# Output of l20_1364321_O2.sage: the concatenation of the six runs 'sage l20_1364321_O2.sage <regex>' for the subsets '^A1', '^A2', '^A3a0', '^A3a1', '^A3b', '^B' (in this order; together all twenty cases), executed by ./run_all.sh --full on 2026-10-11 (one random seed per case, so each run prints the same lines for its cases as the full run).
A1 l''=Y family I: dim of the tail space L = 5; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; b^x = (15, 1, -8), b^z = (0, -1, 0), identities b_2^z = 0, 4 b_0^z = gamma b_2^x: True; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 232 s
    the triple (seed 1364321, random triple number 1 after the construction of the member): [x^6 + x^5*y + 2*x^4*y^2 - 2*x^3*y^3 - 3*x*y^5 - 1981/10800*y^6 - x^5*z - x^4*y*z - 3*x^3*y^2*z + x*y^4*z - 3*y^5*z + 3*x^4*z^2 - x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 + 2*x*y^2*z^3 + y^3*z^3 + x^2*z^4 - 2*x*y*z^4 - 2*y^2*z^4 - 2*x*z^5 - y*z^5 + 3*z^6 + 61/120*x^5 - 2*x^4*y + x^3*y^2 + x^2*y^3 + 2*x*y^4 + 7/225*y^5 - 3*x^4*z + 3*x^3*y*z - 3*x^2*y^2*z + x*y^3*z + 2*y^4*z - 2*x^3*z^2 + x^2*y*z^2 + 2*x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 - 2*x*y*z^3 + y^2*z^3 - 3*x*z^4 - 3*z^5 + 1/4*x^4 - 2*x^2*y^2 + x*y^3 + 1/10*y^4 - 2*x^2*y*z - x*y^2*z + y^3*z + 3*x^2*z^2 + 3*x*y*z^2 + 3*y^2*z^2 - x*z^3 + y*z^3 + x*y*z + 3*y^2*z + 2*x*z^2 + 3*y*z^2, 3*x^6 + x^5*y - 2*x^4*y^2 + x^3*y^3 - 3*x^2*y^4 - 2*x*y^5 - 301/5400*y^6 + 2*x^5*z + 3*x^4*y*z + 2*x^3*y^2*z - 2*x^2*y^3*z - 2*x*y^4*z + 3*x^4*z^2 + 3*x^2*y^2*z^2 + 2*x*y^3*z^2 - x^3*z^3 - x^2*y*z^3 + 3*y^3*z^3 - 3*x^2*z^4 + x*y*z^4 + 2*y^2*z^4 + 2*x*z^5 + 3*y*z^5 - 2*z^6 + 337/600*x^5 + 2*x^4*y + 3*x^3*y^2 + x^2*y^3 - 2*x*y^4 + 143/900*y^5 - 2*x^4*z - x^3*y*z - 2*x^2*y^2*z - 2*x*y^3*z - y^4*z - x^3*z^2 - x^2*y*z^2 + 2*x*y^2*z^2 + 3*y^3*z^2 + x^2*z^3 + 3*x*y*z^3 - y^2*z^3 + 3*y*z^4 + z^5 + 3/20*x^4 - 1/6*x^3*y - x^2*y^2 - 2*x*y^3 - 1/30*y^4 + x^3*z - x^2*y*z - 2*x*y^2*z + y^3*z + 2*x^2*z^2 + x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 - 2*y*z^3 + z^4 + 2*x*y^2 + 3*x*y*z + y^2*z + 2*x*z^2 - y*z^2 + 2*z^3, -x^6 + x^4*y^2 - x^3*y^3 - x^2*y^4 + 3*x*y^5 - 463/21600*y^6 - x^5*z + 2*x^4*y*z - x^3*y^2*z + 3*x*y^4*z - 3*y^5*z - x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 + 2*x^2*y*z^3 - x*y*z^4 + 3*y^2*z^4 + 2*x*z^5 - z^6 + 61/100*x^5 + 2*x^4*y + x^3*y^2 + x*y^4 + 91/1800*y^5 - 2*x^4*z - 2*x^3*y*z - x^2*y^2*z - 2*x*y^3*z + 2*y^4*z - 2*x^3*z^2 + 3*x*y^2*z^2 - 2*x^2*z^3 - 2*y^2*z^3 - 2*x*z^4 + 2*y*z^4 + z^5 - 1/20*x^4 + 1/4*x^3*y + 2*x^2*y^2 - x*y^3 + 1/5*y^4 + 3*x^2*y*z - 2*x*y^2*z + 2*y^3*z + x^2*z^2 - 2*x*y*z^2 + y^2*z^2 + 3*x*z^3 - y*z^3 - 3*x*y^2 - x*y*z + 3*y^2*z - 3*x*z^2 + 3*y*z^2 + 2*z^3]
A1 l''=Y family II: dim of the tail space L = 5; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; b^x = (10, -1, 0), b^z = (0, 1, 0), identities b_2^z = 0, 4 b_0^z = gamma b_2^x: True; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (10, 34); 528 s
    the triple (seed 1364322, random triple number 1 after the construction of the member): [-2*x^6 - 2*x^5*y - x^4*y^2 - x^3*y^3 + x^2*y^4 + 3*x*y^5 - 9/100*y^6 - x^5*z - 2*x^4*y*z - x^3*y^2*z + 2*x*y^4*z + 2*y^5*z + x^4*z^2 + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 - 3*y^4*z^2 + 2*x^2*y*z^3 - x*y^2*z^3 + x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - 3*x*z^5 - 3*y*z^5 + 3*z^6 + 421/600*x^5 - 2*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 - 19/120*y^5 - 3*x^4*z + x^3*y*z - 3*x^2*y^2*z - y^4*z - 2*x^3*z^2 + x^2*y*z^2 - 2*x*y^2*z^2 - y^3*z^2 + 3*x*y*z^3 - 3*y^2*z^3 + 2*y*z^4 - 1/10*x^4 + 3/2*x^3*y + 2*x^2*y^2 - 2*x*y^3 - x^3*z - x^2*y*z + 2*y^3*z + 2*x^2*z^2 + 2*y^2*z^2 + z^4 - 3*x*y^2 - x*y*z - 3*y^2*z + 2*x*z^2 - y*z^2 - 2*z^3, -3*x^6 - 2*x^4*y^2 - 3*x^3*y^3 - 3*x^2*y^4 + 2*x*y^5 - 37/225*y^6 + x^5*z - 3*x^4*y*z + 3*x^3*y^2*z - x^2*y^3*z - 3*x^3*y*z^2 - 2*x^2*y^2*z^2 - 3*x*y^3*z^2 - 2*x^3*z^3 + 2*x^2*y*z^3 + 3*x*y^2*z^3 + 2*y^3*z^3 - x^2*z^4 - 3*x*y*z^4 - y^2*z^4 + x*z^5 - 3*y*z^5 - 2*z^6 + 52/75*x^5 + 2*x^4*y + x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 - 2/25*y^5 + x^3*y*z + 2*x*y^3*z - 2*y^4*z - 3*x^3*z^2 - 3*x^2*y*z^2 - 2*x*y^2*z^2 + 3*y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 - y^2*z^3 - 3*x*z^4 - 3*z^5 + 2/5*x^4 + 5*x^3*y + x^2*y^2 - 3*x*y^3 - x^3*z + 2*x^2*y*z - 2*x*y^2*z + y^2*z^2 + 3*x*z^3 - y*z^3 + 3*z^4 + 2*x*y^2 + 2*y^2*z + 2*x*z^2 - 3*y*z^2 + 2*z^3, -2*x^6 + x^5*y + 2*x^4*y^2 + 2263/10800*y^6 + 2*x^5*z - 3*x^4*y*z - x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z + 2*y^5*z - 2*x^4*z^2 + x^3*y*z^2 - 3*x^2*y^2*z^2 + 2*y^4*z^2 - 2*x^3*z^3 - 2*x*y^2*z^3 - 3*y^3*z^3 - 2*x^2*z^4 - 3*x*y*z^4 + y^2*z^4 + x*z^5 - y*z^5 - 2*z^6 - 233/300*x^5 + 2*x^4*y - 3*x^3*y^2 - x^2*y^3 - 2*x*y^4 - 299/1800*y^5 - 2*x^4*z - x^2*y^2*z + 3*y^4*z + x^3*z^2 + x^2*y*z^2 + 3*x*y^2*z^2 - y^3*z^2 + 2*x^2*z^3 - 3*x*y*z^3 - 3*y^2*z^3 - 2*x*z^4 - z^5 - 1/10*x^4 - 13/3*x^3*y - 3*x*y^3 + 1/30*y^4 + 2*x^3*z + 2*x^2*y*z + 2*x*y^2*z + 2*y^3*z + x^2*z^2 - 3*x*y*z^2 - 2*y^2*z^2 + 3*x*z^3 + 3*z^4 + 2*x*y^2 + y^2*z - 3*x*z^2 - 3*y*z^2 - 2*z^3]
A1 l''=Z family I: dim of the tail space L = 5; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; b^x = (-15, 2, 8), b^z = (2, -2, 0), identities b_2^z = 0, 4 b_0^z = gamma b_2^x: True; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 228 s
