N=4: generators X_(x,y): 4; antisymmetric & span so_N(C) (dim 6) with Cartan: True
N=4 m=2: unknowns=4 eqs=8 nullity=1 (exact: rank(M^TM) mod p = 3) Catalan=1 Banica in kernel=True rank(Banica)=1 | equal: True  [0.0s]
N=4 m=4: unknowns=28 eqs=96 nullity=2 (exact: rank(M^TM) mod p = 26) Catalan=2 Banica in kernel=True rank(Banica)=2 | equal: True  [0.0s]
N=4 m=6: unknowns=232 eqs=1080 nullity=5 (exact: rank(M^TM) mod p = 227) Catalan=5 Banica in kernel=True rank(Banica)=5 | equal: True  [0.0s]
N=5: generators X_(x,y): 8; antisymmetric & span so_N(C) (dim 10) with Cartan: True
N=5 m=2: unknowns=5 eqs=16 nullity=1 (exact: rank(M^TM) mod p = 4) Catalan=1 Banica in kernel=True rank(Banica)=1 | equal: True  [0.0s]
N=5 m=3: unknowns=13 eqs=72 nullity=0 (exact: rank(M^TM) mod p = 13) Catalan=0 Banica in kernel=True rank(Banica)=0 | equal: True  [0.0s]
N=5 m=4: unknowns=53 eqs=304 nullity=2 (exact: rank(M^TM) mod p = 51) Catalan=2 Banica in kernel=True rank(Banica)=2 | equal: True  [0.0s]
N=5 m=5: unknowns=181 eqs=1300 nullity=0 (exact: rank(M^TM) mod p = 181) Catalan=0 Banica in kernel=True rank(Banica)=0 | equal: True  [0.0s]
N=5 m=6: unknowns=713 eqs=5544 nullity=5 (exact: rank(M^TM) mod p = 708) Catalan=5 Banica in kernel=True rank(Banica)=5 | equal: True  [0.5s]
N=6: generators X_(x,y): 13; antisymmetric & span so_N(C) (dim 15) with Cartan: True
N=6 m=2: unknowns=8 eqs=44 nullity=1 (exact: rank(M^TM) mod p = 7) Catalan=1 Banica in kernel=True rank(Banica)=1 | equal: True  [0.0s]
N=6 m=3: unknowns=32 eqs=248 nullity=0 (exact: rank(M^TM) mod p = 32) Catalan=0 Banica in kernel=True rank(Banica)=0 | equal: True  [0.0s]
N=6 m=4: unknowns=140 eqs=1232 nullity=2 (exact: rank(M^TM) mod p = 138) Catalan=2 Banica in kernel=True rank(Banica)=2 | equal: True  [0.0s]
N=6 m=5: unknowns=632 eqs=6472 nullity=0 (exact: rank(M^TM) mod p = 632) Catalan=0 Banica in kernel=True rank(Banica)=0 | equal: True  [0.2s]
N=6 m=6: unknowns=2936 eqs=33160 nullity=5 (exact: rank(M^TM) mod p = 2931) Catalan=5 Banica in kernel=True rank(Banica)=5 | equal: True  [26.5s]
