Cohomology of group number 823 of order 128

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

General information on the group

  • The group has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 1.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 4.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 1.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    t6  −  2·t5  +  2·t4  −  t  +  1
    (t  −  1)4 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-4,-4,-4,-4. They were obtained using the filter regular HSOP of the Benson test.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring generators

The cohomology ring has 20 minimal generators of maximal degree 9:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. b_1_2, an element of degree 1
  4. b_2_3, an element of degree 2
  5. b_2_4, an element of degree 2
  6. a_3_6, a nilpotent element of degree 3
  7. a_4_6, a nilpotent element of degree 4
  8. a_4_7, a nilpotent element of degree 4
  9. b_4_10, an element of degree 4
  10. a_5_13, a nilpotent element of degree 5
  11. b_5_14, an element of degree 5
  12. b_5_15, an element of degree 5
  13. b_5_16, an element of degree 5
  14. a_7_20, a nilpotent element of degree 7
  15. a_7_15, a nilpotent element of degree 7
  16. a_8_21, a nilpotent element of degree 8
  17. a_8_22, a nilpotent element of degree 8
  18. b_8_43, an element of degree 8
  19. c_8_44, a Duflot regular element of degree 8
  20. a_9_25, a nilpotent element of degree 9

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring relations

There are 144 minimal relations of maximal degree 18:

  1. a_1_12 + a_1_0·a_1_1 + a_1_02
  2. a_1_1·b_1_2
  3. a_1_0·b_1_2 + a_1_12
  4. b_2_4·a_1_0 + b_2_3·a_1_1
  5. a_1_1·a_3_6 + b_2_3·a_1_0·a_1_1
  6. a_1_0·a_3_6
  7. b_2_3·b_2_4·a_1_1 + b_2_32·a_1_1
  8. a_4_6·b_1_2 + b_2_3·a_3_6 + b_2_32·a_1_0
  9. a_4_6·a_1_1
  10. a_4_6·a_1_0
  11. a_4_7·b_1_2 + b_2_4·a_3_6 + b_2_3·a_3_6 + b_2_32·a_1_1 + b_2_32·a_1_0
  12. a_4_7·a_1_1
  13. a_4_7·a_1_0
  14. b_4_10·a_1_1 + b_2_42·a_1_1
  15. b_4_10·a_1_0 + b_2_32·a_1_0
  16. a_3_62
  17. a_1_1·a_5_13
  18. a_1_0·a_5_13
  19. b_1_2·b_5_14 + b_2_42·b_1_22 + b_2_3·b_4_10 + b_2_3·b_2_4·b_1_22 + b_2_3·b_2_42
       + b_2_32·b_2_4 + b_2_33 + b_1_2·a_5_13 + a_1_1·b_5_14 + a_1_0·b_5_14 + b_2_4·b_1_2·a_3_6
       + b_2_3·b_1_2·a_3_6 + b_2_3·a_4_7 + b_2_3·a_4_6
  20. a_1_1·b_5_15
  21. b_1_2·b_5_14 + b_2_42·b_1_22 + b_2_3·b_4_10 + b_2_3·b_2_4·b_1_22 + b_2_3·b_2_42
