================================================================================
permrack4_1230 (all ranks exact over Q)
 Im f = A (x) B (x) A :
  weight D=1: dim C_n (n=0..D) = [8, 4], ranks = [4, 4]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=2: dim C_n (n=0..D) = [20, 32, 14], ranks = [2, 18, 14]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=3: dim C_n (n=0..D) = [18, 80, 112, 47], ranks = [1, 17, 63, 47]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): {2: 2}
  weight D=4: dim C_n (n=0..D) = [14, 72, 280, 376, 152], ranks = [1, 13, 59, 221, 152]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): {3: 3}
 quadratic quotient B/<omega> :
  weight D=1: dims = [8, 4], homology: ACYCLIC
  weight D=2: dims = [20, 32, 14], homology: ACYCLIC
  weight D=3: dims = [18, 80, 112, 49], homology: {2: 2, 3: 2}
 time 7s
================================================================================
permrack3_120 (all ranks exact over Q)
 Im f = A (x) B (x) A :
  weight D=1: dim C_n (n=0..D) = [6, 3], ranks = [3, 3]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=2: dim C_n (n=0..D) = [13, 18, 7], ranks = [2, 11, 7]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=3: dim C_n (n=0..D) = [14, 39, 42, 16], ranks = [1, 13, 26, 16]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=4: dim C_n (n=0..D) = [12, 42, 91, 96, 33], ranks = [1, 11, 31, 60, 33]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): {3: 3}
 quadratic quotient B/<omega> :
  weight D=1: dims = [6, 3], homology: ACYCLIC
  weight D=2: dims = [13, 18, 7], homology: ACYCLIC
  weight D=3: dims = [14, 39, 42, 16], homology: ACYCLIC
  weight D=4: dims = [12, 42, 91, 96, 36], homology: {3: 3, 4: 3}
 time 0s
================================================================================
dihedral quandle R3 (all ranks exact over Q)
 Im f = A (x) B (x) A :
  weight D=1: dim C_n (n=0..D) = [6, 3], ranks = [3, 3]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=2: dim C_n (n=0..D) = [19, 18, 4], ranks = [5, 14, 4]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=3: dim C_n (n=0..D) = [42, 57, 24, 3], ranks = [6, 36, 21, 3]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=4: dim C_n (n=0..D) = [73, 126, 76, 18, 1], ranks = [6, 67, 59, 17, 1]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=5: dim C_n (n=0..D) = [108, 219, 168, 57, 6, 0], ranks = [6, 102, 117, 51, 6, 0]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): ACYCLIC
  weight D=6: dim C_n (n=0..D) = [144, 324, 292, 126, 19, 0, 0], ranks = [6, 138, 186, 106, 19, 0, 0]
     homology of Im f (augmented; index -1 = coker of A(x)A->A): {3: 1}
 time 8s
