------
     -5193, 0, 1297, 0, 0, 410}, {0, 0, 5598, -5817, 0, 0, 0, 6020, -194, 0,
     ------------------------------------------------------------------------
     0, 0, 1743, 1527, 0, 0, 0, -3341, 4915, 0, 0, 0, -5346, -2503, 0, 0, 0,
     ------------------------------------------------------------------------
     -94, 2802, 0, 0, 0, 3857, -4574, 0, 0, 0, 4539, -1930, 0}, {0, 0, -1587,
     ------------------------------------------------------------------------
     0, -5817, 0, 0, -4794, 0, -194, 0, 0, 2053, 0, 1527, 0, 0, -43, 0, 4915,
     ------------------------------------------------------------------------
     0, 0, 5113, 0, -2503, 0, 0, 2007, 0, 2802, 0, 0, -5938, 0, -4574, 0, 0,
     ------------------------------------------------------------------------
     1297, 0, -1930}, {0, 0, 0, -1587, -5598, 0, 0, 0, -4794, -6020, 0, 0, 0,
     ------------------------------------------------------------------------
     2053, -1743, 0, 0, 0, -43, 3341, 0, 0, 0, 5113, 5346, 0, 0, 0, 2007, 94,
     ------------------------------------------------------------------------
     0, 0, 0, -5938, -3857, 0, 0, 0, 1297, -4539}, {-3474, 3204, 0, 0, 0,
     ------------------------------------------------------------------------
     1252, -191, 0, 0, 0, -994, 3457, 0, 0, 0, -796, 2727, 0, 0, 0, -1954,
     ------------------------------------------------------------------------
     4059, 0, 0, 0, 895, 5376, 0, 0, 0, -5981, -3566, 0, 0, 0, -971, -559, 0,
     ------------------------------------------------------------------------
     0, 0}, {-1068, 0, 3204, 0, 0, -3519, 0, -191, 0, 0, -2248, 0, 3457, 0,
     ------------------------------------------------------------------------
     0, -286, 0, 2727, 0, 0, -4265, 0, 4059, 0, 0, -4140, 0, 5376, 0, 0,
     ------------------------------------------------------------------------
     -1856, 0, -3566, 0, 0, -3278, 0, -559, 0, 0}, {6133, 0, 0, 3204, 0,
     ------------------------------------------------------------------------
     -1765, 0, 0, -191, 0, 5978, 0, 0, 3457, 0, -3818, 0, 0, 2727, 0, 554, 0,
     ------------------------------------------------------------------------
     0, 4059, 0, 5254, 0, 0, 5376, 0, -3430, 0, 0, -3566, 0, -2462, 0, 0,
     ------------------------------------------------------------------------
     -559, 0}, {4830, 0, 0, 0, 3204, -2338, 0, 0, 0, -191, 3536, 0, 0, 0,
     ------------------------------------------------------------------------
     3457, 3944, 0, 0, 0, 2727, 2272, 0, 0, 0, 4059, -6068, 0, 0, 0, 5376,
     ------------------------------------------------------------------------
     -3556, 0, 0, 0, -3566, -561, 0, 0, 0, -559}, {0, -1068, 3474, 0, 0, 0,
     ------------------------------------------------------------------------
     -3519, -1252, 0, 0, 0, -2248, 994, 0, 0, 0, -286, 796, 0, 0, 0, -4265,
     ------------------------------------------------------------------------
     1954, 0, 0, 0, -4140, -895, 0, 0, 0, -1856, 5981, 0, 0, 0, -3278, 971,
     ------------------------------------------------------------------------
     0, 0}, {0, 6133, 0, 3474, 0, 0, -1765, 0, -1252, 0, 0, 5978, 0, 994, 0,
     ------------------------------------------------------------------------
     0, -3818, 0, 796, 0, 0, 554, 0, 1954, 0, 0, 5254, 0, -895, 0, 0, -3430,
     ------------------------------------------------------------------------