       + b_2_32·b_2_4 + b_2_33 + b_1_2·a_5_13 + a_1_0·b_5_15 + b_2_4·b_1_2·a_3_6
       + b_2_3·b_1_2·a_3_6 + b_2_3·a_4_7 + b_2_3·a_4_6
  22. b_1_2·b_5_16 + b_2_4·b_4_10 + b_2_43 + b_2_3·b_2_42 + b_2_32·b_2_4 + b_2_4·a_4_7
       + b_2_4·a_4_6
  23. b_1_2·b_5_14 + b_2_42·b_1_22 + b_2_3·b_4_10 + b_2_3·b_2_4·b_1_22 + b_2_3·b_2_42
       + b_2_32·b_2_4 + b_2_33 + b_1_2·a_5_13 + a_1_1·b_5_16 + b_2_4·b_1_2·a_3_6 + b_2_4·a_4_6
       + b_2_3·b_1_2·a_3_6
  24. a_1_1·b_5_14 + a_1_0·b_5_16
  25. a_4_6·a_3_6
  26. a_4_7·a_3_6
  27. b_1_22·a_5_13 + b_4_10·a_3_6 + b_2_42·a_3_6 + b_2_3·b_2_4·a_3_6 + b_2_32·a_3_6
  28. b_2_4·b_5_14 + b_2_43·b_1_2 + b_2_3·b_5_16 + b_2_3·b_2_42·b_1_2 + b_2_4·a_5_13
       + b_2_42·a_3_6 + b_2_3·b_2_4·a_3_6 + b_2_33·a_1_1
  29. a_4_62
  30. a_4_6·a_4_7
  31. a_4_72
  32. a_4_6·b_4_10 + b_2_42·a_4_6 + b_2_3·b_1_2·a_5_13 + b_2_3·b_2_4·a_4_6 + b_2_32·a_4_6
  33. a_3_6·a_5_13
  34. a_4_7·b_4_10 + a_4_6·b_4_10 + b_2_4·b_1_2·a_5_13 + b_2_42·a_4_7 + b_2_42·a_4_6
       + b_2_3·b_2_4·a_4_7 + b_2_3·b_2_4·a_4_6 + b_2_32·a_4_7 + b_2_32·a_4_6
  35. a_3_6·b_5_14 + a_4_6·b_4_10 + b_2_42·b_1_2·a_3_6 + b_2_42·a_4_6
       + b_2_3·b_2_4·b_1_2·a_3_6 + b_2_32·a_4_7
  36. b_1_23·b_5_15 + b_4_10·b_1_24 + b_4_102 + b_2_4·b_4_10·b_1_22 + b_2_43·b_1_22
       + b_2_44 + b_2_3·b_2_4·b_1_24 + b_2_32·b_1_24 + b_2_32·b_2_42 + b_2_34
       + b_4_10·b_1_2·a_3_6 + b_2_4·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_2·a_3_6
       + b_2_32·b_1_2·a_3_6
  37. a_3_6·b_5_16 + a_4_7·b_4_10 + a_4_6·b_4_10 + b_2_42·a_4_7 + b_2_42·a_4_6
       + b_2_3·a_1_0·b_5_15 + b_2_3·b_2_4·a_4_7
  38. a_3_6·b_5_15 + b_1_2·a_7_20 + b_4_10·b_1_2·a_3_6 + a_4_6·b_4_10 + b_2_4·b_1_23·a_3_6
       + b_2_42·a_4_6 + b_2_3·b_1_23·a_3_6 + b_2_3·a_1_0·b_5_15 + b_2_3·b_2_4·b_1_2·a_3_6
       + b_2_3·b_2_4·a_4_6 + b_2_32·a_4_6
  39. a_1_1·a_7_20
  40. a_1_0·a_7_20
  41. b_1_2·a_7_15 + b_4_10·b_1_2·a_3_6 + a_4_7·b_4_10 + a_4_6·b_4_10 + b_2_4·b_1_23·a_3_6
       + b_2_42·b_1_2·a_3_6 + b_2_42·a_4_7 + b_2_42·a_4_6 + b_2_3·a_1_0·b_5_15
       + b_2_32·b_1_2·a_3_6
  42. a_1_1·a_7_15
  43. a_1_0·a_7_15
  44. a_4_6·a_5_13
  45. a_4_7·a_5_13
  46. a_4_6·b_5_14 + b_2_3·b_2_42·a_3_6 + b_2_32·a_5_13 + b_2_32·b_2_4·a_3_6
       + b_2_34·a_1_1
  47. a_4_7·b_5_14 + b_2_43·a_3_6 + b_2_3·b_2_4·a_5_13 + b_2_32·a_5_13 + b_2_32·b_2_4·a_3_6
  48. a_4_6·b_5_16 + b_2_3·b_2_4·a_5_13 + b_2_34·a_1_1
  49. b_4_10·b_5_14 + b_2_42·b_4_10·b_1_2 + b_2_3·b_1_22·b_5_15 + b_2_3·b_4_10·b_1_23
