# Output of l20_1364321_c2.sage: the concatenation of the four runs 'sage l20_1364321_c2.sage <family>' for the families c2sA, c2sB, c2tA, c2tB (in this order), executed by ./run_all.sh --full on 2026-10-11 (each family seeded with set_random_seed(64321), so each run prints the same lines as the full run).
c2sA (Q = Y^5, family A): H [1, 3, 6, 4, 3, 2, 1]; <X^4, x o Q, y o Q, Q4> of dimension 3: True; three elements of the ideal: local length 39 (standard basis), m^N certificate (N, length) = (11, 39); 1011 s
    the triple (seed 64321): [-41/200*x^6 + 3*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 + x*y^5 + 2*y^6 - x^5*z + 3*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 2*y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 + x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - y*z^5 + 2*z^6 - 13/36*x^5 - 2*x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 + 1/12*y^5 + 2*x^4*z + 2*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z - x^3*z^2 + 3*x^2*y*z^2 + 2*x*y^2*z^2 - 3*x*y*z^3 - 2*x*z^4 + 2*y*z^4 - 3*z^5 - 3/10*x^4 + 11/3*x^3*y - 3*x^2*y^2 - x*y^3 - 3/10*y^4 + x^3*z - x^2*y*z + x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 + 2*z^4 + 3*x^2*z - 2*x*y*z + 3*y^2*z + 3*x*z^2 + 2*y*z^2 - 2*z^3, 1/3600*x^6 - 2*x^5*y - 2*x^4*y^2 + 2*x^3*y^3 + x^2*y^4 - 2*y^6 - x^5*z - 2*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 2*y^5*z - 2*x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + y^4*z^2 - x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - 2*y*z^5 + 37/450*x^5 - 3*x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 + 1/12*y^5 - x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 3*x^2*y*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 - y^2*z^3 - 2*x*z^4 - z^5 + 3/10*x^4 + 5/3*x^3*y - x^2*y^2 - 2*x*y^3 - 1/10*y^4 - 2*x^3*z - x^2*y*z + y^3*z + x*y*z^2 + y^2*z^2 + x*z^3 + y*z^3 + 3*z^4 - 3*x^2*z + x*y*z + y^2*z + y*z^2 - z^3, -131/1200*x^6 + 3*x^5*y + x^4*y^2 + x^3*y^3 - x^2*y^4 + 3*x*y^5 + y^6 + x^5*z - 3*x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - 2*y^5*z - 2*x^4*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 - x^2*y*z^3 - 3*x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 + 3*x*y*z^4 + 2*y^2*z^4 - 3*y*z^5 - 3*z^6 + 221/900*x^5 - 3*x^2*y^3 - 2*x*y^4 + 1/30*y^5 + x^4*z - 3*x^2*y^2*z + 3*x*y^3*z + y^4*z - x^3*z^2 + 3*x*y^2*z^2 + y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + y^2*z^3 + x*z^4 + y*z^4 - 3*z^5 - 3/10*x^4 - 10/3*x^3*y - x*y^3 + 3/10*y^4 + x^2*y*z + 2*x*y^2*z - 3*y^3*z + 2*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + x*z^3 + 2*y*z^3 + z^4 + 3*x^2*z + x*y*z - 3*y^2*z - 3*x*z^2 - y*z^2 + 2*z^3]

1 of the four families checked; 1011 s in all.