     0, 5981, 0, 0, -2462, 0, 971, 0}, {0, 4830, 0, 0, 3474, 0, -2338, 0, 0,
     ------------------------------------------------------------------------
     -1252, 0, 3536, 0, 0, 994, 0, 3944, 0, 0, 796, 0, 2272, 0, 0, 1954, 0,
     ------------------------------------------------------------------------
     -6068, 0, 0, -895, 0, -3556, 0, 0, 5981, 0, -561, 0, 0, 971}, {0, 0,
     ------------------------------------------------------------------------
     6133, 1068, 0, 0, 0, -1765, 3519, 0, 0, 0, 5978, 2248, 0, 0, 0, -3818,
     ------------------------------------------------------------------------
     286, 0, 0, 0, 554, 4265, 0, 0, 0, 5254, 4140, 0, 0, 0, -3430, 1856, 0,
     ------------------------------------------------------------------------
     0, 0, -2462, 3278, 0}, {0, 0, 4830, 0, 1068, 0, 0, -2338, 0, 3519, 0, 0,
     ------------------------------------------------------------------------
     3536, 0, 2248, 0, 0, 3944, 0, 286, 0, 0, 2272, 0, 4265, 0, 0, -6068, 0,
     ------------------------------------------------------------------------
     4140, 0, 0, -3556, 0, 1856, 0, 0, -561, 0, 3278}, {0, 0, 0, 4830, -6133,
     ------------------------------------------------------------------------
     0, 0, 0, -2338, 1765, 0, 0, 0, 3536, -5978, 0, 0, 0, 3944, 3818, 0, 0,
     ------------------------------------------------------------------------
     0, 2272, -554, 0, 0, 0, -6068, -5254, 0, 0, 0, -3556, 3430, 0, 0, 0,
     ------------------------------------------------------------------------
     -561, 2462}, {165, 5213, 0, 0, 0, 2518, -2320, 0, 0, 0, 810, -1678, 0,
     ------------------------------------------------------------------------
     0, 0, -3026, 4289, 0, 0, 0, 4130, -4903, 0, 0, 0, 684, -4747, 0, 0, 0,
     ------------------------------------------------------------------------
     1408, -5465, 0, 0, 0, 1332, 3618, 0, 0, 0}, {-3623, 0, 5213, 0, 0, 6133,
     ------------------------------------------------------------------------
     0, -2320, 0, 0, 3156, 0, -1678, 0, 0, 4822, 0, 4289, 0, 0, 4139, 0,
     ------------------------------------------------------------------------
     -4903, 0, 0, -3262, 0, -4747, 0, 0, 4979, 0, -5465, 0, 0, 766, 0, 3618,
     ------------------------------------------------------------------------
     0, 0}, {2122, 0, 0, 5213, 0, 5462, 0, 0, -2320, 0, -3246, 0, 0, -1678,
     ------------------------------------------------------------------------
     0, -1261, 0, 0, 4289, 0, -1871, 0, 0, -4903, 0, -2212, 0, 0, -4747, 0,
     ------------------------------------------------------------------------
     -2730, 0, 0, -5465, 0, 796, 0, 0, 3618, 0}, {1591, 0, 0, 0, 5213, 3704,
     ------------------------------------------------------------------------
     0, 0, 0, -2320, -3648, 0, 0, 0, -1678, 2381, 0, 0, 0, 4289, 723, 0, 0,
     ------------------------------------------------------------------------
     0, -4903, 5897, 0, 0, 0, -4747, -1860, 0, 0, 0, -5465, -1851, 0, 0, 0,
     ------------------------------------------------------------------------
     3618}, {0, -3623, -165, 0, 0, 0, 6133, -2518, 0, 0, 0, 3156, -810, 0, 0,
     ------------------------------------------------------------------------
     0, 4822, 3026, 0, 0, 0, 4139, -4130, 0, 0, 0, -3262, -684, 0, 0, 0,
     ------------------------------------------------------------------------