    the triple (seed 1364323, random triple number 1 after the construction of the member): [-x^5*y - x^4*y^2 - 3*x^3*y^3 + 2*x^2*y^4 + 3*x*y^5 + 11957/43200*y^6 - x^5*z - x^4*y*z + x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z - 3*y^5*z + 2*x^4*z^2 - 2*x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 - y^4*z^2 - 3*x^3*z^3 - 3*x^2*y*z^3 + 2*x*y^2*z^3 - y^3*z^3 - x^2*z^4 - 2*x*z^5 + 3*y*z^5 + 3*z^6 + 713/2400*x^5 - 3*x^4*y + x^3*y^2 - 3*x^2*y^3 - x*y^4 + 103/1800*y^5 - 2*x^4*z + 2*x^2*y^2*z - x*y^3*z - 2*y^4*z + x^2*y*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 + x^2*z^3 - 3*x*y*z^3 + 2*y^2*z^3 + 2*x*z^4 - 2*z^5 - 1/5*x^4 + x^2*y^2 + x*y^3 + 1/15*y^4 + 97/120*x^3*z + x^2*y*z + 3*x*y^2*z + 2*y^3*z + x^2*z^2 + 2*y^2*z^2 - 2*y*z^3 - z^4 - x*y^2 - 3*x*y*z + 3*x*z^2 + 3*y*z^2 - 3*z^3, x^6 + 3*x^4*y^2 + x^3*y^3 + 5603/43200*y^6 - 3*x^5*z + 2*x^4*y*z - 2*x^3*y^2*z + 3*x^2*y^3*z - 3*y^5*z - x^4*z^2 - 2*x^3*y*z^2 - 2*x^2*y^2*z^2 - 3*x*y^3*z^2 + 2*y^4*z^2 - 2*x^3*z^3 + 3*x^2*y*z^3 + 3*x*y^2*z^3 + 2*y^3*z^3 + 2*x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - x*z^5 + 2*y*z^5 - z^6 - 507/800*x^5 + 2*x^4*y - 3*x^2*y^3 - 2*x*y^4 - 203/1800*y^5 - 3*x^3*y*z + 2*x^2*y^2*z + 2*y^4*z + 3*x^3*z^2 + 3*x^2*y*z^2 - 3*y^3*z^2 - x^2*z^3 + 2*x*y*z^3 - 3*x*z^4 + y*z^4 - z^5 + 2/5*x^4 - 3*x^2*y^2 + 3*x*y^3 - 1/15*y^4 - 73/120*x^3*z - 3*x^2*y*z + x*y^2*z + y^3*z + x^2*z^2 + y^2*z^2 + 2*x*z^3 - y*z^3 + 3*x*y^2 + 3*x*y*z + 2*y^2*z - 3*x*z^2 + 2*y*z^2 + 2*z^3, -3*x^6 + 2*x^5*y - x^4*y^2 - 3*x^3*y^3 + 16777/43200*y^6 + 2*x^5*z + x^4*y*z - 2*x^3*y^2*z + 2*x^2*y^3*z + 2*x*y^4*z - 2*y^5*z - x^4*z^2 + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 + x^3*z^3 + 3*x^2*y*z^3 - 2*x*y^2*z^3 - 2*y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 - 2*y^2*z^4 - 2*x*z^5 - y*z^5 + 269/2400*x^5 + 2*x^4*y - 2*x^3*y^2 - x^2*y^3 - 2*x*y^4 - 341/900*y^5 - 2*x^4*z - x^3*y*z + 2*x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 2*x^2*y*z^2 - x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 + 2*x*y*z^3 - 2*x*z^4 - y*z^4 + 1/5*x^4 - 3*x^3*y - 3*x^2*y^2 + 3*x*y^3 - 4/15*y^4 - 43/120*x^3*z + 3*x^2*y*z + x*y^2*z + 3*x^2*z^2 - x*y*z^2 - y^2*z^2 + 3*x*z^3 + 2*y*z^3 - 3*z^4 + 3*x*y^2 - 3*x*y*z - y^2*z - x*z^2 + y*z^2 + 2*z^3]
A1 l''=Z family II: dim of the tail space L = 5; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; b^x = (15, -2, 0), b^z = (0, 0, 0), identities b_2^z = 0, 4 b_0^z = gamma b_2^x: True; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (10, 34); 474 s
    the triple (seed 1364324, random triple number 1 after the construction of the member): [-x^6 + 3*x^5*y - x^2*y^4 - 3*x*y^5 + 659/10800*y^6 - x^5*z - x^4*y*z + 3*x^3*y^2*z + 2*x^2*y^3*z + 2*y^5*z + 3*x^4*z^2 + 3*x^2*y^2*z^2 - x*y^3*z^2 - 2*y^4*z^2 + x^3*z^3 + 3*x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + x^2*z^4 + 2*x*y*z^4 - 2*x*z^5 + 2*y*z^5 - z^6 - 169/600*x^5 - x^4*y + x^3*y^2 + x*y^4 - 7/180*y^5 - 2*x^3*y*z + 3*x^2*y^2*z - x*y^3*z - x^3*z^2 - x^2*y*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 + y^2*z^3 - 3*y*z^4 + 3*z^5 + 3/20*x^4 + x^2*y^2 - 2/15*y^4 + 1/6*x^3*z - x^2*y*z + 2*x*y^2*z - 3*y^3*z + 3*x^2*z^2 + 3*x*y*z^2 - y^2*z^2 - 3*x*z^3 - 2*z^4 - 2*x*y^2 + 3*x*y*z - y^2*z, x^6 + 3*x^5*y - 3*x^4*y^2 + x^3*y^3 - 2*x^2*y^4 + x*y^5 - 1171/10800*y^6 + 2*x^5*z + 2*x^4*y*z - x^2*y^3*z - 2*x*y^4*z + 2*y^5*z - x^4*z^2 - 3*x^2*y^2*z^2 + 3*y^4*z^2 + 3*x^3*z^3 + x^2*y*z^3 - 3*x*y^2*z^3 + y^3*z^3 + x^2*z^4 - 3*x*y*z^4 - 3*z^6 - 47/200*x^5 + 2*x^4*y - 3*x^3*y^2 - 3*x^2*y^3 - 2*x*y^4 - 13/180*y^5 + 2*x^4*z - 2*x^3*y*z - x*y^3*z - 3*y^4*z - 3*x^3*z^2 + 3*x^2*y*z^2 + y^3*z^2 + x^2*z^3 + 3*x*y*z^3 + 2*y^2*z^3 - 2*x*z^4 + 3*y*z^4 - 1/12*x^4 + 3*x^3*y - 3*x^2*y^2 - 2/15*y^4 - 23/6*x^3*z - x^2*y*z + 3*x*y^2*z + 3*y^3*z + 3*x*y*z^2 + 3*x*z^3 + 3*y*z^3 + 3*z^4 - 2*x*y^2 - 3*x*y*z - 3*y^2*z - 2*x*z^2 - y*z^2 + z^3, -2*x^6 - x^5*y + x^3*y^3 + 2*x^2*y^4 + 3*x*y^5 + 397/3600*y^6 - 2*x^5*z + x^4*y*z + x^3*y^2*z + 3*x^2*y^3*z - 2*x*y^4*z + 2*y^5*z - 3*x^4*z^2 - 3*x^2*y^2*z^2 + 3*x*y^3*z^2 + 3*y^4*z^2 - x^3*z^3 + x^2*y*z^3 + x*y^2*z^3 - y^3*z^3 - 2*x^2*z^4 + x*y*z^4 - y^2*z^4 + x*z^5 + 2*y*z^5 - 1/24*x^5 + 2*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 + 1/15*y^5 - 3*x^4*z + 2*x^3*y*z - 3*x*y^3*z + 3*y^4*z + 2*x^2*y*z^2 - x*y^2*z^2 + y^3*z^2 + 2*x^2*z^3 + 2*x*y*z^3 + 3*y^2*z^3 + 3*y*z^4 + 2*z^5 - 7/60*x^4 + x^3*y + x^2*y^2 + 2*x*y^3 - 1/5*y^4 + 1/2*x^3*z - 2*x*y^2*z + 2*y^3*z - 3*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 - 3*x*z^3 - 3*y*z^3 - 3*x*y^2 - 3*x*y*z - 2*y^2*z - x*z^2 - 2*y*z^2 - z^3]

4 cases (families) checked.
ALL CHECKS PASSED
A2 l''=Y: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 245 s
    the triple (seed 1364325, random triple number 1 after the construction of the member): [3587/1200*x^6 - 3*x^5*y + x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 - 3*y^6 - 2*x^5*z - 3*x^4*y*z + 2*x^3*y^2*z + 3*x*y^4*z + 2*y^5*z - 2*x^3*y*z^2 - 3*x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 + x^3*z^3 - 2*x^2*y*z^3 + 2*x*y^2*z^3 - 2*y^3*z^3 + 3*x^2*z^4 - 2*x*y*z^4 + 3*y^2*z^4 + x*z^5 - y*z^5 + 3*z^6 - 13/100*x^5 - x^4*y + 3*x^3*y^2 - x^2*y^3 + x*y^4 + 77/900*y^5 + 2*x^4*z - 3*x^3*y*z + 2*x^2*y^2*z + x*y^3*z - y^4*z - 3*x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + x*z^4 + 2*y*z^4 - z^5 + 1/60*x^4 + 9/2*x^3*y + 3*x^2*y^2 + 3*x*y^3 - 2/15*y^4 - 2*x^3*z - 2*x^2*y*z - x*y^2*z - 2*y^3*z + 3*x^2*z^2 - 3*x*y*z^2 + y^2*z^2 - z^4 - x*y^2 + 3*x*y*z + 2*y^2*z + 2*x*z^2 - 2*y*z^2, 3569/2160*x^6 - 2*x^5*y - x^4*y^2 + 2*x^3*y^3 + x^2*y^4 + 3*x*y^5 - 2*y^6 + 3*x^4*y*z + x^3*y^2*z - 3*x^2*y^3*z - 3*x*y^4*z + y^5*z - 3*x^4*z^2 - x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 - y^4*z^2 + x^3*z^3 - 2*x^2*y*z^3 - x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 - 2*y*z^5 + 3*z^6 - 91/450*x^5 + 2*x^4*y - x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 - 3/100*y^5 + 3*x^4*z - x^2*y^2*z + 3*x*y^3*z + y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 - y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 + 3*x*z^4 + y*z^4 + z^5 + 1/60*x^4 + 35/6*x^3*y - x^2*y^2 - 3*x*y^3 - 1/6*y^4 - 3*x^3*z + 3*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 - 3*x*z^3 + y*z^3 - 2*z^4 + x*y^2 - x*y*z + y^2*z + 3*x*z^2 + 2*y*z^2 + 2*z^3, -16583/10800*x^6 + 3*x^5*y - x^4*y^2 - x^3*y^3 - 2*x^2*y^4 + y^6 - 3*x^5*z - 3*x^4*y*z + 2*x^3*y^2*z + 2*x^2*y^3*z + x*y^4*z - 2*y^5*z + 2*x^4*z^2 - 2*x^3*y*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 - 3*x^3*z^3 + 2*x^2*y*z^3 + 3*y^3*z^3 - 2*x*y*z^4 + 3*y^2*z^4 + 3*y*z^5 + 2*z^6 - 221/360*x^5 - 3*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 + 3*x*y^4 + 53/1800*y^5 + 2*x^4*z + 3*x^3*y*z + x^2*y^2*z - 3*x*y^3*z + 2*y^4*z - x^3*z^2 + 3*x^2*y*z^2 - 2*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 + y^2*z^3 + 3*x*z^4 - 3*y*z^4 + z^5 + 2/15*x^4 + 20/3*x^3*y - 2*x^2*y^2 - 2/5*y^4 + x^3*z - 3*x^2*y*z + y^3*z + 3*x^2*z^2 + 3*x*y*z^2 + y^2*z^2 - 3*x*z^3 + y*z^3 + 3*z^4 + 3*x*y^2 + 2*x*y*z + 2*y^2*z + x*z^2 - y*z^2 + z^3]
A2 l''=Z: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 232 s
    the triple (seed 1364326, random triple number 1 after the construction of the member): [-2011/720*x^6 - 2*x^4*y^2 - 2*x^3*y^3 - x^2*y^4 + 3*x*y^5 + 3*y^6 - 2*x^5*z + 3*x^4*y*z - 2*x^3*y^2*z - 3*x^2*y^3*z - 3*x*y^4*z + 3*y^5*z - x^4*z^2 + 3*x^3*y*z^2 - 3*x^2*y^2*z^2 + 3*x*y^3*z^2 - 2*y^4*z^2 + 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 - x*z^5 + 2*y*z^5 + 3*z^6 + 17/180*x^5 - x^4*y - x^3*y^2 - 3*x^2*y^3 - x*y^4 - 11/600*y^5 - 3*x^4*z - 2*x^2*y^2*z - 2*x*y^3*z - 3*y^4*z - x^3*z^2 - 2*x^2*y*z^2 - x*y^2*z^2 - y^3*z^2 - 3*x^2*z^3 - x*y*z^3 + 2*y^2*z^3 - x*z^4 + 1/10*x^4 - x^3*y + 3*x*y^3 - 1/15*y^4 - 3*x^3*z - 3*x^2*y*z - 3*y^3*z + 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - x*z^3 - y*z^3 + 3*x*y^2 + 2*x*y*z - y^2*z - y*z^2 + 2*z^3, -911/3600*x^6 + 2*x^5*y + 3*x^4*y^2 - x^3*y^3 - x^2*y^4 - 2*x*y^5 + 3*x^5*z - 2*x^4*y*z - 3*x^3*y^2*z + 2*x^2*y^3*z - x*y^4*z - y^5*z + 2*x^4*z^2 - 3*x*y^3*z^2 + 2*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 - x*y^2*z^3 + 3*y^3*z^3 + 2*x^2*z^4 - x*y*z^4 - y*z^5 + 3*z^6 - 37/900*x^5 - x^4*y + x^3*y^2 + 3*x*y^4 + 2/75*y^5 + 2*x^4*z + 3*x^3*y*z - x^2*y^2*z + y^4*z + x^3*z^2 + x^2*y*z^2 - 2*y^3*z^2 - x^2*z^3 + x*y*z^3 - 2*y^2*z^3 - x*z^4 + z^5 - 13/60*x^4 + x^3*y + 2*x^2*y^2 + x*y^3 + 1/15*y^4 + 5/3*x^3*z - x^2*y*z - 3*x*y^2*z + y^3*z - 2*x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 - 3*x*z^3 - 3*z^4 - 2*x*y^2 + x*y*z - 3*x*z^2 + y*z^2, -6299/10800*x^6 - 3*x^5*y - 3*x^4*y^2 - 3*x^3*y^3 - x^2*y^4 + 3*x*y^5 + y^6 + x^5*z + x^2*y^3*z + 2*x*y^4*z - 3*y^5*z - x^4*z^2 - 3*x^3*y*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 - 2*y^4*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 + x*y^2*z^3 + 3*y^3*z^3 - 2*y^2*z^4 - 2*y*z^5 + 2*z^6 - 21/50*x^5 + x^4*y - 2*x^3*y^2 + x^2*y^3 - 3*x*y^4 + 37/1800*y^5 - x^4*z + 3*x^2*y^2*z + y^4*z + x*y^2*z^2 + x*y*z^3 + y^2*z^3 + x*z^4 - y*z^4 - z^5 - 1/60*x^4 + 3*x^3*y - 2*x^2*y^2 - 2*x*y^3 + 1/6*y^4 + 11/3*x^3*z + x^2*y*z + 2*x*y^2*z + y^3*z - x^2*z^2 - 2*x*y*z^2 - y^2*z^2 - x*z^3 - 3*y*z^3 - 2*x*y^2 + 2*x*y*z - 3*y^2*z + x*z^2 - y*z^2 + 3*z^3]

2 cases (families) checked.
ALL CHECKS PASSED
A3a0 (q=[Y]) Q2=X^3Z: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 164 s
    the triple (seed 1364327, random triple number 1 after the construction of the member): [-1849/1000*x^5*y + 2*x^4*y^2 + 3*x^3*y^3 - 2*x^2*y^4 - x^5*z + 2*x^4*y*z + 3*y^5*z + x^4*z^2 - 3*x^3*y*z^2 - x^2*y^2*z^2 - 3*x*y^3*z^2 + 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 + 2*x*z^5 - 2*y*z^5 - 2*z^6 + 6979/1200*x^5 - 323/300*x^4*y - 2*x^3*y^2 + x^2*y^3 + x*y^4 + y^5 - 3*x^4*z + x^3*y*z + 2*x^2*y^2*z - 2*x*y^3*z - y^4*z - 2*x^2*y*z^2 + 2*x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 + 2*x*y*z^3 + 3*y^2*z^3 + y*z^4 - z^5 + 1/10*x^4 + 19/20*x^3*y + 3*x^2*y^2 + 2*x*y^3 + 3*y^4 - 8/3*x^3*z + 3*x^2*y*z - 2*x*y^2*z + 3*y^3*z - 2*x^2*z^2 + 2*x*y*z^2 - 3*y^2*z^2 - 3*x*z^3 - 2*y*z^3 - x*y^2 - 3*x*y*z + y^2*z - x*z^2 + 2*y*z^2 - 3*z^3, -20257/3000*x^5*y - x^4*y^2 + 3*x^2*y^4 + 3*x*y^5 - 2*x^5*z + x^4*y*z + 2*x^3*y^2*z - 2*x^2*y^3*z - 2*x*y^4*z + x^4*z^2 - 2*x^3*y*z^2 - x^2*y^2*z^2 - x*y^3*z^2 - y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 + y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 - 2*y^2*z^4 - x*z^5 + 7169/1200*x^5 + 697/300*x^4*y + 3*x^2*y^3 - 2*x*y^4 - x^3*y*z - 2*x^2*y^2*z - 3*x*y^3*z - y^4*z - 2*x^3*z^2 - x^2*y*z^2 - 3*x*y^2*z^2 - 3*y^3*z^2 - 2*x^2*z^3 - 3*x*y*z^3 + y^2*z^3 + x*z^4 + 2*y*z^4 + 3*z^5 - 1/10*x^4 + x^2*y^2 + x*y^3 + 3*y^4 - 20/3*x^3*z + x^2*y*z - 2*x*y^2*z + 2*y^3*z + 3*x^2*z^2 - x*y*z^2 - 3*x*z^3 - 3*y*z^3 - 2*z^4 + x*y^2 + 2*x*y*z + 2*y^2*z - 3*x*z^2 + 3*z^3, -x^6 + 1727/3000*x^5*y + 3*x^4*y^2 + x^3*y^3 + 2*x^2*y^4 + 2*y^6 - x^5*z + 2*x^4*y*z - x^2*y^3*z + 2*y^5*z - 3*x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + x*y^3*z^2 + y^4*z^2 + 2*x^3*z^3 + 2*x*y^2*z^3 + 2*x^2*z^4 + 3*x*y*z^4 + 2*y^2*z^4 + x*z^5 + 3*y*z^5 + 3*z^6 - 61/150*x^5 + 2107/1200*x^4*y + x^2*y^3 + y^5 + x^4*z + 2*x^3*y*z - 2*x^2*y^2*z + x*y^3*z + 2*x^3*z^2 - x^2*y*z^2 + 2*x*y^2*z^2 + 2*y^3*z^2 + x^2*z^3 - 3*y^2*z^3 + 2*x*z^4 + 3*y*z^4 - 3*z^5 - 3/10*x^4 - 21/20*x^3*y - 2*x^2*y^2 - 2*x*y^3 - 2/3*x^3*z + 2*x^2*y*z + x*y^2*z + 2*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 + 3*y^2*z^2 + 2*x*z^3 - 2*y*z^3 + 3*x*y^2 + x*y*z - 2*y^2*z + 3*y*z^2 + 2*z^3]
A3a0 (q=[Y]) Q2=Q^4: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (10, 34); 464 s