ALL CHECKS PASSED
c2sB (Q = Y^5, family B): H [1, 3, 6, 4, 3, 2, 1]; <X^4, x o Q, y o Q, Q4> of dimension 3: True; three elements of the ideal: local length 38 (standard basis), m^N certificate (N, length) = (10, 38); 411 s
    the triple (seed 64321): [-103/400*x^6 + 3*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 + x*y^5 + 2*y^6 - x^5*z + 3*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 2*y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 + x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - y*z^5 + 2*z^6 - 23/450*x^5 - 2*x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 - 7/60*y^5 + 2*x^4*z + 2*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z - x^3*z^2 + 3*x^2*y*z^2 + 2*x*y^2*z^2 - 3*x*y*z^3 - 2*x*z^4 + 2*y*z^4 - 3*z^5 - 3/10*x^4 - 1/3*x^3*y - 3*x^2*y^2 - x*y^3 - 3/10*y^4 + x^3*z - x^2*y*z + x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 + 2*z^4 + 3*x^2*z - 2*x*y*z + 3*y^2*z + 3*x*z^2 + 2*y*z^2 - 2*z^3, -11/360*x^6 - 2*x^5*y - 2*x^4*y^2 + 2*x^3*y^3 + x^2*y^4 - 2*y^6 - x^5*z - 2*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 2*y^5*z - 2*x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + y^4*z^2 - x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - 2*y*z^5 + 419/1800*x^5 - 3*x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 - 1/120*y^5 - x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 3*x^2*y*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 - y^2*z^3 - 2*x*z^4 - z^5 + 3/10*x^4 - 1/6*x^3*y - x^2*y^2 - 2*x*y^3 - 1/10*y^4 - 2*x^3*z - x^2*y*z + y^3*z + x*y*z^2 + y^2*z^2 + x*z^3 + y*z^3 + 3*z^4 - 3*x^2*z + x*y*z + y^2*z + y*z^2 - z^3, -7/100*x^6 + 3*x^5*y + x^4*y^2 + x^3*y^3 - x^2*y^4 + 3*x*y^5 + y^6 + x^5*z - 3*x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - 2*y^5*z - 2*x^4*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 - x^2*y*z^3 - 3*x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 + 3*x*y*z^4 + 2*y^2*z^4 - 3*y*z^5 - 3*z^6 + 17/900*x^5 - 3*x^2*y^3 - 2*x*y^4 + 5/24*y^5 + x^4*z - 3*x^2*y^2*z + 3*x*y^3*z + y^4*z - x^3*z^2 + 3*x*y^2*z^2 + y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + y^2*z^3 + x*z^4 + y*z^4 - 3*z^5 - 3/10*x^4 + 1/6*x^3*y - x*y^3 + 3/10*y^4 + x^2*y*z + 2*x*y^2*z - 3*y^3*z + 2*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + x*z^3 + 2*y*z^3 + z^4 + 3*x^2*z + x*y*z - 3*y^2*z - 3*x*z^2 - y*z^2 + 2*z^3]

1 of the four families checked; 411 s in all.
ALL CHECKS PASSED
c2tA (Q = X^4*Y, family A): H [1, 3, 6, 4, 3, 2, 1]; <X^4, x o Q, y o Q, Q4> of dimension 3: True; three elements of the ideal: local length 39 (standard basis), m^N certificate (N, length) = (11, 39); 934 s
    the triple (seed 64321): [-65/288*x^6 + 3*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 + x*y^5 + 2*y^6 - x^5*z + 3*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 2*y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 + x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - y*z^5 + 2*z^6 - 103/1200*x^5 + 1/10*x^4*y - 2*x^2*y^3 + 3*x*y^4 - 2*y^5 + 2*x^4*z + 2*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z - x^3*z^2 + 3*x^2*y*z^2 + 2*x*y^2*z^2 - 3*x*y*z^3 - 2*x*z^4 + 2*y*z^4 - 3*z^5 - 3/10*x^4 - 11/20*x^3*y - 1/2*x^2*y^2 - 3*x*y^3 - y^4 + x^3*z - x^2*y*z + x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 + 2*z^4 + 3*x^2*z - 2*x*y*z + 3*y^2*z + 3*x*z^2 + 2*y*z^2 - 2*z^3, 67/1440*x^6 - 2*x^5*y - 2*x^4*y^2 + 2*x^3*y^3 + x^2*y^4 - 2*y^6 - x^5*z - 2*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 2*y^5*z - 2*x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + y^4*z^2 - x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - 2*y*z^5 + 227/2400*x^5 - 49/60*x^4*y - 3*x^2*y^3 + 3*x*y^4 - 2*y^5 - x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 3*x^2*y*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 - y^2*z^3 - 2*x*z^4 - z^5 + 3/10*x^4 + 13/20*x^3*y - 7*x^2*y^2 - x*y^3 - 2*y^4 - 2*x^3*z - x^2*y*z + y^3*z + x*y*z^2 + y^2*z^2 + x*z^3 + y*z^3 + 3*z^4 - 3*x^2*z + x*y*z + y^2*z + y*z^2 - z^3, 73/7200*x^6 + 3*x^5*y + x^4*y^2 + x^3*y^3 - x^2*y^4 + 3*x*y^5 + y^6 + x^5*z - 3*x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - 2*y^5*z - 2*x^4*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 - x^2*y*z^3 - 3*x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 + 3*x*y*z^4 + 2*y^2*z^4 - 3*y*z^5 - 3*z^6 + 1/2400*x^5 - 8/5*x^4*y - 3*x*y^4 - 2*y^5 + x^4*z - 3*x^2*y^2*z + 3*x*y^3*z + y^4*z - x^3*z^2 + 3*x*y^2*z^2 + y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + y^2*z^3 + x*z^4 + y*z^4 - 3*z^5 - 3/10*x^4 - 17/20*x^3*y - 19/2*x^2*y^2 - y^4 + x^2*y*z + 2*x*y^2*z - 3*y^3*z + 2*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + x*z^3 + 2*y*z^3 + z^4 + 3*x^2*z + x*y*z - 3*y^2*z - 3*x*z^2 - y*z^2 + 2*z^3]

1 of the four families checked; 934 s in all.