     4979, -1408, 0, 0, 0, 766, -1332, 0, 0}, {0, 2122, 0, -165, 0, 0, 5462,
     ------------------------------------------------------------------------
     0, -2518, 0, 0, -3246, 0, -810, 0, 0, -1261, 0, 3026, 0, 0, -1871, 0,
     ------------------------------------------------------------------------
     -4130, 0, 0, -2212, 0, -684, 0, 0, -2730, 0, -1408, 0, 0, 796, 0, -1332,
     ------------------------------------------------------------------------
     0}, {0, 1591, 0, 0, -165, 0, 3704, 0, 0, -2518, 0, -3648, 0, 0, -810, 0,
     ------------------------------------------------------------------------
     2381, 0, 0, 3026, 0, 723, 0, 0, -4130, 0, 5897, 0, 0, -684, 0, -1860, 0,
     ------------------------------------------------------------------------
     0, -1408, 0, -1851, 0, 0, -1332}, {0, 0, 2122, 3623, 0, 0, 0, 5462,
     ------------------------------------------------------------------------
     -6133, 0, 0, 0, -3246, -3156, 0, 0, 0, -1261, -4822, 0, 0, 0, -1871,
     ------------------------------------------------------------------------
     -4139, 0, 0, 0, -2212, 3262, 0, 0, 0, -2730, -4979, 0, 0, 0, 796, -766,
     ------------------------------------------------------------------------
     0}, {0, 0, 1591, 0, 3623, 0, 0, 3704, 0, -6133, 0, 0, -3648, 0, -3156,
     ------------------------------------------------------------------------
     0, 0, 2381, 0, -4822, 0, 0, 723, 0, -4139, 0, 0, 5897, 0, 3262, 0, 0,
     ------------------------------------------------------------------------
     -1860, 0, -4979, 0, 0, -1851, 0, -766}, {0, 0, 0, 1591, -2122, 0, 0, 0,
     ------------------------------------------------------------------------
     3704, -5462, 0, 0, 0, -3648, 3246, 0, 0, 0, 2381, 1261, 0, 0, 0, 723,
     ------------------------------------------------------------------------
     1871, 0, 0, 0, 5897, 2212, 0, 0, 0, -1860, 2730, 0, 0, 0, -1851, -796},
     ------------------------------------------------------------------------
     {-3295, -6216, 0, 0, 0, 2577, -605, 0, 0, 0, -4725, 5529, 0, 0, 0,
     ------------------------------------------------------------------------
     -3524, 2979, 0, 0, 0, 3316, 5195, 0, 0, 0, -772, 5091, 0, 0, 0, 4684,
     ------------------------------------------------------------------------
     -3157, 0, 0, 0, 4155, 1499, 0, 0, 0}, {-3626, 0, -6216, 0, 0, 1435, 0,
     ------------------------------------------------------------------------
     -605, 0, 0, -4321, 0, 5529, 0, 0, -2039, 0, 2979, 0, 0, 4642, 0, 5195,
     ------------------------------------------------------------------------
     0, 0, -3503, 0, 5091, 0, 0, 5633, 0, -3157, 0, 0, -2193, 0, 1499, 0, 0},
     ------------------------------------------------------------------------
     {-1380, 0, 0, -6216, 0, 2171, 0, 0, -605, 0, -3604, 0, 0, 5529, 0,
     ------------------------------------------------------------------------
     -5968, 0, 0, 2979, 0, 3759, 0, 0, 5195, 0, 2020, 0, 0, 5091, 0, 4370, 0,
     ------------------------------------------------------------------------
     0, -3157, 0, -3811, 0, 0, 1499, 0}, {-2824, 0, 0, 0, -6216, -978, 0, 0,
     ------------------------------------------------------------------------
     0, -605, 2454, 0, 0, 0, 5529, -1796, 0, 0, 0, 2979, 5471, 0, 0, 0, 5195,
     ------------------------------------------------------------------------