       + b_2_3·b_2_4·b_5_16 + b_2_3·b_2_43·b_1_2 + b_2_32·b_5_16 + b_2_32·b_5_14
       + b_2_32·b_2_4·b_1_23 + b_2_32·b_2_42·b_1_2 + b_2_33·b_1_23
       + b_2_33·b_2_4·b_1_2 + b_4_10·a_5_13 + b_2_4·b_4_10·a_3_6 + b_2_3·b_2_4·a_5_13
       + b_2_3·b_2_4·b_1_22·a_3_6 + b_2_32·a_5_13
  50. b_4_10·b_5_16 + b_4_10·b_5_14 + b_2_4·b_1_22·b_5_15 + b_2_4·b_4_10·b_1_23
       + b_2_42·b_5_16 + b_2_44·b_1_2 + b_2_3·b_1_22·b_5_15 + b_2_3·b_4_10·b_1_23
       + b_2_3·b_2_42·b_1_23 + b_2_3·b_2_43·b_1_2 + b_2_32·b_5_14 + b_2_32·b_2_42·b_1_2
       + b_2_33·b_1_23 + b_2_33·b_2_4·b_1_2 + b_4_10·a_5_13 + b_2_42·a_5_13
       + b_2_42·b_1_22·a_3_6 + b_2_3·b_2_4·a_5_13 + b_2_3·b_2_4·b_1_22·a_3_6
       + b_2_3·b_2_42·a_3_6 + b_2_32·a_5_13 + b_2_32·b_2_4·a_3_6
  51. a_4_7·b_5_16 + b_2_42·a_5_13 + b_2_3·b_2_4·a_5_13
  52. b_1_22·a_7_20 + b_4_10·a_5_13 + b_2_4·b_1_24·a_3_6 + b_2_4·b_4_10·a_3_6
       + b_2_42·a_5_13 + b_2_43·a_3_6 + b_2_3·b_1_24·a_3_6 + b_2_3·b_4_10·a_3_6
       + b_2_3·b_2_4·a_5_13 + b_2_3·b_2_42·a_3_6 + b_2_32·a_5_13 + b_2_32·b_1_22·a_3_6
       + b_2_32·b_2_4·a_3_6 + b_2_33·a_3_6
  53. a_4_6·b_5_15 + b_2_3·a_7_20 + b_2_3·b_4_10·a_3_6 + b_2_3·b_2_4·b_1_22·a_3_6
       + b_2_32·a_5_13 + b_2_32·b_1_22·a_3_6 + b_2_32·b_2_4·a_3_6 + b_2_34·a_1_1
       + b_2_34·a_1_0
  54. a_4_7·b_5_15 + a_4_6·b_5_15 + b_2_4·a_7_20 + b_2_4·b_4_10·a_3_6 + b_2_42·b_1_22·a_3_6
       + b_2_3·b_2_4·a_5_13 + b_2_3·b_2_4·b_1_22·a_3_6 + b_2_3·b_2_42·a_3_6
  55. a_8_21·b_1_2 + b_4_10·a_5_13 + a_4_6·b_5_15 + b_2_4·b_4_10·a_3_6 + b_2_42·a_5_13
       + b_2_42·b_1_22·a_3_6 + b_2_3·b_1_24·a_3_6 + b_2_3·b_4_10·a_3_6
       + b_2_3·b_2_4·b_1_22·a_3_6 + b_2_32·b_1_22·a_3_6 + b_2_32·b_2_4·a_3_6
       + b_2_34·a_1_0
  56. a_8_21·a_1_1
  57. a_8_21·a_1_0
  58. a_8_22·b_1_2 + b_4_10·a_5_13 + a_4_7·b_5_15 + a_4_6·b_5_15 + b_2_4·b_1_24·a_3_6
       + b_2_4·b_4_10·a_3_6 + b_2_42·a_5_13 + b_2_42·b_1_22·a_3_6 + b_2_43·a_3_6
       + b_2_3·b_2_4·a_5_13 + b_2_3·b_2_4·b_1_22·a_3_6 + b_2_3·b_2_42·a_3_6 + b_2_32·a_5_13
       + b_2_32·b_2_4·a_3_6 + b_2_33·a_3_6 + b_2_34·a_1_0
  59. a_8_22·a_1_1
  60. a_8_22·a_1_0
  61. b_8_43·b_1_2 + b_4_10·b_5_15 + b_4_10·b_1_25 + b_4_102·b_1_2 + b_2_4·b_4_10·b_1_23
       + b_2_42·b_5_15 + b_2_3·b_2_4·b_5_15 + b_2_3·b_2_4·b_1_25 + b_2_32·b_5_15
       + b_2_32·b_1_25 + b_2_32·b_4_10·b_1_2 + b_2_32·b_2_4·b_1_23
       + b_4_10·b_1_22·a_3_6 + a_4_7·b_5_15 + a_4_6·b_5_15 + b_2_4·b_4_10·a_3_6