ALL CHECKS PASSED
c2tB (Q = X^4*Y, family B): H [1, 3, 6, 4, 3, 2, 1]; <X^4, x o Q, y o Q, Q4> of dimension 3: True; three elements of the ideal: local length 38 (standard basis), m^N certificate (N, length) = (10, 38); 340 s
    the triple (seed 64321): [-51/160*x^6 + 3*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 + x*y^5 + 2*y^6 - x^5*z + 3*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 2*y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 + x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - y*z^5 + 2*z^6 - 91/900*x^5 + 1/10*x^4*y - 2*x^2*y^3 + 3*x*y^4 - 2*y^5 + 2*x^4*z + 2*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z - x^3*z^2 + 3*x^2*y*z^2 + 2*x*y^2*z^2 - 3*x*y*z^3 - 2*x*z^4 + 2*y*z^4 - 3*z^5 - 3/10*x^4 - 11/20*x^3*y - 13/2*x^2*y^2 - 3*x*y^3 - y^4 + x^3*z - x^2*y*z + x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 + 2*z^4 + 3*x^2*z - 2*x*y*z + 3*y^2*z + 3*x*z^2 + 2*y*z^2 - 2*z^3, -1/32*x^6 - 2*x^5*y - 2*x^4*y^2 + 2*x^3*y^3 + x^2*y^4 - 2*y^6 - x^5*z - 2*x^4*y*z + x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 2*y^5*z - 2*x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + y^4*z^2 - x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - 2*y*z^5 + 37/400*x^5 - 49/60*x^4*y - 3*x^2*y^3 + 3*x*y^4 - 2*y^5 - x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 3*x^2*y*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 - y^2*z^3 - 2*x*z^4 - z^5 + 3/10*x^4 + 13/20*x^3*y - 39/4*x^2*y^2 - x*y^3 - 2*y^4 - 2*x^3*z - x^2*y*z + y^3*z + x*y*z^2 + y^2*z^2 + x*z^3 + y*z^3 + 3*z^4 - 3*x^2*z + x*y*z + y^2*z + y*z^2 - z^3, -107/7200*x^6 + 3*x^5*y + x^4*y^2 + x^3*y^3 - x^2*y^4 + 3*x*y^5 + y^6 + x^5*z - 3*x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - 2*y^5*z - 2*x^4*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 - x^2*y*z^3 - 3*x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 + 3*x*y*z^4 + 2*y^2*z^4 - 3*y*z^5 - 3*z^6 + 41/900*x^5 - 8/5*x^4*y - 3*x*y^4 - 2*y^5 + x^4*z - 3*x^2*y^2*z + 3*x*y^3*z + y^4*z - x^3*z^2 + 3*x*y^2*z^2 + y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + y^2*z^3 + x*z^4 + y*z^4 - 3*z^5 - 3/10*x^4 - 17/20*x^3*y - 17/4*x^2*y^2 - y^4 + x^2*y*z + 2*x*y^2*z - 3*y^3*z + 2*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + x*z^3 + 2*y*z^3 + z^4 + 3*x^2*z + x*y*z - 3*y^2*z - 3*x*z^2 - y*z^2 + 2*z^3]

1 of the four families checked; 340 s in all.
ALL CHECKS PASSED