     -5699, 0, 0, 0, 5091, 4088, 0, 0, 0, -3157, -4707, 0, 0, 0, 1499}, {0,
     ------------------------------------------------------------------------
     -3626, 3295, 0, 0, 0, 1435, -2577, 0, 0, 0, -4321, 4725, 0, 0, 0, -2039,
     ------------------------------------------------------------------------
     3524, 0, 0, 0, 4642, -3316, 0, 0, 0, -3503, 772, 0, 0, 0, 5633, -4684,
     ------------------------------------------------------------------------
     0, 0, 0, -2193, -4155, 0, 0}, {0, -1380, 0, 3295, 0, 0, 2171, 0, -2577,
     ------------------------------------------------------------------------
     0, 0, -3604, 0, 4725, 0, 0, -5968, 0, 3524, 0, 0, 3759, 0, -3316, 0, 0,
     ------------------------------------------------------------------------
     2020, 0, 772, 0, 0, 4370, 0, -4684, 0, 0, -3811, 0, -4155, 0}, {0,
     ------------------------------------------------------------------------
     -2824, 0, 0, 3295, 0, -978, 0, 0, -2577, 0, 2454, 0, 0, 4725, 0, -1796,
     ------------------------------------------------------------------------
     0, 0, 3524, 0, 5471, 0, 0, -3316, 0, -5699, 0, 0, 772, 0, 4088, 0, 0,
     ------------------------------------------------------------------------
     -4684, 0, -4707, 0, 0, -4155}, {0, 0, -1380, 3626, 0, 0, 0, 2171, -1435,
     ------------------------------------------------------------------------
     0, 0, 0, -3604, 4321, 0, 0, 0, -5968, 2039, 0, 0, 0, 3759, -4642, 0, 0,
     ------------------------------------------------------------------------
     0, 2020, 3503, 0, 0, 0, 4370, -5633, 0, 0, 0, -3811, 2193, 0}, {0, 0,
     ------------------------------------------------------------------------
     -2824, 0, 3626, 0, 0, -978, 0, -1435, 0, 0, 2454, 0, 4321, 0, 0, -1796,
     ------------------------------------------------------------------------
     0, 2039, 0, 0, 5471, 0, -4642, 0, 0, -5699, 0, 3503, 0, 0, 4088, 0,
     ------------------------------------------------------------------------
     -5633, 0, 0, -4707, 0, 2193}, {0, 0, 0, -2824, 1380, 0, 0, 0, -978,
     ------------------------------------------------------------------------
     -2171, 0, 0, 0, 2454, 3604, 0, 0, 0, -1796, 5968, 0, 0, 0, 5471, -3759,
     ------------------------------------------------------------------------
     0, 0, 0, -5699, -2020, 0, 0, 0, 4088, -4370, 0, 0, 0, -4707, 3811},
     ------------------------------------------------------------------------
     {-3804, -1544, 0, 0, 0, -1642, 2397, 0, 0, 0, -2279, -3119, 0, 0, 0,
     ------------------------------------------------------------------------
     -1388, 1037, 0, 0, 0, 2427, 4898, 0, 0, 0, 4324, -4478, 0, 0, 0, 1964,
     ------------------------------------------------------------------------
     -2572, 0, 0, 0, -4810, 4860, 0, 0, 0}, {5133, 0, -1544, 0, 0, -3997, 0,
     ------------------------------------------------------------------------
     2397, 0, 0, -3371, 0, -3119, 0, 0, -4937, 0, 1037, 0, 0, -136, 0, 4898,
     ------------------------------------------------------------------------
     0, 0, 5792, 0, -4478, 0, 0, 5458, 0, -2572, 0, 0, -2642, 0, 4860, 0, 0},
     ------------------------------------------------------------------------
     {-4563, 0, 0, -1544, 0, -4859, 0, 0, 2397, 0, -4831, 0, 0, -3119, 0,
     ------------------------------------------------------------------------
     4527, 0, 0, 1037, 0, 5481, 0, 0, 4898, 0, -6223, 0, 0, -4478, 0, 2960,