       + b_2_42·b_1_22·a_3_6 + b_2_3·b_1_24·a_3_6 + b_2_3·b_4_10·a_3_6
       + b_2_3·b_2_4·b_1_22·a_3_6 + b_2_32·b_2_4·a_3_6 + b_2_34·a_1_0
  62. b_8_43·a_1_1 + b_2_44·a_1_1 + b_2_34·a_1_1
  63. b_8_43·a_1_0
  64. a_5_132
  65. b_5_162 + b_5_14·b_5_16 + b_5_142 + b_2_42·b_1_2·b_5_15 + b_2_42·b_4_10·b_1_22
       + b_2_44·b_1_22 + b_2_3·b_2_4·b_1_2·b_5_15 + b_2_3·b_2_4·b_4_10·b_1_22
       + b_2_3·b_2_43·b_1_22 + b_2_3·b_2_44 + b_2_32·b_1_2·b_5_15
       + b_2_32·b_4_10·b_1_22 + b_2_32·b_2_4·b_4_10 + b_2_32·b_2_42·b_1_22
       + b_2_32·b_2_43 + b_2_33·b_2_42 + b_2_34·b_1_22 + a_5_13·b_5_16
       + b_2_43·b_1_2·a_3_6 + b_2_43·a_4_6 + b_2_3·b_2_42·b_1_2·a_3_6 + b_2_3·b_2_42·a_4_7
       + b_2_32·b_1_2·a_5_13 + b_2_32·b_2_4·b_1_2·a_3_6
  66. a_5_13·b_5_14 + b_2_42·b_1_2·a_5_13 + b_2_3·b_1_2·a_7_20 + b_2_3·b_2_4·b_1_23·a_3_6
       + b_2_32·b_1_2·a_5_13 + b_2_32·b_1_23·a_3_6 + b_2_32·b_2_4·a_4_7
       + b_2_33·b_1_2·a_3_6
  67. a_3_6·a_7_20
  68. a_5_13·b_5_16 + b_2_4·b_1_2·a_7_20 + b_2_42·b_1_2·a_5_13 + b_2_42·b_1_23·a_3_6
       + b_2_3·b_2_4·b_1_2·a_5_13 + b_2_3·b_2_4·b_1_23·a_3_6 + b_2_3·b_2_42·a_4_7
       + b_2_32·b_2_4·b_1_2·a_3_6
  69. a_3_6·a_7_15
  70. b_5_152 + b_4_102·b_1_22 + b_2_4·b_4_10·b_1_24 + b_2_4·b_4_102
       + b_2_42·b_1_26 + b_2_43·b_1_24 + b_2_44·b_1_22 + b_2_45
       + b_2_3·b_4_10·b_1_24 + b_2_3·b_4_102 + b_2_3·b_2_4·b_1_2·b_5_15
       + b_2_3·b_2_42·b_1_24 + b_2_3·b_2_43·b_1_22 + b_2_3·b_2_44
       + b_2_32·b_1_2·b_5_15 + b_2_32·b_2_4·b_1_24 + b_2_32·b_2_42·b_1_22
       + b_2_33·b_2_42 + b_2_35 + a_5_13·b_5_16 + b_4_10·b_1_23·a_3_6
       + b_2_4·b_4_10·b_1_2·a_3_6 + b_2_42·b_1_2·a_5_13 + b_2_43·b_1_2·a_3_6
       + b_2_3·b_1_25·a_3_6 + b_2_3·b_4_10·b_1_2·a_3_6 + b_2_3·b_2_4·b_1_2·a_5_13
       + b_2_3·b_2_4·b_1_23·a_3_6 + b_2_3·b_2_42·a_4_7 + b_2_32·b_1_2·a_5_13
       + b_2_32·b_1_23·a_3_6 + c_8_44·b_1_22
  71. b_5_14·b_5_16 + b_2_43·b_4_10 + b_2_45 + b_2_3·b_2_4·b_1_2·b_5_15
       + b_2_3·b_2_4·b_4_10·b_1_22 + b_2_3·b_2_44 + b_2_32·b_2_42·b_1_22
       + b_2_33·b_2_4·b_1_22 + b_2_33·b_2_42 + a_5_13·b_5_16 + b_2_42·b_1_2·a_5_13
       + b_2_43·a_4_7 + b_2_43·a_4_6 + b_2_3·b_2_42·b_1_2·a_3_6 + c_8_44·a_1_0·a_1_1
  72. b_5_142 + b_2_44·b_1_22 + b_2_32·b_1_2·b_5_15 + b_2_32·b_4_10·b_1_22
       + b_2_32·b_2_4·b_4_10 + b_2_32·b_2_42·b_1_22 + b_2_32·b_2_43
       + b_2_33·b_2_4·b_1_22 + b_2_34·b_1_22 + b_2_32·b_1_2·a_5_13
       + b_2_32·a_1_0·b_5_15 + b_2_32·b_2_4·b_1_2·a_3_6 + b_2_32·b_2_4·a_4_7