    the triple (seed 1364328, random triple number 1 after the construction of the member): [-x^6 - 17489/6000*x^5*y + x^4*y^2 + 2*x^3*y^3 - x^2*y^4 + x*y^5 - 3*y^6 - 2*x^5*z + 3*x^4*y*z - x^3*y^2*z + 3*x^2*y^3*z + 2*x*y^4*z - y^5*z - x^4*z^2 - 2*x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 - 3*y^4*z^2 + x^3*z^3 + 3*y^3*z^3 - x*y*z^4 + x*z^5 + y*z^5 + 3*z^6 - 403/300*x^5 + 709/600*x^4*y + x^3*y^2 - 2*x^2*y^3 - x*y^4 + 2*y^5 - 2*x^4*z - x^3*y*z - x^2*y^2*z - 2*x*y^3*z - 3*y^4*z + 2*x^3*z^2 + x^2*y*z^2 + 3*x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 - x*y*z^3 + 2*x*z^4 - 2*y*z^4 + z^5 - 3/10*x^4 + 1/4*x^3*y - 2*x*y^3 + 29/24*y^4 + 3*x^3*z + 2*x^2*y*z + 2*x*y^2*z - y^3*z + x*y*z^2 + y^2*z^2 + 2*x*z^3 + y*z^3 + x*y^2 + 3*x*y*z + 2*y^2*z + 2*x*z^2 - 2*y*z^2 + 2*z^3, 2*x^6 - 7517/1200*x^5*y + 3*x^4*y^2 + 3*x^3*y^3 + 2*x^2*y^4 - 3*y^6 + x^5*z + 3*x^4*y*z - 3*x^3*y^2*z + y^5*z - 2*x^4*z^2 + x^3*y*z^2 - 2*x*y^3*z^2 + 3*y^4*z^2 - x^3*z^3 + 2*x^2*y*z^3 - 3*x*y^2*z^3 - y^3*z^3 + x^2*z^4 - x*y*z^4 + 2*y^2*z^4 - 2*y*z^5 - 2*z^6 - 3629/1200*x^5 - 3*x^3*y^2 + 2*x^2*y^3 - 2*x*y^4 + 2*y^5 + 2*x^4*z - 2*x^3*y*z + 2*x^2*y^2*z + y^4*z - 2*x^3*z^2 - x^2*y*z^2 + 2*x*y^2*z^2 + 2*x^2*z^3 + 2*x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 + 2*y*z^4 - 2*z^5 - 3/10*x^4 - 1/20*x^3*y + 3*x^2*y^2 - x*y^3 + 31/24*y^4 - 2*x^3*z - 3*x^2*y*z + 3*y^3*z + 3*x^2*z^2 + 2*x*y*z^2 + 3*y^2*z^2 - 2*z^4 + x*y^2 - 3*x*y*z + 3*y^2*z - 3*x*z^2 - 2*y*z^2 + z^3, -97/3000*x^5*y + 2*x^3*y^3 - x^2*y^4 - 2*x*y^5 + 2*x^5*z + x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + 2*x*y^4*z - y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 - 3*x^2*y^2*z^2 - x*y^3*z^2 - 2*y^4*z^2 - 3*x^3*z^3 + 3*x^2*y*z^3 + x*y^2*z^3 - y^3*z^3 + x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 + 3*z^6 + 421/400*x^5 - 17/75*x^4*y + y^5 - 2*x^4*z - 3*x^3*y*z - 2*x^2*y^2*z - x*y^3*z + y^4*z + 3*x^3*z^2 + 2*x^2*y*z^2 - 2*y^3*z^2 - x^2*z^3 - 3*x*y*z^3 - y^2*z^3 + 3*x*z^4 + 2*y*z^4 + z^5 + 9/10*x^4 - 2/5*x^3*y + x^2*y^2 + 2*x*y^3 - 3/4*y^4 - x^3*z - 2*x*y^2*z - 2*y^3*z - 2*x^2*z^2 - x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 + 3*y*z^3 + 2*z^4 - 3*x*y^2 - 2*x*y*z + 3*x*z^2 - 3*z^3]
A3a0 (q=[Y]) Q2=X^3Z+Q^4: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (10, 34); 431 s
    the triple (seed 1364329, random triple number 1 after the construction of the member): [-2*x^6 - 12857/3000*x^5*y - 3*x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 + x*y^5 + 2*y^6 - 2*x^5*z + 3*x^4*y*z + x^3*y^2*z + 3*x^2*y^3*z + 3*x*y^4*z - y^5*z - 2*x^3*y*z^2 + 2*x^2*y^2*z^2 + 3*x*y^3*z^2 + y^4*z^2 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 - 3*x*y*z^4 - 2*y^2*z^4 - 2*x*z^5 + y*z^5 - 871/600*x^5 - 53/300*x^4*y + x^3*y^2 + 2*x^2*y^3 + x*y^4 - 3*y^5 - x^4*z + x^3*y*z + 2*x^2*y^2*z + 3*y^4*z + 2*x^3*z^2 - 3*x^2*y*z^2 - x*y^2*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 - x*z^4 + y*z^4 + 3*z^5 + 3/5*x^4 - 3/4*x^3*y - x^2*y^2 + x*y^3 - 11/24*y^4 + x^3*z - 2*x^2*y*z - 3*y^3*z - 3*x^2*z^2 - 2*x*y*z^2 - 3*y^2*z^2 - 2*x*z^3 + 2*z^4 + 2*x*y^2 - x*y*z - 3*y^2*z + 2*x*z^2 + 2*y*z^2 + z^3, 3*x^6 + 51/20*x^5*y + x^4*y^2 + 3*x^3*y^3 + 3*x^2*y^4 - 2*x*y^5 + 3*x^4*y*z - x^3*y^2*z - x^2*y^3*z - x*y^4*z + 3*y^5*z + x^4*z^2 + 2*x^3*y*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 + 3*x*y^2*z^3 - 3*y^3*z^3 + 3*x^2*z^4 - x*y*z^4 + 3*y^2*z^4 + 3*x*z^5 + 3*y*z^5 - z^6 + 679/240*x^5 - 73/60*x^4*y + 3*x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 + 3*y^5 + x^4*z - 2*x^3*y*z - x^2*y^2*z - x*y^3*z - 2*y^4*z + x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 - 2*x*y*z^3 + 3*x*z^4 + 3*y*z^4 + z^5 + 3/10*x^4 + 3*x^2*y^2 - 3*x*y^3 + 13/12*y^4 - 2*x^3*z + 3*x^2*y*z + x*y^2*z + 3*y^3*z + 3*x^2*z^2 - 3*x*y*z^2 - y^2*z^2 + 3*x*z^3 - 3*y*z^3 + 2*z^4 + x*y^2 + 2*x*y*z + 3*x*z^2 + 2*z^3, -2*x^6 - 249/40*x^5*y + 2*x^4*y^2 - x^3*y^3 + x^2*y^4 + x*y^5 - 3*y^6 + 2*x^5*z + x^4*y*z + x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - 3*y^5*z + 3*x^4*z^2 + x^3*y*z^2 + x^2*y^2*z^2 - 2*x*y^3*z^2 + 3*y^4*z^2 - x^3*z^3 + 2*x^2*y*z^3 + x*y^2*z^3 + x^2*z^4 + 2*y^2*z^4 + 2*x*z^5 + 2*y*z^5 - z^6 - 63/100*x^5 - 7/20*x^4*y - 3*x^2*y^3 + 2*x*y^4 - 3*y^5 + 3*x^3*y*z - x^2*y^2*z + 2*x*y^3*z + 2*y^4*z - 3*x^2*y*z^2 + 3*x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 + 3*y^2*z^3 + 3*x*z^4 + y*z^4 + z^5 - 9/10*x^4 + 9/10*x^3*y + x^2*y^2 - 1/4*y^4 - 2*x^3*z - 3*x^2*y*z - 3*y^3*z + 3*x^2*z^2 + 2*x*y*z^2 - y^2*z^2 - 3*x*z^3 - 3*y*z^3 - 2*z^4 - 3*x*y^2 - y^2*z - 2*y*z^2]

3 cases (families) checked.
ALL CHECKS PASSED
A3a1 (q=[X+Y]) Q2=X^3Z: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 217 s
    the triple (seed 1364330, random triple number 1 after the construction of the member): [3*x^6 - 104381/6000*x^5*y - x^4*y^2 + 2*x^3*y^3 + x*y^5 - y^6 - 2*x^5*z - 2*x^3*y^2*z - 3*x^2*y^3*z + 3*x*y^4*z - 2*x^4*z^2 + 3*x^3*y*z^2 - 2*x^2*y^2*z^2 + 3*x*y^3*z^2 - x^3*z^3 + 3*x^2*y*z^3 - x*y^2*z^3 - 2*x^2*z^4 - 3*x*y*z^4 - y^2*z^4 - 2*x*z^5 + y*z^5 - 2*z^6 + 1501/200*x^5 - 14083/600*x^4*y + 2*x^3*y^2 - 3*y^5 + x^4*z + 3*x^3*y*z - 2*x^2*y^2*z - y^4*z + x^3*z^2 - 3*x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 + 3*x^2*z^3 + 3*x*y*z^3 + y^2*z^3 + x*z^4 + 3*y*z^4 - 2*z^5 + 63/10*x^4 - 19/10*x^3*y - 2*x^2*y^2 - 3*x*y^3 + y^4 + 8*x^3*z - x^2*y*z + 3*x*y^2*z + 3*y^3*z - 3*x^2*z^2 - 3*x*y*z^2 + x*z^3 + 2*y*z^3 - 3*z^4 + 3*x*y^2 - 3*y^3 - 2*x*y*z + 2*y^2*z - 2*x*z^2 - 2*y*z^2 + 2*z^3, 3329/1200*x^5*y + 2*x^4*y^2 - 3*x^3*y^3 + 3*x^2*y^4 - y^6 + 3*x^5*z - 2*x^4*y*z + 2*x^3*y^2*z - 2*x^2*y^3*z - 2*y^5*z - 3*x^4*z^2 + 2*x^3*y*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 + 2*y^4*z^2 - 3*x^2*y*z^3 - 3*x*y^2*z^3 - 2*x^2*z^4 + 2*x*y*z^4 + y^2*z^4 + 3*x*z^5 + 3*y*z^5 - z^6 + 86/25*x^5 + 163/30*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 - x*y^4 - 3*y^5 + x^3*y*z + 2*x^2*y^2*z - x*y^3*z + 2*y^4*z + 2*x^3*z^2 + x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 - 2*x*z^4 - 3*y*z^4 - 2*z^5 - 13/20*x^3*y - 3*x^2*y^2 - x*y^3 - y^4 - 8*x^3*z - 2*x^2*y*z - y^3*z + 2*x^2*z^2 - x*y*z^2 - 3*y^2*z^2 + 3*x*z^3 - 3*y*z^3 - 3*z^4 - x*y*z - y^2*z - 2*x*z^2 - 2*z^3, -x^6 + 20027/6000*x^5*y - 3*x^4*y^2 + x^3*y^3 - 3*x^2*y^4 - 2*x*y^5 + 3*y^6 + 2*x^5*z + 3*x^4*y*z - 3*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 + 2*x^3*y*z^2 - 2*x^2*y^2*z^2 + 3*x*y^3*z^2 + 2*y^4*z^2 - 2*x^3*z^3 + 2*x*y^2*z^3 - y^3*z^3 - x^2*z^4 - 3*x*y*z^4 + y^2*z^4 - 2*x*z^5 + 3*y*z^5 + z^6 + 4/75*x^5 - 13813/1200*x^4*y - x^2*y^3 + x*y^4 - 2*y^5 + 2*x^4*z + x^3*y*z - 2*x*y^3*z - 3*x^3*z^2 + 3*x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 - 2*y^2*z^3 - 2*y*z^4 + 3*z^5 + 63/10*x^4 - 11/10*x^3*y - x^2*y^2 + 3*x*y^3 - 2*y^4 - 34/3*x^3*z + x^2*y*z - 2*x*y^2*z - 2*y^3*z - x^2*z^2 + 2*x*y*z^2 + 2*y^2*z^2 + 3*x*z^3 + z^4 + 3*x*y^2 - 3*y^3 + 2*x*y*z - 2*y^2*z + y*z^2 - 3*z^3]
A3a1 (q=[X+Y]) Q2=Q^4: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 35 (standard basis), m^N certificate (N, length) = (10, 35); 423 s
    the triple (seed 1364331, random triple number 1 after the construction of the member): [9017/6000*x^5*y - 3*x^4*y^2 - 2*x^3*y^3 - 3*x^2*y^4 - 3*y^6 + 3*x^5*z - 2*x^4*y*z + x^2*y^3*z - 2*x*y^4*z - 2*x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 + x*y^3*z^2 - y^4*z^2 - 3*x^3*z^3 - 3*x^2*y*z^3 - 3*x*y^2*z^3 - 3*y^3*z^3 + x^2*z^4 - 2*x*y*z^4 - 2*y^2*z^4 + 3*x*z^5 + 2*y*z^5 - 2*z^6 - 1/300*x^5 - 539/1200*x^4*y - 3*x^3*y^2 + 3*x^2*y^3 + 2*y^5 + 2*x^4*z + 3*x^2*y^2*z + x*y^3*z - 2*y^4*z + 3*x^3*z^2 + 2*x^2*y*z^2 - 3*x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 + x*y*z^3 - 3*y^2*z^3 - 2*x*z^4 - 3*y*z^4 + 3*z^5 + 1/5*x^4 - 1/20*x^3*y + 19/15*x^2*y^2 - 2*x*y^3 - 2*y^4 - x^3*z + 3*x*y^2*z + 2*y^3*z + 2*x^2*z^2 - x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 + 2*y*z^3 + 3*z^4 - x*y^2 + y^3 + x*y*z - 3*y^2*z - 3*y*z^2 + 3*z^3, 2*x^6 + 29197/6000*x^5*y + x^4*y^2 + 3*x^3*y^3 + 2*x^2*y^4 - 3*x*y^5 + 2*y^6 - 2*x^4*y*z + 3*x^2*y^3*z - 3*x*y^4*z - y^5*z - x^3*y*z^2 + 2*x^2*y^2*z^2 + 3*x*y^3*z^2 + 2*y^4*z^2 - 2*x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 + 3*y^3*z^3 - 2*x^2*z^4 + 3*x*y*z^4 - y^2*z^4 - x*z^5 - 3*z^6 - 469/600*x^5 - 2359/1200*x^4*y - 3*x^3*y^2 - 2*x*y^4 + 2*y^5 + 3*x^4*z - x^3*y*z - x^2*y^2*z - x*y^3*z - 2*y^4*z + 3*x^3*z^2 - 3*x^2*y*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 - 2*y^2*z^3 + x*z^4 + y*z^4 + 1/10*x^3*y + 26/15*x^2*y^2 - x*y^3 - 2*y^4 - 2*x^3*z + x^2*y*z + 2*x*y^2*z + 3*y^3*z + 3*x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 + 2*x*z^3 + 2*y*z^3 - z^4 - 2*x*y*z + 3*y^2*z + 2*x*z^2 - 3*y*z^2 + 2*z^3, -3*x^6 - 953/250*x^5*y + 3*x^4*y^2 - 2*x^3*y^3 + 2*x^2*y^4 - 2*x*y^5 + 3*y^6 - 2*x^5*z - x^4*y*z + 3*x^3*y^2*z + x^2*y^3*z + 3*x*y^4*z + 2*y^5*z - 2*x^4*z^2 + 2*x^3*y*z^2 + 2*x^2*y^2*z^2 + y^4*z^2 + x^3*z^3 + 3*x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 - 3*x^2*z^4 + 3*x*z^5 + y*z^5 + 221/200*x^5 + 733/400*x^4*y - 3*x^3*y^2 + 2*x^2*y^3 + 2*x*y^4 + 2*y^5 + 2*x^4*z + 2*x^3*y*z + 3*x*y^3*z + 2*y^4*z + 2*x^2*y*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 + x^2*z^3 - x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 + 2*y*z^4 + 2*z^5 - 1/10*x^3*y - 17/5*x^2*y^2 + x*y^3 + 3*y^4 + 2*x^3*z + 3*x^2*y*z - 3*x*y^2*z + 3*y^3*z + x^2*z^2 - x*y*z^2 - y^2*z^2 - 2*y*z^3 + z^4 + 2*x*y*z - 3*y^2*z + 2*x*z^2 + 3*y*z^2 - 2*z^3]
A3a1 (q=[X+Y]) Q2=X^3Z+Q^4: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (10, 34); 476 s
    the triple (seed 1364332, random triple number 1 after the construction of the member): [x^6 + 88883/18000*x^5*y - 3*x^4*y^2 + 3*x^3*y^3 - 3*x*y^5 - 2*y^6 - 3*x^5*z + 3*x^4*y*z + x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z - y^5*z + 3*x^4*z^2 - 2*x^3*y*z^2 + x^2*y^2*z^2 - x*y^3*z^2 + y^4*z^2 + x^3*z^3 - 3*x*y*z^4 + y^2*z^4 + 2*x*z^5 - 3*y*z^5 - z^6 + 659/300*x^5 - 647/200*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 - 3*x*y^4 - 3*y^5 - 3*x^4*z + 3*x^3*y*z + 3*x^2*y^2*z + x*y^3*z + y^4*z + 3*x^3*z^2 - x^2*y*z^2 - 2*x*y^2*z^2 + 3*y^3*z^2 - x^2*z^3 - x*y*z^3 - y^2*z^3 + 2*x*z^4 - y*z^4 + 2*z^5 - 3/5*x^4 + 8/5*x^3*y - 43/12*x^2*y^2 - x*y^3 + 3*y^4 - 2*x^3*z - x^2*y*z + 3*x*y^2*z - y^3*z + 3*x^2*z^2 + x*y*z^2 - 3*y^2*z^2 - 3*y*z^3 + 3*z^4 + 3*x*y^2 - 3*y^3 - 2*x*y*z + 2*y^2*z - z^3, 2*x^6 - 1367/500*x^5*y - x^4*y^2 - 3*x^3*y^3 - 3*x^2*y^4 + 3*y^6 + 3*x^5*z - 3*x^3*y^2*z + 2*x^2*y^3*z + 2*x*y^4*z - y^5*z + x^4*z^2 + 3*x^3*y*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 + x^3*z^3 + x^2*y*z^3 - x*y^2*z^3 - y^3*z^3 - x^2*z^4 - 2*x*y*z^4 + 3*x*z^5 - 3*y*z^5 - 2*z^6 - 541/400*x^5 - 37/200*x^4*y + 2*x^3*y^2 - x*y^4 - 2*y^5 + x^4*z - x^3*y*z + 2*x^2*y^2*z - x*y^3*z - 3*y^4*z - x^3*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 - 3*x^2*z^3 - 2*x*z^4 - y*z^4 + z^5 + 3/5*x^4 - 29/20*x^3*y - 81/40*x^2*y^2 + 2*x*y^3 + y^4 - x^3*z + 2*x^2*y*z + 2*x*y^2*z - y^3*z - 3*x^2*z^2 - 2*x*y*z^2 - y^2*z^2 + x*z^3 - y*z^3 - z^4 - 3*x*y^2 + 3*y^3 - x*y*z + 2*y^2*z + x*z^2 - y*z^2 - 3*z^3, 2*x^6 - 22589/18000*x^5*y + 2*x^4*y^2 - 2*x^3*y^3 - 3*x*y^5 - 3*y^6 - 3*x^5*z - x^4*y*z - 2*x^3*y^2*z - x^2*y^3*z + 2*x*y^4*z + 3*y^5*z - 3*x^4*z^2 - 2*x^3*y*z^2 - 3*x^2*y^2*z^2 - x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 + 2*x^2*y*z^3 - x*y^2*z^3 - 3*y^3*z^3 - 2*x*y*z^4 + 3*y^2*z^4 - x*z^5 - 2*z^6 - 73/60*x^5 + 31/1200*x^4*y - 3*x^2*y^3 - 2*y^5 + x^4*z + x^3*y*z - 3*x*y^3*z + y^4*z - 2*y^3*z^2 + x^2*z^3 - 2*y^2*z^3 + 3*x*z^4 - 2*z^5 + 1/5*x^4 - 13/20*x^3*y + 79/120*x^2*y^2 - x*y^3 + y^4 - 2*x^3*z - x*y^2*z - y^3*z - 2*x^2*z^2 + 3*x*z^3 - 3*y*z^3 + 3*z^4 - x*y^2 + y^3 + 3*x*y*z + 3*y^2*z + 2*x*z^2 - 2*y*z^2 + 2*z^3]

3 cases (families) checked.
