Generated 8/31/05 2-cocycle twisted invariants Z_2[t,t^(-1)]/( 5 element quandles [0 0 0 0 0] [ ] [1 1 1 1 1] [ ] [2 2 2 4 3] [ ] [3 3 4 3 2] [ ] [4 4 3 2 4] Knot, 1 [[11, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 2 [[5, 0], [1, (x[6] + x[1] + x[12] + x[2] + x[11]) t + (x[11] + x[2] + x[5]) t + x[2] + x[5] + x[1] + x[11]], [1, 2 (x[12] + x[2] + x[6] + x[1]) t + (x[1] + x[5] + x[6] + x[11]) t 2 + x[11] + x[1]], [1, (x[11] + x[1] + x[2] + x[6]) t + (x[2] + x[6] + x[12]) t + x[12] + x[2] + x[5]], 2 [1, x[12] t + (x[6] + x[5] + x[12] + x[11]) t + x[1] + x[12] + x[11]] 2 , [1, (x[6] + x[1] + x[12] + x[2] + x[11]) t + (x[1] + x[12]) t 2 + x[2] + x[1] + x[12] + x[5]], [1, x[11] t + (x[6] + x[5] + x[12] + x[11]) t + x[2] + x[12] + x[5] + x[11]]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 2 [[5, 0], [2, (x[6] + x[1] + x[12] + x[2]) t + (x[12] + x[2] + x[6]) t 2 + x[1] + x[12]], [2, (x[12] + x[11]) t + (x[1] + x[2] + x[5] + x[11] + x[12]) t + x[1] + x[2] + x[5] + x[11] 2 + x[12]], [2, (x[2] + x[6] + x[1] + x[11]) t + (x[1] + x[11] + x[5] + x[6]) t + x[2] + x[5] + x[11]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 2 [[5, 0], [2, x[12] t + (x[2] + x[6] + x[1]) t + x[1]], 2 [2, (x[12] + x[11]) t + x[1] + x[5] + x[2]], 2 [2, x[11] t + (x[2] + x[6] + x[1]) t + x[2] + x[5]]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[11, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[11, 0]] Knot, 25 2 [[5, 0], [2, (x[12] + x[11]) t + (x[2] + x[1] + x[5] + x[11] + x[12]) t + x[2] + x[1] + x[5] + x[11] + x[12]], [2, 2 (x[2] + x[6] + x[1] + x[12]) t + (x[6] + x[12] + x[2]) t + x[1] 2 + x[12]], [2, (x[2] + x[6] + x[1] + x[11]) t + (x[11] + x[1] + x[5] + x[6]) t + x[5] + x[2] + x[11]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[11, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 2 [[5, 0], [8, (x[2] + x[6] + x[1]) t + (x[1] + x[12]) t + x[12]], 2 [8, (x[2] + x[6] + x[1]) t + (x[2] + x[11] + x[5]) t + x[11]], [8, (x[2] + x[5] + x[12] + x[11] + x[1]) t + x[12] + x[11]]] Knot, 33 [[11, 0]] Knot, 34 [[11, 0]] Knot, 35 [[11, 0]] [0 0 1 1 1] [ ] [1 1 0 0 0] [ ] [2 2 2 4 3] [ ] [3 3 4 3 2] [ ] [4 4 3 2 4] Knot, 1 [[11, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 2 [[5, 0], [1, (x[11] + x[6] + x[4] + x[7] + x[3]) t + (x[3] + x[7] + x[10]) t + x[7] + x[10] + x[6] + x[3]], [1, 2 (x[3] + x[6] + x[7] + x[11]) t + (x[7] + x[11] + x[4]) t + x[4] + x[7] + x[10]], 2 [1, x[4] t + (x[11] + x[10] + x[4] + x[3]) t + x[6] + x[4] + x[3]], [ 2 1, (x[11] + x[6] + x[4] + x[7] + x[3]) t + (x[6] + x[4]) t + x[7] + x[6] + x[4] + x[10]], [1, 2 x[3] t + (x[11] + x[10] + x[4] + x[3]) t + x[7] + x[4] + x[10] + x[3] 2 ], [1, (x[4] + x[7] + x[11] + x[6]) t + (x[6] + x[10] + x[11] + x[3]) t + x[3] + x[6]]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 2 [[5, 0], [2, (x[11] + x[6] + x[4] + x[7]) t + (x[4] + x[7] + x[11]) t 2 + x[6] + x[4]], [2, (x[4] + x[3]) t + (x[6] + x[7] + x[10] + x[3] + x[4]) t + x[6] + x[7] + x[10] + x[3] 2 + x[4]], [2, (x[7] + x[11] + x[6] + x[3]) t + (x[6] + x[3] + x[10] + x[11]) t + x[7] + x[10] + x[3]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 2 [[5, 0], [2, x[4] t + (x[11] + x[6] + x[7]) t + x[6]], 2 [2, (x[4] + x[3]) t + x[6] + x[10] + x[7]], 2 [2, x[3] t + (x[11] + x[6] + x[7]) t + x[7] + x[10]]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[11, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[11, 0]] Knot, 25 2 [[5, 0], [2, (x[4] + x[3]) t + (x[7] + x[6] + x[10] + x[3] + x[4]) t + x[7] 2 + x[6] + x[10] + x[3] + x[4]], [2, (x[7] + x[11] + x[6] + x[4]) t + (x[11] + x[4] + x[7]) t + x[6] + x[4]], [2, 2 (x[7] + x[11] + x[6] + x[3]) t + (x[3] + x[6] + x[10] + x[11]) t + x[10] + x[7] + x[3]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[11, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 2 [[5, 0], [8, (x[11] + x[6] + x[7]) t + (x[6] + x[4]) t + x[4]], 2 [8, (x[11] + x[6] + x[7]) t + (x[7] + x[3] + x[10]) t + x[3]], [8, (x[7] + x[10] + x[4] + x[3] + x[6]) t + x[4] + x[3]]] Knot, 33 [[11, 0]] Knot, 34 [[11, 0]] Knot, 35 [[11, 0]] [0 0 0 0 0] [ ] [1 1 1 2 2] [ ] [2 2 2 1 1] [ ] [3 4 4 3 3] [ ] [4 3 3 4 4] Knot, 1 [[5, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 [[5, 0]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[5, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[5, 0]] Knot, 25 [[5, 0]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[5, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[5, 0]] Knot, 33 [[5, 0]] Knot, 34 [[5, 0]] Knot, 35 [[5, 0]] [0 0 0 0 0] [ ] [1 1 4 2 3] [ ] [2 3 2 4 1] [ ] [3 4 1 3 2] [ ] [4 2 3 1 4] Knot, 1 [[17, 0]] Knot, 2 [[5, 0], [12, (x[5] + x[1] + x[10] + x[9] + x[8]) t + x[8] + x[10] + x[9]]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0], [12, (x[5] + x[1] + x[10] + x[9] + x[8]) t + x[9] + x[8] + x[10]]] Knot, 10 [[5, 0], [12, (x[5] + x[1] + x[10] + x[9] + x[8]) t + x[9] + x[8] + x[10]]] Knot, 11 [[5, 0]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0]] Knot, 15 [[5, 0], [12, 2 (x[1] + x[5]) t + (x[1] + x[5]) t + x[10] + x[5] + x[1] + x[9] + x[8] ]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 2 [[5, 0], [12, (x[8] + x[9] + x[10]) t + x[1] + x[5]]] Knot, 19 [[17, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[17, 0]] Knot, 25 2 [[5, 0], [12, (x[8] + x[10] + x[9]) t + (x[5] + x[1] + x[8] + x[10] + x[9]) t + x[5] + x[1] + x[8] + x[10] + x[9]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0], [12, (x[8] + x[10] + x[5] + x[1] + x[9]) t + x[10] + x[8] + x[9]]] Knot, 28 [[5, 0]] Knot, 29 [[17, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 [[17, 0], [48, (x[8] + x[9] + x[10] + x[5] + x[1]) t + x[9] + x[10] + x[8]]] Knot, 33 [[17, 0]] Knot, 34 [[17, 0]] Knot, 35 [[17, 0]] [0 0 1 1 1] [ ] [1 1 0 0 0] [ ] [3 4 2 4 3] [ ] [4 2 4 3 2] [ ] [2 3 3 2 4] Knot, 1 [[11, 0]] Knot, 2 [[5, 0]] Knot, 3 [[5, 0]] Knot, 4 [[5, 0]] Knot, 5 2 [[5, 0], [1, (x[6] + x[8] + x[12] + x[2] + x[11]) t + (x[8] + x[12]) t 2 + x[2] + x[8] + x[12] + x[5]], [1, x[11] t + (x[6] + x[5] + x[12] + x[11]) t + x[12] + x[2] + x[5] + x[11]], [1, 2 (x[12] + x[2] + x[6] + x[8]) t + (x[8] + x[6] + x[5] + x[11]) t 2 + x[11] + x[8]], [1, (x[11] + x[8] + x[2] + x[6]) t + (x[2] + x[6] + x[12]) t + x[12] + x[2] + x[5]], 2 [1, x[12] t + (x[6] + x[5] + x[12] + x[11]) t + x[8] + x[11] + x[12]] 2 , [1, (x[6] + x[8] + x[12] + x[2] + x[11]) t + (x[11] + x[2] + x[5]) t + x[2] + x[5] + x[8] + x[11]]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 2 [[5, 0], [2, (x[6] + x[8] + x[12] + x[2]) t + (x[12] + x[2] + x[6]) t 2 + x[8] + x[12]], [2, (x[11] + x[12]) t + (x[8] + x[2] + x[5] + x[11] + x[12]) t + x[8] + x[2] + x[5] + x[11] 2 + x[12]], [2, (x[2] + x[6] + x[8] + x[11]) t + (x[8] + x[11] + x[6] + x[5]) t + x[2] + x[5] + x[11]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 2 [[5, 0], [2, x[11] t + (x[6] + x[8] + x[2]) t + x[2] + x[5]], 2 [2, x[12] t + (x[6] + x[8] + x[2]) t + x[8]], 2 [2, (x[11] + x[12]) t + x[8] + x[5] + x[2]]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[11, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0]] Knot, 23 [[5, 0]] Knot, 24 [[11, 0]] Knot, 25 2 [[5, 0], [2, (x[2] + x[6] + x[8] + x[12]) t + (x[6] + x[12] + x[2]) t 2 + x[8] + x[12]], [2, (x[2] + x[6] + x[8] + x[11]) t + (x[11] + x[8] + x[6] + x[5]) t + x[5] + x[2] + x[11]], [2, 2 (x[11] + x[12]) t + (x[2] + x[8] + x[5] + x[12] + x[11]) t + x[2] + x[8] + x[5] + x[12] + x[11]]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[11, 0]] Knot, 30 [[5, 0]] Knot, 31 [[5, 0]] Knot, 32 2 [[5, 0], [8, (x[6] + x[8] + x[2]) t + (x[2] + x[11] + x[5]) t + x[11]], [8, (x[2] + x[5] + x[12] + x[11] + x[8]) t + x[11] + x[12]], 2 [8, (x[6] + x[8] + x[2]) t + (x[8] + x[12]) t + x[12]]] Knot, 33 [[11, 0]] Knot, 34 [[11, 0]] Knot, 35 [[11, 0]] [0 3 4 2 1] [ ] [2 1 3 4 0] [ ] [1 4 2 0 3] [ ] [4 0 1 3 2] [ ] [3 2 0 1 4] Knot, 1 [[5, 0]] Knot, 2 2 [[5, 0], [4, (x[6] + x[8] + x[9]) t + (x[8] + x[12] + x[9] + x[3] + x[4] + x[10] + x[1]) t + x[1] + x[3] 2 + x[4]], [4, (x[6] + x[8] + x[9]) t + (x[6] + x[12] + x[9] + x[3] + x[4] + x[2]) t + x[4] + x[2] + x[3]], 2 [4, (x[8] + x[5] + x[6] + x[7] + x[9] + x[12] + x[10]) t + (x[8] + x[12] + x[7] + x[3] + x[1] + x[2]) t + x[1] + x[3] + x[2]], [4, (x[4] + x[2] + x[9] + x[7] + x[1] + x[3] + x[11] + x[5]) t + x[1] + x[4] + x[2] + x[3]], [4, 2 (x[8] + x[5] + x[6] + x[7] + x[9] + x[12] + x[10]) t + (x[5] + x[6] + x[9] + x[11] + x[12] + x[10] + x[2] + x[1] + x[4]) t + x[1] + x[2] + x[4]]] Knot, 3 [[25, 0]] Knot, 4 [[5, 0]] Knot, 5 [[5, 0]] Knot, 6 [[5, 0]] Knot, 7 [[5, 0]] Knot, 8 [[5, 0]] Knot, 9 [[5, 0]] Knot, 10 [[5, 0]] Knot, 11 2 [[5, 0], [1, (x[4] + x[8] + x[6] + x[1] + x[9] + x[2]) t + (x[3] + x[7] + x[10] + x[5] + x[8] + x[4] + x[2]) t + x[6] + x[10] + x[11] + x[3] + x[4] + x[12] + x[5] + x[9] + x[2]], [1, ( x[3] + x[10] + x[5] + x[7] + x[4] + x[2] + x[6] + x[8] + x[9] + x[12]) 2 t + (x[10] + x[11] + x[8] + x[2] + x[1] + x[12] + x[5] + x[4]) t + x[1] + x[4] + x[6] + x[2] + x[9] + x[12]], [1, 2 (x[1] + x[2] + x[4]) t + (x[3] + x[6] + x[8] + x[11] + x[12] + x[10] + x[1] + x[4] + x[2]) t + x[6] + x[12] + x[5] + x[2] + x[3] + x[10] + x[11] + x[4] + x[9] + x[1]], [1, ( x[3] + x[10] + x[5] + x[7] + x[4] + x[2] + x[6] + x[8] + x[9] + x[12]) 2 t + (x[6] + x[3] + x[2] + x[1] + x[7] + x[9] + x[12]) t + x[1] + x[2] + x[6] + x[3] + x[12] + x[9]], [1, (x[3] + x[12] + x[8] + x[7] + x[5] 2 + x[9] + x[1] + x[6] + x[10] + x[4] + x[2]) t + (x[8] + x[12] + x[7] + x[3] + x[1] + x[2]) t + x[9] + x[1] + x[5] + x[2] + x[3] + x[11] + x[7]], [1, 2 (x[4] + x[8] + x[6] + x[1] + x[9] + x[2]) t + (x[5] + x[3] + x[6] + x[4] + x[7] + x[1]) t + x[3] + x[6] + x[9] + x[1] + x[10] + x[12] + x[5] + x[4] + x[11]], [1, 2 (x[3] + x[4] + x[1]) t + (x[1] + x[4] + x[3] + x[6] + x[8] + x[5] + x[7] + x[11] + x[2]) t + x[9] + x[4] + x[2] + x[8] + x[1] + x[3] + x[10] + x[12]], [1, ( x[1] + x[10] + x[9] + x[7] + x[5] + x[3] + x[6] + x[8] + x[12] + x[4]) 2 t + (x[6] + x[3] + x[2] + x[1] + x[7] + x[9] + x[12]) t + x[10] + x[2] + x[3] + x[8] + x[1] + x[12] + x[9]], [1, 2 (x[4] + x[2] + x[6] + x[8] + x[3] + x[9]) t + (x[1] + x[6] + x[10] + x[12] + x[3] + x[4]) t + x[6] + x[3] + x[4] + x[1] + x[12] + x[9]], [1, 2 (x[6] + x[1] + x[2] + x[3] + x[4] + x[8] + x[9]) t + (x[8] + x[9] + x[12] + x[10] + x[1] + x[3] + x[4]) t + x[4] + x[7] + x[1] + x[3] + x[5] + x[11] + x[9]], [1, (x[3] + x[12] + x[8] + x[7] 2 + x[5] + x[9] + x[1] + x[6] + x[10] + x[4] + x[2]) t + (x[4] + x[6] + x[9] + x[12] + x[5] + x[10] + x[11] + x[1] + x[2]) t + x[5] + x[2] + x[11] + x[1] + x[4] + x[9] + x[7]], [1, 2 (x[4] + x[8] + x[6] + x[9] + x[1] + x[3]) t + (x[8] + x[4] + x[2] + x[3] + x[12]) t + x[8] + x[2] + x[12] + x[3] 2 + x[4] + x[9] + x[10]], [1, (x[2] + x[1] + x[3]) t + (x[3] + x[6] + x[8] + x[11] + x[12] + x[10] + x[1] + x[4] + x[2]) t + x[1] + x[4] + x[8] + x[2] + x[3] + x[7] + x[12]], [1, 2 (x[1] + x[6] + x[8] + x[9] + x[2] + x[3]) t + (x[5] + x[3] + x[6] + x[4] + x[7] + x[1]) t + x[4] + x[8] + x[12] + x[1] + x[3] + x[7]], [1, 2 (x[1] + x[6] + x[8] + x[9] + x[2] + x[3]) t + (x[3] + x[7] + x[10] + x[5] + x[8] + x[4] + x[2]) t + x[2] + x[8] + x[7] + x[3] + x[4] + x[12]], [1, ( x[2] + x[3] + x[6] + x[8] + x[9] + x[12] + x[1] + x[7] + x[10] + x[5]) 2 t + (x[4] + x[7] + x[11] + x[8] + x[1] + x[2]) t + x[4] + x[1] + x[2] + x[7] + x[8] + x[12]], [1, ( x[6] + x[7] + x[10] + x[2] + x[8] + x[9] + x[12] + x[5] + x[1] + x[4]) 2 t + (x[2] + x[6] + x[5] + x[3] + x[9] + x[1] + x[10]) t + x[6] + x[10] + x[3] + x[11] + x[12] + x[9] + x[2] + x[5] + x[1]], [1, 2 (x[4] + x[3] + x[2]) t + (x[1] + x[4] + x[3] + x[6] + x[8] + x[5] + x[7] + x[11] + x[2]) t + x[1] + x[3] + x[6] + x[4] + x[2] + x[9] + x[12]], [1, 2 (x[6] + x[1] + x[2] + x[3] + x[4] + x[8] + x[9]) t + (x[9] + x[2] + x[6] + x[12] + x[3] + x[4]) t + x[9] + x[11] + x[4] + x[2] + x[7] + x[3] + x[5]], [1, ( x[1] + x[10] + x[9] + x[7] + x[5] + x[3] + x[6] + x[8] + x[12] + x[4]) 2 t + (x[10] + x[11] + x[8] + x[2] + x[1] + x[12] + x[5] + x[4]) t + x[9] + x[1] + x[2] + x[12] + x[4] + x[10] + x[8]]] Knot, 12 [[5, 0]] Knot, 13 [[5, 0]] Knot, 14 [[5, 0]] Knot, 15 [[5, 0]] Knot, 16 [[5, 0]] Knot, 17 [[5, 0]] Knot, 18 [[5, 0]] Knot, 19 [[5, 0]] Knot, 20 [[5, 0]] Knot, 21 [[5, 0]] Knot, 22 [[5, 0], [1, 2 (x[8] + x[6] + x[7] + x[12] + x[5] + x[10] + x[9] + x[3] + x[2]) t + (x[1] + x[7] + x[9] + x[11] + x[4] + x[2] + x[6]) t + x[5] + x[6] + x[8] + x[11] + x[4] + x[1] + x[2]], [1, 2 (x[5] + x[6] + x[7] + x[9] + x[12] + x[10] + x[3] + x[8]) t + (x[4] + x[8] + x[7] + x[1] + x[2] + x[11]) t + x[4] + x[2] + x[12] + x[6] + x[7] + x[1] + x[10]], [1, 2 (x[6] + x[8] + x[2] + x[9] + x[1]) t + (x[3] + x[4] + x[1] + x[10] + x[12] + x[8] + x[9]) t + x[3] + x[4] 2 + x[1] + x[6] + x[10] + x[8]], [1, (x[6] + x[8] + x[9] + x[1]) t + (x[3] + x[4] + x[2] + x[8] + x[12]) t + x[12] + x[11] + x[4] + x[3] + x[5] + x[2] + x[6] + x[7]], [1, 