       + b_2_33·a_4_7 + b_2_33·a_4_6 + c_8_44·a_1_02
  73. b_5_14·b_5_16 + b_5_14·b_5_15 + b_5_142 + b_2_42·b_1_2·b_5_15 + b_2_43·b_4_10
       + b_2_44·b_1_22 + b_2_45 + b_2_3·b_8_43 + b_2_3·b_4_10·b_1_24 + b_2_3·b_4_102
       + b_2_3·b_2_44 + b_2_32·b_1_2·b_5_15 + b_2_32·b_4_10·b_1_22
       + b_2_32·b_2_4·b_1_24 + b_2_32·b_2_4·b_4_10 + b_2_32·b_2_43 + b_2_33·b_1_24
       + b_2_33·b_4_10 + b_2_33·b_2_4·b_1_22 + b_2_33·b_2_42 + b_2_34·b_1_22
       + a_5_13·b_5_15 + a_5_13·b_5_14 + b_2_4·b_4_10·b_1_2·a_3_6 + b_2_42·b_1_2·a_5_13
       + b_2_43·a_4_7 + b_2_43·a_4_6 + b_2_3·b_2_4·b_1_2·a_5_13 + b_2_3·b_2_42·b_1_2·a_3_6
       + b_2_32·b_1_23·a_3_6 + b_2_32·b_2_4·a_4_7 + b_2_32·b_2_4·a_4_6
       + b_2_33·b_1_2·a_3_6 + b_2_33·a_4_6
  74. b_5_15·b_5_16 + b_2_4·b_8_43 + b_2_4·b_4_10·b_1_24 + b_2_4·b_4_102
       + b_2_42·b_4_10·b_1_22 + b_2_3·b_2_42·b_1_24 + b_2_32·b_2_4·b_1_24
       + b_2_32·b_2_4·b_4_10 + b_2_32·b_2_42·b_1_22 + b_2_4·b_4_10·b_1_2·a_3_6
       + b_2_42·b_1_2·a_5_13 + b_2_43·b_1_2·a_3_6 + b_2_43·a_4_7 + b_2_43·a_4_6
       + b_2_3·b_2_4·b_1_2·a_5_13 + b_2_3·b_2_4·b_1_23·a_3_6 + b_2_3·b_2_42·b_1_2·a_3_6
       + b_2_32·a_1_0·b_5_15 + b_2_32·b_2_4·a_4_7 + b_2_32·b_2_4·a_4_6 + b_2_33·a_4_7
       + b_2_33·a_4_6
  75. a_5_13·b_5_15 + b_1_2·a_9_25 + b_4_10·b_1_23·a_3_6 + b_2_42·b_1_2·a_5_13
       + b_2_43·b_1_2·a_3_6 + b_2_3·b_2_4·b_1_23·a_3_6 + b_2_32·b_1_2·a_5_13
       + b_2_33·b_1_2·a_3_6
  76. a_1_1·a_9_25
  77. a_1_0·a_9_25
  78. a_4_6·a_7_20
  79. a_4_7·a_7_20
  80. a_4_6·a_7_15
  81. b_4_10·a_7_15 + b_4_102·a_3_6 + b_2_4·b_4_10·a_5_13 + b_2_4·b_4_10·b_1_22·a_3_6
       + b_2_42·a_7_15 + b_2_43·a_5_13 + b_2_43·b_1_22·a_3_6 + b_2_44·a_3_6
       + b_2_3·b_2_4·a_7_15 + b_2_3·b_2_4·b_4_10·a_3_6 + b_2_3·b_2_42·b_1_22·a_3_6
       + b_2_3·b_2_43·a_3_6 + b_2_32·a_7_15 + b_2_32·b_2_4·b_1_22·a_3_6
       + b_2_33·b_2_4·a_3_6 + b_2_34·a_3_6
  82. a_4_7·a_7_15
  83. a_8_21·a_3_6
  84. a_8_22·a_3_6
  85. b_8_43·a_3_6 + b_4_10·a_7_20 + b_4_10·b_1_24·a_3_6 + b_2_42·a_7_20
       + b_2_42·b_4_10·a_3_6 + b_2_43·b_1_22·a_3_6 + b_2_3·b_4_10·a_5_13
       + b_2_3·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_4·a_7_20 + b_2_3·b_2_4·b_1_24·a_3_6
       + b_2_3·b_2_42·a_5_13 + b_2_3·b_2_43·a_3_6 + b_2_32·a_7_20 + b_2_32·b_1_24·a_3_6
       + b_2_32·b_2_4·a_5_13 + b_2_32·b_2_4·b_1_22·a_3_6 + b_2_32·b_2_42·a_3_6
       + b_2_33·a_5_13 + b_2_33·b_1_22·a_3_6 + b_2_33·b_2_4·a_3_6