ALL CHECKS PASSED
A3b (q=[Z]) Q2=X^3Z: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 35 (standard basis), m^N certificate (N, length) = (10, 35); 373 s
    the triple (seed 1364333, random triple number 1 after the construction of the member): [-3*x^6 + 437/200*x^5*y - x^4*y^2 - x^3*y^3 + 2*x^2*y^4 - x*y^5 + 3*y^6 + x^5*z - 2*x^4*y*z + 2*x^3*y^2*z - 2*x^2*y^3*z - x*y^4*z + x^4*z^2 - 2*x^3*y*z^2 + 3*x^2*y^2*z^2 - 3*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 - 3*x*y^2*z^3 - y^3*z^3 + 3*x*y*z^4 + 3*x*z^5 + y*z^5 - 3*z^6 - 71/100*x^5 - 1/12*x^4*y - 3*x^3*y^2 + 3*x*y^4 - 3*y^5 + x^4*z - 2*x^3*y*z - 3*x^2*y^2*z + 3*x*y^3*z + 3*y^4*z + 2*x^3*z^2 - 3*x^2*y*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 + y^2*z^3 - 2*x*z^4 - y*z^4 + 3*z^5 - 1/10*x^4 - 3/10*x^3*y - 2*x^2*y^2 + 2*x*y^3 + 3*y^4 + 2/3*x^3*z + x^2*y*z - 2*x*y^2*z - y^3*z + 3*x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 + x*z^3 - 2*y*z^3 + z^4 + x*y^2 - 2*y^3 + 2*x*y*z - 2*y^2*z + 3*x*z^2 + y*z^2, 2*x^6 + 2329/3000*x^5*y + 3*x^4*y^2 - 3*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - y^6 + 2*x^5*z + x^4*y*z + 3*x^3*y^2*z + x^2*y^3*z + 2*x*y^4*z + 2*y^5*z - 3*x^4*z^2 + 2*x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 + 3*y^4*z^2 + 3*x^2*y*z^3 + 3*x*y^2*z^3 - 3*y^3*z^3 + 3*x^2*z^4 + 3*y^2*z^4 - x*z^5 - 2*y*z^5 - z^6 + 161/150*x^5 + 61/25*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 - x*y^4 + y^5 - 2*x^3*y*z - 3*x^2*y^2*z - 3*x*y^3*z - 2*y^4*z - x^3*z^2 - 2*x^2*y*z^2 - 3*x*y^2*z^2 + 2*x^2*z^3 + 3*x*y*z^3 + 2*y^2*z^3 + x*z^4 + 2*y*z^4 + 3*z^5 - 3/10*x^4 - 11/10*x^3*y - 3*x*y^3 + 3*y^4 - 11*x^3*z - 3*x^2*y*z + 2*x*y^2*z + y^3*z - 2*x*y*z^2 - 2*y^2*z^2 - 2*x*z^3 + y*z^3 - z^4 + 3*x*y^2 + 3*y^3 + x*y*z - 2*y^2*z + 3*x*z^2 + y*z^2, -3*x^6 - 692/375*x^5*y + 2*x^3*y^3 + 2*x^2*y^4 - 2*x*y^5 - y^6 - 2*x^5*z + 3*x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z - 2*x^4*z^2 - 2*x^3*y*z^2 - 3*x*y^3*z^2 - 2*y^4*z^2 + x^3*z^3 + 2*x^2*y*z^3 + 2*x*y^2*z^3 + 3*y^3*z^3 + 2*x^2*z^4 + 2*x*y*z^4 - y^2*z^4 + x*z^5 - y*z^5 - z^6 - 77/300*x^5 + 277/300*x^4*y - x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 + 3*y^5 - 3*x^4*z + 3*x^3*y*z + x*y^3*z - 2*y^4*z + 2*x^3*z^2 + x*y^2*z^2 - 3*x^2*z^3 - 3*x*y*z^3 + 3*y^2*z^3 + x*z^4 + 2*y*z^4 + 2*z^5 - 1/5*x^4 - 2/5*x^3*y + 2*x^2*y^2 - 3*x*y^3 - 3*y^4 - 5*x^3*z - x^2*y*z - x*y^2*z + 3*y^3*z + x^2*z^2 - 3*x*y*z^2 + 2*y^2*z^2 + 3*x*z^3 + 2*y*z^3 + 2*x*y^2 + y^3 - x*y*z - 2*y*z^2]
A3b (q=[Z]) Q2=Q^4: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (10, 34); 463 s
    the triple (seed 1364334, random triple number 1 after the construction of the member): [3*x^6 + 287/60*x^5*y - x^4*y^2 + 2*x^3*y^3 - 3*x^2*y^4 + y^6 - 3*x^5*z + 3*x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z - y^5*z + 2*x^4*z^2 - 3*x^3*y*z^2 + 3*x^2*y^2*z^2 + 3*x*y^3*z^2 - 2*y^4*z^2 - x^3*z^3 + 2*y^3*z^3 + 3*x^2*z^4 + 3*x*y*z^4 + y^2*z^4 - 3*x*z^5 + 3*y*z^5 + 3*z^6 + 1781/1200*x^5 - 223/240*x^4*y + 3*x^3*y^2 - x^2*y^3 - 2*x*y^4 + 3*y^5 + 2*x^4*z - 2*x^3*y*z - 3*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 + 2*x^2*z^3 + 3*x*y*z^3 + 2*y^2*z^3 + 3*x*z^4 + 3*y*z^4 + 3*z^5 - 9/10*x^4 + 3/20*x^3*y - 3*x^2*y^2 - 2*y^4 + 3*x^3*z - 3*x^2*y*z - 2*x*y^2*z + 2*y^3*z - 2*x^2*z^2 - x*y*z^2 + y^2*z^2 + 2*y*z^3 - 25/24*z^4 + 3*x*y^2 + 3*x*y*z + y^2*z + x*z^2 + 3*y*z^2, -x^6 + 13289/6000*x^5*y - x^2*y^4 + x*y^5 + y^6 + 2*x^5*z - 3*x^4*y*z - 2*x^2*y^3*z + 2*x*y^4*z + x^4*z^2 - 2*x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 - 3*x^3*z^3 - x^2*y*z^3 + 2*x*y^2*z^3 + 2*y^3*z^3 + 2*x^2*z^4 + 2*x*y*z^4 + y^2*z^4 - x*z^5 - y*z^5 + z^6 + 39/200*x^5 + 1571/1200*x^4*y + x^3*y^2 + 3*x^2*y^3 - 3*x*y^4 + y^5 - x^4*z - 3*x^3*y*z + 3*x^2*y^2*z + y^4*z + x^3*z^2 - x^2*y*z^2 - y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 + 2*y*z^4 + 3*z^5 + 3/5*x^4 - 3/10*x^3*y - x*y^3 - 3*y^4 + x^3*z - x^2*y*z - x*y^2*z - 2*y^3*z - 3*x^2*z^2 + 2*y^2*z^2 + x*z^3 + 13/12*z^4 - 2*x*y^2 + y^3 + y^2*z - 3*y*z^2, x^6 + 10859/6000*x^5*y - 3*x^4*y^2 + x^3*y^3 - 3*x^2*y^4 + x*y^5 - 3*y^6 + x^5*z + 3*x^4*y*z - x^3*y^2*z - 3*x*y^4*z - y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 + 2*x^2*y^2*z^2 + x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 - x^2*y*z^3 + y^3*z^3 - 2*x^2*z^4 - 2*x*y*z^4 - 3*y^2*z^4 + 3*x*z^5 + 2*y*z^5 + 2*z^6 + 369/400*x^5 + 17/400*x^4*y - 3*x^3*y^2 + x*y^4 - 2*y^5 + 3*x^4*z + 3*x^2*y^2*z - 2*y^4*z + 3*x^3*z^2 + x*y^2*z^2 + y^3*z^2 + x^2*z^3 - 2*x*y*z^3 + 2*y^2*z^3 - x*z^4 - 2*y*z^4 + z^5 + 3/5*x^4 - 4/5*x^3*y - 3*x^2*y^2 + 3*x*y^3 + 3*y^4 - x^3*z - 3*x^2*y*z + x*y^2*z + y^3*z - 3*x^2*z^2 - x*y*z^2 - 3*y^2*z^2 - 3*x*z^3 - 3*y*z^3 + 1/12*z^4 - 2*x*y^2 + 3*y^3 + 2*x*y*z - 2*y^2*z + x*z^2 - 3*y*z^2]
A3b (q=[Z]) Q2=X^3Z+Q^4: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 196 s
    the triple (seed 1364335, random triple number 1 after the construction of the member): [2*x^6 + 2917/500*x^5*y + 3*x^4*y^2 + 2*x^3*y^3 - 2*y^6 - x^5*z + x^4*y*z + 2*x^3*y^2*z - 3*x^2*y^3*z - 3*x*y^4*z - y^5*z + x^4*z^2 - x^2*y^2*z^2 + x*y^3*z^2 + 3*x^3*z^3 - x^2*y*z^3 + x*y^2*z^3 + 2*y^3*z^3 + x^2*z^4 - 2*y^2*z^4 - 3*x*z^5 + y*z^5 + 3*z^6 + 139/1200*x^5 - 671/1200*x^4*y + 2*x^3*y^2 + 3*x^2*y^3 + 2*x*y^4 - 2*x^4*z - 3*x^3*y*z - 2*x^2*y^2*z + 2*x*y^3*z - 3*y^4*z + x^3*z^2 - 3*x^2*y*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 + 3*x*z^4 + z^5 + 3/10*x^4 - 9/20*x^3*y - x^2*y^2 - x*y^3 + 2*y^4 + 25/3*x^3*z + x^2*y*z + x*y^2*z - 2*y^3*z + 2*x^2*z^2 - 3*x*y*z^2 + 3*x*z^3 + 2*y*z^3 - z^4 - 3*x*y^2 + 3*y^3 + 3*y^2*z + x*z^2 + y*z^2, 2*x^6 + 19799/1500*x^5*y - x^4*y^2 + x^3*y^3 - 2*x*y^5 - y^6 - 2*x^5*z + 2*x^4*y*z + x^2*y^3*z + y^5*z + 3*x^4*z^2 - x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 - 3*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 + 2*x*z^5 - 3*y*z^5 - 2*z^6 - 787/400*x^5 + 1267/400*x^4*y + 2*x^3*y^2 + x*y^4 - y^5 - 3*x^4*z - x^2*y^2*z + 3*x*y^3*z - 3*y^4*z + x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 + 2*x^2*z^3 + 3*x*y*z^3 - y^2*z^3 - 3*x*z^4 + 3*z^5 - 1/5*x^4 - 33/20*x^3*y + 3*x^2*y^2 - 2*x*y^3 + 3*y^4 + x^3*z - 3*x^2*y*z + 2*x*y^2*z - 2*y^3*z + 2*x^2*z^2 + x*y*z^2 - y^2*z^2 - 3*x*z^3 - 2*y*z^3 - z^4 + 2*x*y^2 + 3*y^2*z - 3*x*z^2 + y*z^2, -2*x^6 - 11813/3000*x^5*y + x^4*y^2 + 3*x^3*y^3 - x^2*y^4 + 2*y^6 + x^5*z + 2*x^4*y*z + x^3*y^2*z - x^2*y^3*z + 3*x*y^4*z - 3*x^4*z^2 - x^3*y*z^2 - x^2*y^2*z^2 + 2*y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 - x*y^2*z^3 + 3*y^3*z^3 + 2*x^2*z^4 + 2*x*y*z^4 - 2*y^2*z^4 - 3*x*z^5 + z^6 + 13/25*x^5 - 2981/1200*x^4*y + 2*x^2*y^3 + 2*x*y^4 - y^5 + 3*x^4*z - 2*x^3*y*z - 3*x^2*y^2*z + 2*x*y^3*z + 3*y^4*z + x^3*z^2 - 2*x^2*y*z^2 - 2*x*y^2*z^2 - y^3*z^2 + 3*x^2*z^3 + 3*x*y*z^3 - 2*y^2*z^3 - x*z^4 - 3*y*z^4 - z^5 - 3/10*x^4 + 12/5*x^3*y - 3*x^2*y^2 - 2*x*y^3 + 3*x^3*z + 2*x^2*y*z + x*y^2*z + y^3*z + x^2*z^2 - 2*x*y*z^2 - y^2*z^2 + x*z^3 - 2*y*z^3 - z^4 + 3*x*y^2 + y^3 - 2*x*y*z - 3*y^2*z + 2*x*z^2 - y*z^2]

3 cases (families) checked.