2 (x[10] + x[9] + x[7] + x[8] + x[6] + x[12] + x[5] + x[4] + x[1]) t + (x[2] + x[5] + x[3] + x[10] + x[1] + x[8]) t + x[7] + x[8] + x[9] + x[3] + x[6] + x[1] + x[2]], [1, 2 (x[6] + x[8] + x[9] + x[12] + x[7] + x[10] + x[5] + x[3] + x[4]) t + (x[10] + x[6] + x[11] + x[5] + x[9] + x[12] + x[4] + x[1] + x[2]) t + x[9] + x[7] + x[1] + x[5] + x[4] + x[10] + x[6] + x[8] + x[2] 2 + x[11]], [1, (x[6] + x[8] + x[2] + x[9] + x[1]) t + (x[2] + x[3] + x[9] + x[4] + x[6] + x[12]) t + x[4] + x[2] + x[10] 2 + x[8] + x[3] + x[6]], [1, x[4] t + (x[4] + x[2] + x[3] + x[6] + x[8] + x[12] + x[1] + x[11] + x[10]) t + x[3] + x[4] + x[5] + x[8] + x[9] + x[11] + x[12] + x[1] + x[2]], [ 2 1, (x[6] + x[8] + x[9] + x[1] + x[4]) t + (x[2] + x[4] + x[6] + x[5] + x[3] + x[10] + x[9] + x[7]) t + x[6] + x[4] + x[2] + x[8] + x[3] + x[7] + x[9]], [1, 2 (x[6] + x[9] + x[8] + x[2]) t + (x[6] + x[12] + x[1] + x[10] + x[3] + x[4]) t + x[12] + x[8] + x[5] 2 + x[1] + x[11] + x[4] + x[7] + x[10] + x[3]], [1, x[1] t + (x[2] + x[3] + x[6] + x[8] + x[7] + x[1] + x[4] + x[11] + x[5]) t + x[3] + x[4] + x[5] + x[6] + x[7] + x[11] + x[12] + x[1] + x[2]], [ 2 1, (x[10] + x[9] + x[7] + x[5] + x[4] + x[6] + x[8] + x[12] + x[2]) t + (x[2] + x[5] + x[3] + x[10] + x[1] + x[8]) t + x[1] + x[2] + x[3] + x[10] + x[9] + x[7]], [1, 2 (x[6] + x[7] + x[10] + x[4] + x[12] + x[8] + x[5] + x[9]) t + (x[1] + x[2] + x[6] + x[5] + x[9] + x[10] + x[3]) t + x[11] + x[1] + x[12] + x[8] + x[2] + x[9] + x[3] + x[5]], [1, 2 (x[6] + x[8] + x[9] + x[12] + x[7] + x[10] + x[5] + x[3] + x[4]) t + (x[8] + x[2] + x[3] + x[12] + x[7] + x[1]) t + x[9] + x[6] + x[5] + x[2] + x[8] + x[3] + x[11] + x[7] + x[10] + x[1]], [1, 2 (x[10] + x[5] + x[7] + x[3] + x[6] + x[8] + x[12] + x[9] + x[1]) t + (x[1] + x[7] + x[9] + x[11] + x[4] + x[2] + x[6]) t + x[2] + x[1] 2 + x[4] + x[10] + x[11] + x[5]], [1, x[3] t + (x[4] + x[2] + x[3] + x[6] + x[8] + x[12] + x[1] + x[11] + x[10]) t + x[12] + x[2] + x[3] + x[6] + x[10] + x[7] + x[1] + x[4]], [1, 2 (x[8] + x[6] + x[9] + x[2] + x[3]) t + (x[1] + x[3] + x[8] + x[9] + x[7] + x[4] + x[5]) t + x[8] + x[1] + x[3] + x[6] + x[4] + x[5] + x[11]], [1, 2 (x[6] + x[8] + x[9] + x[2] + x[4]) t + (x[1] + x[3] + x[8] + x[9] + x[7] + x[4] + x[5]) t + x[1] + x[3] + x[4] + x[9] + x[10] + x[7]], [1, 2 (x[6] + x[8] + x[9] + x[1] + x[3]) t + (x[2] + x[4] + x[6] + x[5] + x[3] + x[10] + x[9] + x[7]) t + x[3] 2 + x[4] + x[10] + x[11] + x[2] + x[5]], [1, x[2] t + (x[2] + x[3] + x[6] + x[8] + x[7] + x[1] + x[4] + x[11] + x[5]) t + x[3] + x[4] + x[5] + x[7] + x[8] + x[10] + x[11] + x[12] + x[2] + x[1]]] Knot, 