  86. b_1_22·a_9_25 + b_4_10·a_7_20 + b_4_10·b_1_24·a_3_6 + b_4_102·a_3_6
       + b_2_4·b_4_10·b_1_22·a_3_6 + b_2_42·a_7_20 + b_2_44·a_3_6 + b_2_3·b_4_10·a_5_13
       + b_2_3·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_4·a_7_20 + b_2_3·b_2_4·b_1_24·a_3_6
       + b_2_3·b_2_42·a_5_13 + b_2_32·a_7_20 + b_2_32·b_2_4·a_5_13 + b_2_32·b_2_42·a_3_6
       + b_2_33·a_5_13 + b_2_34·a_3_6
  87. a_5_13·a_7_20
  88. a_5_13·a_7_15
  89. b_5_15·a_7_20 + b_5_14·a_7_20 + b_4_10·b_1_2·a_7_20 + b_2_4·b_4_10·b_1_23·a_3_6
       + b_2_42·b_1_2·a_7_20 + b_2_42·b_1_25·a_3_6 + b_2_42·b_4_10·b_1_2·a_3_6
       + b_2_43·b_1_23·a_3_6 + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_2·a_7_20
       + b_2_3·b_2_4·b_4_10·b_1_2·a_3_6 + b_2_3·b_2_43·b_1_2·a_3_6
       + b_2_32·b_2_4·b_1_23·a_3_6 + b_2_32·b_2_42·b_1_2·a_3_6 + b_2_32·b_2_42·a_4_7
       + b_2_33·b_1_23·a_3_6 + b_2_33·b_2_4·b_1_2·a_3_6 + c_8_44·b_1_2·a_3_6
       + b_2_3·c_8_44·a_1_0·a_1_1
  90. a_4_6·a_8_21
  91. b_5_16·a_7_15 + b_5_16·a_7_20 + b_5_15·a_7_15 + b_5_14·a_7_15 + b_4_10·b_1_2·a_7_20
       + b_4_102·b_1_2·a_3_6 + b_2_4·b_4_10·b_1_2·a_5_13 + b_2_42·b_1_2·a_7_20
       + b_2_42·a_8_21 + b_2_42·b_4_10·b_1_2·a_3_6 + b_2_44·b_1_2·a_3_6 + b_2_44·a_4_7
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_2·a_7_20 + b_2_3·b_2_4·a_8_21
       + b_2_3·b_2_42·b_1_23·a_3_6 + b_2_3·b_2_43·a_4_7 + b_2_32·b_1_2·a_7_20
       + b_2_32·b_4_10·b_1_2·a_3_6 + b_2_32·b_2_42·b_1_2·a_3_6 + b_2_32·b_2_42·a_4_7
       + b_2_33·b_1_23·a_3_6 + b_2_33·a_1_0·b_5_15 + b_2_33·b_2_4·a_4_7
       + b_2_33·b_2_4·a_4_6 + b_2_34·a_4_7 + b_2_34·a_4_6 + b_2_3·c_8_44·a_1_0·a_1_1
  92. b_5_16·a_7_15 + b_5_16·a_7_20 + b_5_15·a_7_15 + b_5_14·a_7_15 + b_5_14·a_7_20
       + b_4_10·a_8_21 + b_4_102·b_1_2·a_3_6 + b_2_4·b_4_10·b_1_2·a_5_13
       + b_2_4·b_4_10·b_1_23·a_3_6 + b_2_42·b_1_2·a_7_20 + b_2_43·b_1_2·a_5_13
       + b_2_43·b_1_23·a_3_6 + b_2_44·a_4_7 + b_2_3·b_4_10·b_1_2·a_5_13
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_42·b_1_23·a_3_6
       + b_2_3·b_2_43·b_1_2·a_3_6 + b_2_3·b_2_43·a_4_7 + b_2_32·a_8_21
       + b_2_32·b_2_42·b_1_2·a_3_6 + b_2_33·b_1_2·a_5_13 + b_2_33·b_1_23·a_3_6
       + b_2_33·a_1_0·b_5_15 + b_2_33·b_2_4·a_4_7 + b_2_33·b_2_4·a_4_6
       + b_2_34·b_1_2·a_3_6 + b_2_34·a_4_7 + b_2_34·a_4_6 + b_2_3·c_8_44·a_1_0·a_1_1
  93. a_4_7·a_8_21
  94. b_5_14·a_7_15 + b_2_42·b_4_10·b_1_2·a_3_6 + b_2_43·b_1_2·a_5_13
       + b_2_43·b_1_23·a_3_6 + b_2_44·b_1_2·a_3_6 + b_2_3·b_4_10·b_1_2·a_5_13