ALL CHECKS PASSED
B l'=Y Q2=X^3Z: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 37 (standard basis), m^N certificate (N, length) = (10, 37); 405 s
    the triple (seed 1364336, random triple number 1 after the construction of the member): [-3*x^6 - 17701/6000*x^5*y - x^4*y^2 - x^3*y^3 - 2*x^2*y^4 + 2*x*y^5 - 3*y^6 - 2*x^5*z - 3*x^4*y*z + x^3*y^2*z + x^2*y^3*z + 2*x*y^4*z + 3*y^5*z - 2*x^4*z^2 - 3*x^3*y*z^2 + 2*x^2*y^2*z^2 + 3*x*y^3*z^2 - 3*y^4*z^2 + 2*x^3*z^3 - 3*x^2*y*z^3 - 2*x*y^2*z^3 - 2*y^3*z^3 - 3*x^2*z^4 - 2*x*y*z^4 + 3*y^2*z^4 - x*z^5 + y*z^5 - 3*z^6 + 1/3*x^5 - 519/400*x^4*y - x^3*y^2 - x^2*y^3 + 2*x*y^4 + y^5 + 3*x^4*z - x^3*y*z - x^2*y^2*z + 2*y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 - 3*x*z^4 + y*z^4 + 1/5*x^3*y - 3*x*y^3 + 10/3*x^3*z - 3*x^2*y*z - 2*x*y^2*z + 3*y^3*z + 2*x*y*z^2 - y^2*z^2 - x*z^3 + 3*y*z^3 + z^4 - y^3 - 2*y^2*z + 3*y*z^2 - z^3, -x^6 + 24849/2000*x^5*y + 2*x^4*y^2 + 2*x^2*y^4 + 2*x*y^5 + 3*y^6 + 2*x^5*z + 2*x^4*y*z + x^3*y^2*z - x^2*y^3*z + x*y^4*z - y^5*z + x^4*z^2 + x^3*y*z^2 + 3*x*y^3*z^2 - y^4*z^2 + 2*x^3*z^3 + 3*x^2*y*z^3 - 2*x*y^2*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + x*y*z^4 - 3*y^2*z^4 - 3*y*z^5 + 3*z^6 - 17/8*x^5 + 7499/1200*x^4*y - x^2*y^3 + x*y^4 - 2*y^5 - 2*x^4*z - 2*x^3*y*z - 3*x^2*y^2*z + x*y^3*z - y^4*z - 2*x^3*z^2 - 2*x^2*y*z^2 + x*y^2*z^2 + 3*y^3*z^2 + x*y*z^3 - y^2*z^3 + 2*x*z^4 - 2*y*z^4 - 3*z^5 - 3/5*x^4 - 13/20*x^3*y - 2*x^2*y^2 - 2*x*y^3 + 3*y^4 - 53/6*x^3*z + 2*x^2*y*z + x*y^2*z - 3*y^3*z - 2*x^2*z^2 + 2*x*y*z^2 + 3*x*z^3 + 2*y*z^3 - z^4 + 3*x*y^2 - 2*y^3 - 3*x*y*z + y^2*z - y*z^2 + 2*z^3, -2*x^6 - 7157/1000*x^5*y - 2*x^4*y^2 + 3*x^3*y^3 + x^2*y^4 + 2*x*y^5 - 2*y^6 + x^5*z - 2*x^4*y*z + 2*x^2*y^3*z - 3*x*y^4*z + 2*x^4*z^2 - x^3*y*z^2 + 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 3*y^4*z^2 - 2*x^3*z^3 + 2*x^2*y*z^3 - x*y^2*z^3 - 3*y^3*z^3 + y^2*z^4 - 2*x*z^5 - 2*y*z^5 + 341/600*x^5 - 503/150*x^4*y + 2*x^3*y^2 - 2*x*y^4 + 3*y^5 + 3*x^4*z - 2*x^3*y*z - 3*x^2*y^2*z - x*y^3*z - y^4*z - x^3*z^2 + 3*x^2*y*z^2 - 3*x*y^2*z^2 - 2*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 - z^5 + 1/5*x^4 + 11/20*x^3*y + 3*x^2*y^2 - 3*x*y^3 - 3*y^4 + 49/6*x^3*z + 3*x^2*y*z + 2*x*y^2*z - 3*y^3*z + x^2*z^2 - 2*x*y*z^2 + 2*y^2*z^2 - x*z^3 - x*y^2 - y^3 + x*y*z - 3*z^3]
B l'=Y Q2=X^2Z^2: dim of the tail space L = 7; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 155 s
    the triple (seed 1364337, random triple number 1 after the construction of the member): [2*x^6 - 227/150*x^5*y - 3*x^4*y^2 + 3*x^2*y^4 - 2*x*y^5 - 2*y^6 + x^5*z + 2*x^4*y*z + 3*x^3*y^2*z - x^2*y^3*z - 3*x*y^4*z - 2*y^5*z - 3*x^4*z^2 - x^3*y*z^2 + 2*x^2*y^2*z^2 + 3*x*y^3*z^2 + 2*y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 + 2*x*y^2*z^3 - y^3*z^3 - 2*x*y*z^4 - 3*y^2*z^4 - x*z^5 - 2*y*z^5 - 579/100*x^5 - 1/240*x^4*y - 2*x^3*y^2 + x^2*y^3 + x*y^4 + 3*x^4*z + x^3*y*z - x^2*y^2*z - x*y^3*z - 2*y^4*z + x^3*z^2 + 2*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 - 3*y^2*z^3 + 2*x*z^4 - 2*z^5 + 2/5*x^4 - 9/20*x^3*y - 3*x^2*y^2 + 2*x*y^3 - x^3*z + x^2*y*z - 3*x*y^2*z + 7/4*x^2*z^2 + x*y*z^2 - 3*x*z^3 + y*z^3 - 2*z^4 + 2*x*y^2 - 2*y^3 + x*y*z - 2*y^2*z + y*z^2 - 2*z^3, 3*x^6 - 10157/6000*x^5*y + x^4*y^2 - 2*x^3*y^3 + 3*x^2*y^4 + x*y^5 - y^6 - 2*x^5*z - 3*x^4*y*z - 3*x^2*y^3*z - x*y^4*z + 2*y^5*z - 2*x^2*y^2*z^2 + 2*y^4*z^2 - x^3*z^3 - x^2*y*z^3 - 2*x*y^2*z^3 - 3*y^3*z^3 + 3*y^2*z^4 - 3*x*z^5 - 3*y*z^5 - 2*z^6 + 28/25*x^5 + 229/1200*x^4*y - 2*x^3*y^2 + x^2*y^3 + x*y^4 + 3*y^5 + x*y^3*z - 3*y^4*z + x^3*z^2 + x^2*y*z^2 - x*y^2*z^2 + y^3*z^2 + x^2*z^3 + x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 + 2*y*z^4 + 3*z^5 + 2/5*x^4 + 23/20*x^3*y + 3*x*y^3 + 2*y^4 - 2*x^3*z + 2*x^2*y*z - 2*x*y^2*z - 3*y^3*z - 39/4*x^2*z^2 - 3*x*z^3 - y*z^3 - z^4 + 2*x*y^2 + 3*y^3 + x*y*z - y*z^2, x^6 - 1247/6000*x^5*y - x^4*y^2 + 3*x^3*y^3 - 3*x^2*y^4 + 2*x*y^5 - y^6 + x^5*z + 2*x^4*y*z + x^3*y^2*z - 3*x^2*y^3*z + 2*x*y^4*z + y^5*z - 2*x^4*z^2 + 2*x^2*y^2*z^2 - x*y^3*z^2 - 3*y^4*z^2 - 3*x^3*z^3 - x^2*y*z^3 - x*y^2*z^3 - 2*y^3*z^3 - x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 - x*z^5 + y*z^5 - 2*z^6 + 47/100*x^5 - 731/1200*x^4*y + x^3*y^2 + 2*x*y^4 - 2*y^5 - 3*x^4*z - 3*x^3*y*z + 3*x^2*y^2*z - x*y^3*z + 2*y^4*z + 3*x^3*z^2 - 3*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 + 2*x^2*z^3 + 3*x*y*z^3 - 3*y^2*z^3 + x*z^4 + 2*y*z^4 - z^5 - 1/5*x^4 - 9/5*x^3*y + x^2*y^2 + 2*x*y^3 - y^4 - 3*x^3*z + 3*x^2*y*z - 2*x*y^2*z - y^3*z + 3/2*x^2*z^2 - 3*x*y*z^2 + 2*x*z^3 - y*z^3 - x*y^2 - 2*y^3 - 2*x*y*z + y^2*z - y*z^2 - 3*z^3]
B l'=Z Q2=X^3Y: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 146 s
    the triple (seed 1364338, random triple number 1 after the construction of the member): [3*x^6 - x^5*y + 3*x^2*y^4 - 2*x*y^5 - 3*y^6 - 373/250*x^5*z - 2*x^4*y*z + x^3*y^2*z + 2*x^2*y^3*z + x*y^4*z - y^5*z - 3*x^4*z^2 + 2*x^3*y*z^2 + 2*x^2*y^2*z^2 - 3*x*y^3*z^2 + x^3*z^3 - x*y^2*z^3 + 3*y^3*z^3 + 3*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 + y*z^5 + 3*z^6 - 149/1200*x^5 - 2*x^4*y + x^3*y^2 - x^2*y^3 - 3*x*y^4 + 3*y^5 + 2813/1200*x^4*z - 3*x^3*y*z - y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 - y^3*z^2 + 3*x^2*z^3 - 2*x*y*z^3 - y^2*z^3 + 3*x*z^4 + 2*y*z^4 - 2*z^5 - 4/5*x^4 - 4/3*x^3*y + 3*x^2*y^2 + x*y^3 - y^4 - 7/20*x^3*z + 3*x^2*y*z + x*y^2*z - 3*x*y*z^2 - 3*y^2*z^2 - 2*x*z^3 - 3*y*z^3 - 3*z^4 - x*y^2 + 3*y^3 - x*y*z - y^2*z + y*z^2 + 2*z^3, -x^6 + 3*x^5*y + x^4*y^2 - 2*x^3*y^3 - x^2*y^4 - 3*x*y^5 + 3*y^6 + 10319/3000*x^5*z + 2*x^4*y*z - 2*x^3*y^2*z + 3*x^2*y^3*z - x*y^4*z + y^5*z - 2*x^4*z^2 - x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + y^4*z^2 + 3*y^3*z^3 - 3*x^2*z^4 - x*y*z^4 + 3*y^2*z^4 - x*z^5 - 2*z^6 + 199/1200*x^5 + x^4*y - 3*x^3*y^2 + 2*x^2*y^3 - 2*y^5 + 1129/600*x^4*z + 3*x^3*y*z - x^2*y^2*z + x*y^3*z - 3*y^4*z - 2*x^3*z^2 + 2*x^2*y*z^2 + 3*x^2*z^3 + x*y*z^3 + 2*y^2*z^3 + x*z^4 - y*z^4 + z^5 + 2/5*x^4 + 20/3*x^3*y - 3*x^2*y^2 - x*y^3 + 9/20*x^3*z - 2*x^2*y*z + 2*x*y^2*z - y^3*z - 3*x^2*z^2 + 3*x*y*z^2 + 3*y^2*z^2 + x*z^3 - 3*y*z^3 - 2*z^4 - x*y^2 + 2*y^3 - 3*x*y*z + 2*y^2*z + 3*y*z^2 - z^3, -3*x^5*y + 3*x^4*y^2 - 2*x^3*y^3 + 2*x^2*y^4 - 3*x*y^5 - y^6 - 1771/750*x^5*z - 2*x^4*y*z - 3*x^3*y^2*z - 2*x^2*y^3*z - 2*x*y^4*z + 3*y^5*z + 3*x^2*y^2*z^2 + 3*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 + 2*x*y^2*z^3 - 3*y^3*z^3 - x^2*z^4 + 2*x*y*z^4 + 3*y^2*z^4 + 3*x*z^5 - y*z^5 - 583/400*x^5 - 3*x^4*y - x^3*y^2 - x^2*y^3 + 2*x*y^4 - 2*y^5 - 333/200*x^4*z + 2*x^3*y*z + 3*x^2*y^2*z - 2*x*y^3*z + 3*y^4*z - 2*x^3*z^2 - 3*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 + x^2*z^3 - 2*y^2*z^3 + 3*x*z^4 + 3*y*z^4 - z^5 - 4/5*x^4 - 2*x^3*y + x^2*y^2 + 2*y^4 - 7/5*x^3*z - 2*x^2*y*z - 3*y^3*z + 2*x^2*z^2 + x*y*z^2 + 2*y^2*z^2 + 3*x*z^3 + 3*y*z^3 + z^4 + 3*x*y^2 + y^3 + 2*x*y*z - 2*y*z^2 + 2*z^3]
B l'=Z Q2=X^2Z^2: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 33 (standard basis), m^N certificate (N, length) = (9, 33); 147 s
    the triple (seed 1364339, random triple number 1 after the construction of the member): [-x^6 - x^4*y^2 - 3*x^3*y^3 + 2*x^2*y^4 + 3*x*y^5 + 77/20*x^5*z - 3*x^2*y^3*z + x*y^4*z + 3*x^4*z^2 - 3*x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + 3*y^4*z^2 + 2*x^3*z^3 + 2*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 + y^2*z^4 + 3*y*z^5 + z^6 + 1489/600*x^5 - 2*x^4*y + 2*x^3*y^2 + 3*x^2*y^3 + 3*x*y^4 - 3*y^5 + 23/8*x^4*z - 2*x^3*y*z - x^2*y^2*z - 2*y^4*z - 2*x^3*z^2 - x^2*y*z^2 - x*y^2*z^2 + y^3*z^2 - x^2*z^3 - 3*x*y*z^3 + y^2*z^3 - 3*x*z^4 + 2*y*z^4 - z^5 - 2/5*x^4 + 2*x^3*y + x^2*y^2 - 3*x*y^3 - 3*y^4 + 1/5*x^3*z - 2*x*y^2*z - y^3*z - 10*x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 + x*z^3 - 2*z^4 - x*y^2 - 2*y^3 - 2*x*y*z + y^2*z + 3*y*z^2 + z^3, -3*x^6 + 3*x^4*y^2 + x^3*y^3 + 2*x^2*y^4 - 2*x*y^5 - 2*y^6 + 1573/1500*x^5*z + 3*x^4*y*z + 2*x^3*y^2*z - 2*x^2*y^3*z + 2*x*y^4*z + 2*x^4*z^2 + 3*x^3*y*z^2 + 2*x^2*y^2*z^2 - 3*x*y^3*z^2 - 3*y^4*z^2 + 3*x^3*z^3 - 3*x^2*y*z^3 + 3*y^3*z^3 - 3*x^2*z^4 + 3*x*y*z^4 - y^2*z^4 - 3*x*z^5 + y*z^5 - 18/25*x^5 + 3*x^4*y + 2*x^3*y^2 + 3*x^2*y^3 + 3*x*y^4 - 3*y^5 + 487/600*x^4*z + 2*x^3*y*z - 3*x^2*y^2*z + x*y^3*z + 2*y^4*z - 3*x^3*z^2 - x^2*y*z^2 + 3*y^3*z^2 + 2*x^2*z^3 + 3*x*y*z^3 + 2*y^2*z^3 - 2*y*z^4 + z^5 - 3/10*x^4 + 3*x^3*y - 3*x^2*y^2 + 3*x*y^3 - y^4 - 1/5*x^3*z + 3*x*y^2*z + 2*y^3*z + 3/4*x^2*z^2 + 3*x*y*z^2 - y^2*z^2 - 2*x*z^3 - z^4 + x*y^2 - 3*x*y*z - 2*y^2*z - 2*y*z^2, -x^5*y + 3*x^4*y^2 - x^3*y^3 - 2*x^2*y^4 - 2*x*y^5 + y^6 + 2861/3000*x^5*z - x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + 2*x*y^4*z - y^5*z - x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + 3*x*y^3*z^2 - y^4*z^2 + 2*x^3*z^3 - x*y^2*z^3 - 2*y^3*z^3 - 2*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 + 3*x*z^5 + 3*y*z^5 + z^6 + 127/100*x^5 + 3*x^4*y + x^3*y^2 + 2*x^2*y^3 - 2*y^5 - 46/75*x^4*z + 3*x^3*y*z - 2*x^2*y^2*z + 2*y^4*z - 2*x^3*z^2 + 2*x*y^2*z^2 - 3*y^3*z^2 + 3*y^2*z^3 - x*z^4 - z^5 - 1/10*x^4 - 3*x^3*y + 3*x^2*y^2 - 2*x*y^3 - y^4 - 1/10*x^3*z - x^2*y*z + 2*x*y^2*z + y^3*z - 7/4*x^2*z^2 + 2*x*y*z^2 + y^2*z^2 + 2*x*z^3 - 3*y*z^3 + z^4 - 3*x*y^2 + 2*y^3 + 3*x*y*z + y^2*z + y*z^2 + 2*z^3]
B l'=Z Q2=X^3Y+X^2Z^2: dim of the tail space L = 8; H [1, 3, 6, 4, 3, 2, 1]; graded data as prescribed: True; cubic base scheme Hilbert polynomial 4; complete intersection of local length 34 (standard basis), m^N certificate (N, length) = (9, 34); 152 s
    the triple (seed 1364340, random triple number 1 after the construction of the member): [-2*x^5*y + 3*x^4*y^2 - x^3*y^3 - x^2*y^4 - 2*x*y^5 + y^6 + 2207/400*x^5*z - x^3*y^2*z + x^2*y^3*z - x*y^4*z + 2*y^5*z - 3*x^4*z^2 + 2*x^3*y*z^2 + x*y^3*z^2 - y^4*z^2 - 2*x^3*z^3 - x*y^2*z^3 - 3*y^3*z^3 + 3*x*y*z^4 - 2*y^2*z^4 - 3*x*z^5 - 3*y*z^5 - 467/400*x^5 + 2*x^4*y + x^3*y^2 - 3*x^2*y^3 - 2*x*y^4 - 3*y^5 - 911/1200*x^4*z - x^3*y*z + 3*x*y^3*z + y^4*z - 3*x^3*z^2 + 2*x*y^2*z^2 + 2*y^3*z^2 + 2*x^2*z^3 + x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 - 3*y*z^4 + 2*z^5 + 2/5*x^4 - 4/3*x^3*y + 3*x^2*y^2 + x*y^3 - y^4 - 3/20*x^3*z - 2*x^2*y*z + 3*x*y^2*z - x^2*z^2 - 2*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 + 3*y*z^3 - 3*z^4 + x*y^2 - x*y*z - 3*y^2*z + y*z^2 - z^3, -3*x^6 - 2*x^5*y + 2*x^3*y^3 - 3*x*y^5 + 43/120*x^5*z + 3*x^4*y*z + 2*x^3*y^2*z + 3*x^2*y^3*z + x*y^4*z - 3*y^5*z + 2*x^4*z^2 - 3*x^3*y*z^2 + x*y^3*z^2 + y^4*z^2 + 3*x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 + y^3*z^3 - 2*x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - 2*y*z^5 - 229/600*x^5 + 2*x^4*y + x^3*y^2 + x^2*y^3 - 2*x*y^4 - 3*y^5 + 3343/1200*x^4*z + 3*x*y^3*z + y^4*z + 3*x^3*z^2 + 3*x^2*y*z^2 + 2*x^2*z^3 + 3*x*y*z^3 - 2*y^2*z^3 + 2*x*z^4 + 3*z^5 - 2/5*x^4 + x^3*y + x^2*y^2 + 3*x*y^3 + 2*y^4 + 3/20*x^3*z - 3*x^2*y*z - x*y^2*z + x^2*z^2 - 3*x*y*z^2 + y^2*z^2 + 3*x*z^3 - 3*y*z^3 - 2*z^4 + y^3 + x*y*z - y^2*z + y*z^2 + z^3, -x^6 - 3*x^5*y + x^4*y^2 + 3*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 + 373/100*x^5*z - 3*x^4*y*z - 3*x^3*y^2*z - 3*x^2*y^3*z + 3*x*y^4*z + 3*y^5*z + x^4*z^2 + x^2*y^2*z^2 + 3*x*y^3*z^2 + 3*x^3*z^3 - 3*x^2*y*z^3 - 3*y^3*z^3 - x^2*z^4 + x*y*z^4 + 2*y^2*z^4 - 3*x*z^5 - 3*y*z^5 + z^6 - 177/200*x^5 + 2*x^4*y - x^3*y^2 - x^2*y^3 - x*y^4 + 3*y^5 - 121/30*x^4*z - 2*x^3*y*z + 3*x*y^3*z - 2*y^4*z + x^3*z^2 + 3*x^2*y*z^2 - 2*y^3*z^2 - 2*x^2*z^3 + x*y*z^3 + 2*x*z^4 - y*z^4 - 2*z^5 + 4/5*x^4 - 3*x^3*y - 3*x^2*y^2 + 2*x*y^3 + 3*y^4 - 1/20*x^3*z + x^2*y*z + x*y^2*z + y^3*z + 2*x^2*z^2 - 3*y^2*z^2 + 3*y*z^3 - z^4 - 2*y^3 + 3*x*y*z - y*z^2 - 2*z^3]

5 cases (families) checked.
ALL CHECKS PASSED