23 2 [[5, 0], [4, (x[6] + x[8] + x[9] + x[12] + x[5] + x[7] + x[10]) t + (x[8] + x[2] + x[3] + x[12] + x[7] + x[1]) t + x[1] + x[2] + x[3]], 2 [4, (x[9] + x[8] + x[6]) t + (x[3] + x[4] + x[1] + x[10] + x[12] + x[8] + x[9]) t + x[3] + x[4] 2 + x[1]], [4, (x[9] + x[8] + x[6]) t + (x[2] + x[3] + x[9] + x[4] + x[6] + x[12]) t + x[2] + x[3] + x[4]], 2 [4, (x[6] + x[8] + x[9] + x[12] + x[5] + x[7] + x[10]) t + (x[10] + x[6] + x[11] + x[5] + x[9] + x[12] + x[4] + x[1] + x[2]) t + x[2] + x[4] + x[1]], [4, (x[7] + x[1] + x[2] + x[3] + x[9] + x[4] + x[5] + x[11]) t + x[1] + x[4] + x[2] + x[3]]] Knot, 24 [[5, 0]] Knot, 25 [[5, 0]] Knot, 26 [[5, 0]] Knot, 27 [[5, 0]] Knot, 28 [[5, 0]] Knot, 29 [[5, 0]] Knot, 30 2 [[5, 0], [2, (x[8] + x[12] + x[5] + x[6] + x[10] + x[9] + x[7]) t + (x[4] + x[8] + x[12] + x[5] + x[11] + x[9]) t + x[4]], [2, 2 (x[8] + x[12] + x[5] + x[6] + x[10] + x[9] + x[7]) t + (x[3] + x[6] + x[7] + x[12] + x[10]) t + x[3]], [2, %1 + (x[6] + x[8] + x[9] + x[1] + x[4] + x[7]) t + x[1] + x[4]], [ 2 2, (x[6] + x[8] + x[9]) t + (x[11] + x[5] + x[1] + x[6] + x[7] + x[12]) t + x[1]], [2, %1 + (x[7] + x[4] + x[2] + x[9] + x[10]) t + x[4] + x[2]], [2, 2 (x[6] + x[8] + x[9]) t + (x[10] + x[7] + x[2] + x[11] + x[12] + x[8] + x[5]) t + x[2]], [2, %1 + (x[6] + x[8] + x[11] + x[2] + x[3] + x[5]) t + x[2] + x[3]], [2, %1 + (x[5] + x[3] + x[1] + x[11] + x[10]) t + x[1] + x[3]], [2, (x[6] + x[8] + x[9] + x[7] + x[3] + x[4] + x[5] + x[10] + x[11]) t + x[3] + x[4]], [2, (x[10] + x[2] + x[1] + x[8] + x[6]) t + x[1] + x[2]]] 2 %1 := (x[12] + x[7] + x[5] + x[10]) t Knot, 31 [[5, 0]] Knot, 32 [[25, 0]] Knot, 33 [[5, 0]] Knot, 34 [[5, 0]] Knot, 35 2 [[5, 0], [2, (x[8] + x[9] + x[6]) t + (x[8] + x[5] + x[11] + x[7] + x[12] + x[10] + x[2]) t + x[2]], [2, %1 + (x[1] + x[4] + x[6] + x[7] + x[8] + x[9]) t + x[1] + x[4]], [ 2 2, (x[6] + x[8] + x[12] + x[9] + x[5] + x[7] + x[10]) t + (x[12] + x[8] + x[11] + x[9] + x[5] + x[4]) t + x[4]], [2, %1 + (x[2] + x[3] + x[5] + x[6] + x[8] + x[11]) t + x[2] + x[3]], 2 [2, (x[8] + x[9] + x[6]) t + (x[6] + x[7] + x[11] + x[12] + x[5] + x[1]) t + x[1]], [2, %1 + (x[9] + x[10] + x[7] + x[2] + x[4]) t + x[4] + x[2]], [2, %1 + (x[10] + x[11] + x[5] + x[1] + x[3]) t + x[1] + x[3]], [2, (x[1] + x[2] + x[6] + x[8] + x[10]) t + x[1] + x[2]], [2, 2 (x[6] + x[8] + x[12] + x[9] + x[5] + x[7] + x[10]) t + (x[12] + x[6] + x[10] + x[7] + x[3]) t + x[3]], [2, (x[3] + x[4] + x[5] + x[6] + x[7] + x[8] + x[9] + x[10] + x[11]) t + x[3] + x[4]]] 2 %1 := (x[7] + x[10] + x[12] + x[5]) t