       + b_2_3·b_2_4·a_8_21 + b_2_3·b_2_42·b_1_2·a_5_13 + b_2_3·b_2_42·b_1_23·a_3_6
       + b_2_3·b_2_43·b_1_2·a_3_6 + b_2_32·b_1_2·a_7_20 + b_2_32·a_8_22
       + b_2_32·b_2_4·b_1_2·a_5_13 + b_2_32·b_2_4·b_1_23·a_3_6 + b_2_33·b_1_23·a_3_6
       + b_2_33·a_1_0·b_5_15 + b_2_33·b_2_4·a_4_7 + b_2_34·b_1_2·a_3_6 + b_2_34·a_4_7
  95. a_4_6·a_8_22
  96. b_5_16·a_7_20 + b_5_15·a_7_15 + b_5_14·a_7_15 + b_4_10·b_1_2·a_7_20
       + b_4_102·b_1_2·a_3_6 + b_2_42·b_1_2·a_7_20 + b_2_44·b_1_2·a_3_6
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·a_8_22 + b_2_3·b_2_4·a_8_21
       + b_2_3·b_2_42·b_1_2·a_5_13 + b_2_3·b_2_43·b_1_2·a_3_6 + b_2_32·b_1_2·a_7_20
       + b_2_32·b_4_10·b_1_2·a_3_6 + b_2_32·b_2_4·b_1_23·a_3_6 + b_2_33·b_1_23·a_3_6
       + b_2_33·a_1_0·b_5_15 + b_2_33·b_2_4·b_1_2·a_3_6 + b_2_33·b_2_4·a_4_6
       + b_2_34·a_4_7 + b_2_34·a_4_6 + b_2_3·c_8_44·a_1_0·a_1_1
  97. b_5_15·a_7_15 + b_4_10·a_8_22 + b_4_102·b_1_2·a_3_6 + b_2_4·b_4_10·b_1_2·a_5_13
       + b_2_42·a_8_22 + b_2_42·b_4_10·b_1_2·a_3_6 + b_2_43·b_1_2·a_5_13
       + b_2_43·b_1_23·a_3_6 + b_2_3·b_2_42·b_1_23·a_3_6 + b_2_32·b_1_2·a_7_20
       + b_2_32·b_2_42·b_1_2·a_3_6 + b_2_32·b_2_42·a_4_7 + b_2_33·b_1_23·a_3_6
       + b_2_33·b_2_4·b_1_2·a_3_6 + b_2_33·b_2_4·a_4_7 + b_2_33·b_2_4·a_4_6 + b_2_34·a_4_6
       + b_2_3·c_8_44·a_1_0·a_1_1
  98. a_4_7·a_8_22
  99. b_5_14·a_7_20 + a_4_6·b_8_43 + b_2_42·b_1_2·a_7_20 + b_2_44·a_4_6
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_2·a_7_20 + b_2_3·b_2_42·b_1_2·a_5_13
       + b_2_3·b_2_43·b_1_2·a_3_6 + b_2_32·b_1_2·a_7_20 + b_2_32·b_4_10·b_1_2·a_3_6
       + b_2_32·b_2_4·b_1_2·a_5_13 + b_2_33·b_1_2·a_5_13 + b_2_33·b_2_4·b_1_2·a_3_6
       + b_2_33·b_2_4·a_4_7 + b_2_33·b_2_4·a_4_6
  100. b_4_10·b_8_43 + b_4_102·b_1_24 + b_2_4·b_4_10·b_1_2·b_5_15 + b_2_4·b_4_10·b_1_26
       + b_2_4·b_4_102·b_1_22 + b_2_42·b_1_28 + b_2_42·b_8_43 + b_2_42·b_4_10·b_1_24
       + b_2_42·b_4_102 + b_2_43·b_1_2·b_5_15 + b_2_43·b_1_26 + b_2_44·b_1_24
       + b_2_44·b_4_10 + b_2_45·b_1_22 + b_2_3·b_4_10·b_1_26 + b_2_3·b_4_102·b_1_22
       + b_2_3·b_2_4·b_8_43 + b_2_3·b_2_4·b_4_10·b_1_24 + b_2_3·b_2_4·b_4_102
       + b_2_3·b_2_42·b_1_26 + b_2_3·b_2_42·b_4_10·b_1_22 + b_2_3·b_2_44·b_1_22
       + b_2_32·b_8_43 + b_2_32·b_4_10·b_1_24 + b_2_32·b_2_4·b_1_26
       + b_2_32·b_2_42·b_1_24 + b_2_32·b_2_43·b_1_22 + b_2_33·b_2_4·b_4_10
       + b_2_34·b_1_24 + b_2_34·b_2_4·b_1_22 + b_2_35·b_1_22 + b_5_16·a_7_20