     ------------------------------------------------------------------------
     0, 0, -2572, 0, 747, 0, 0, 4860, 0}, {-2858, 0, 0, 0, -1544, -2018, 0,
     ------------------------------------------------------------------------
     0, 0, 2397, -2908, 0, 0, 0, -3119, -4997, 0, 0, 0, 1037, -1557, 0, 0, 0,
     ------------------------------------------------------------------------
     4898, 2000, 0, 0, 0, -4478, -2874, 0, 0, 0, -2572, 1273, 0, 0, 0, 4860},
     ------------------------------------------------------------------------
     {0, 5133, 3804, 0, 0, 0, -3997, 1642, 0, 0, 0, -3371, 2279, 0, 0, 0,
     ------------------------------------------------------------------------
     -4937, 1388, 0, 0, 0, -136, -2427, 0, 0, 0, 5792, -4324, 0, 0, 0, 5458,
     ------------------------------------------------------------------------
     -1964, 0, 0, 0, -2642, 4810, 0, 0}, {0, -4563, 0, 3804, 0, 0, -4859, 0,
     ------------------------------------------------------------------------
     1642, 0, 0, -4831, 0, 2279, 0, 0, 4527, 0, 1388, 0, 0, 5481, 0, -2427,
     ------------------------------------------------------------------------
     0, 0, -6223, 0, -4324, 0, 0, 2960, 0, -1964, 0, 0, 747, 0, 4810, 0}, {0,
     ------------------------------------------------------------------------
     -2858, 0, 0, 3804, 0, -2018, 0, 0, 1642, 0, -2908, 0, 0, 2279, 0, -4997,
     ------------------------------------------------------------------------
     0, 0, 1388, 0, -1557, 0, 0, -2427, 0, 2000, 0, 0, -4324, 0, -2874, 0, 0,
     ------------------------------------------------------------------------
     -1964, 0, 1273, 0, 0, 4810}, {0, 0, -4563, -5133, 0, 0, 0, -4859, 3997,
     ------------------------------------------------------------------------
     0, 0, 0, -4831, 3371, 0, 0, 0, 4527, 4937, 0, 0, 0, 5481, 136, 0, 0, 0,
     ------------------------------------------------------------------------
     -6223, -5792, 0, 0, 0, 2960, -5458, 0, 0, 0, 747, 2642, 0}, {0, 0,
     ------------------------------------------------------------------------
     -2858, 0, -5133, 0, 0, -2018, 0, 3997, 0, 0, -2908, 0, 3371, 0, 0,
     ------------------------------------------------------------------------
     -4997, 0, 4937, 0, 0, -1557, 0, 136, 0, 0, 2000, 0, -5792, 0, 0, -2874,
     ------------------------------------------------------------------------
     0, -5458, 0, 0, 1273, 0, 2642}, {0, 0, 0, -2858, 4563, 0, 0, 0, -2018,
     ------------------------------------------------------------------------
     4859, 0, 0, 0, -2908, 4831, 0, 0, 0, -4997, -4527, 0, 0, 0, -1557,
     ------------------------------------------------------------------------
     -5481, 0, 0, 0, 2000, 6223, 0, 0, 0, -2874, -2960, 0, 0, 0, 1273,
     ------------------------------------------------------------------------
     -747}})

o5 : Sequence

i6 : kk=ZZ/p

o6 = kk

o6 : QuotientRing

i7 : M=matrix Mentries;

              50        40
o7 : Matrix kk   <--- kk

i8 : time betti syz M
     -- used 0.006341 seconds

             0 1
o8 = total: 40 1
        -1:  . 1
         0: 40 .

o8 : BettiTally

Ways to use `outputForSingular` :

outputForSingular(ZZ,ZZ)
outputForSingular(ZZ,ZZ,ZZ)

outputForSingular -- get a string for a matrix over a finite field

Synopsis

Description

Ways to use outputForSingular :

Ways to use `outputForSingular` :