       + b_4_10·b_1_2·a_7_20 + b_4_10·b_1_25·a_3_6 + b_4_102·b_1_2·a_3_6
       + b_2_42·b_4_10·b_1_2·a_3_6 + b_2_43·b_1_23·a_3_6 + b_2_3·b_1_27·a_3_6
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_25·a_3_6
       + b_2_3·b_2_4·b_4_10·b_1_2·a_3_6 + b_2_3·b_2_43·b_1_2·a_3_6 + b_2_32·b_1_2·a_7_20
       + b_2_32·b_1_25·a_3_6 + b_2_32·b_2_4·b_1_2·a_5_13 + b_2_32·b_2_4·b_1_23·a_3_6
       + b_2_32·b_2_42·b_1_2·a_3_6 + b_2_32·b_2_42·a_4_7 + b_2_33·b_1_2·a_5_13
       + b_2_34·b_1_2·a_3_6 + c_8_44·b_1_24
  101. b_5_16·a_7_20 + b_5_14·a_7_20 + a_4_7·b_8_43 + b_2_4·b_4_10·b_1_23·a_3_6
       + b_2_42·b_1_2·a_7_20 + b_2_43·b_1_2·a_5_13 + b_2_44·b_1_2·a_3_6 + b_2_44·a_4_7
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·b_4_10·b_1_2·a_3_6
       + b_2_3·b_2_43·b_1_2·a_3_6 + b_2_32·b_1_2·a_7_20 + b_2_32·b_4_10·b_1_2·a_3_6
       + b_2_32·b_2_42·b_1_2·a_3_6 + b_2_32·b_2_42·a_4_7 + b_2_33·b_1_2·a_5_13
       + b_2_33·b_2_4·b_1_2·a_3_6
  102. b_5_14·a_7_20 + b_2_42·b_1_2·a_7_20 + b_2_3·b_1_2·a_9_25 + b_2_3·b_4_10·b_1_2·a_5_13
       + b_2_3·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_2·a_7_20
       + b_2_3·b_2_4·b_4_10·b_1_2·a_3_6 + b_2_3·b_2_42·b_1_2·a_5_13 + b_2_32·b_1_2·a_7_20
       + b_2_32·b_4_10·b_1_2·a_3_6 + b_2_33·b_1_23·a_3_6 + b_2_33·b_2_4·a_4_7
       + b_2_34·b_1_2·a_3_6
  103. a_3_6·a_9_25
  104. b_5_16·a_7_20 + b_2_4·b_1_2·a_9_25 + b_2_4·b_4_10·b_1_2·a_5_13
       + b_2_4·b_4_10·b_1_23·a_3_6 + b_2_42·b_4_10·b_1_2·a_3_6 + b_2_43·b_1_2·a_5_13
       + b_2_3·b_2_4·b_1_2·a_7_20 + b_2_3·b_2_4·b_4_10·b_1_2·a_3_6
       + b_2_32·b_2_4·b_1_23·a_3_6 + b_2_32·b_2_42·a_4_7 + b_2_33·b_2_4·b_1_2·a_3_6
  105. a_8_21·a_5_13
  106. a_8_21·b_5_16 + a_8_21·b_5_15 + a_8_21·b_5_14 + b_4_102·a_5_13 + b_2_4·b_4_10·a_7_20
       + b_2_4·b_4_10·b_1_24·a_3_6 + b_2_42·b_1_26·a_3_6 + b_2_42·b_4_10·a_5_13
       + b_2_43·b_1_24·a_3_6 + b_2_43·b_4_10·a_3_6 + b_2_44·a_5_13 + b_2_45·a_3_6
       + b_2_3·b_2_42·a_7_15 + b_2_3·b_2_42·b_1_24·a_3_6 + b_2_3·b_2_42·b_4_10·a_3_6
       + b_2_3·b_2_43·a_5_13 + b_2_3·b_2_44·a_3_6 + b_2_32·b_2_4·a_7_15
       + b_2_32·b_2_4·a_7_20 + b_2_32·b_2_4·b_1_24·a_3_6 + b_2_32·b_2_42·a_5_13
       + b_2_32·b_2_43·a_3_6 + b_2_33·a_7_20 + b_2_33·b_1_24·a_3_6 + b_2_33·b_4_10·a_3_6
       + b_2_33·b_2_4·a_5_13 + b_2_34·a_5_13 + b_2_34·b_1_22·a_3_6 + b_2_34·b_2_4·a_3_6
       + b_2_35·a_3_6 + c_8_44·b_1_22·a_3_6 + b_2_3·c_8_44·a_3_6 + b_2_32·c_8_44·a_1_0
  107. a_8_22·b_5_14 + a_8_21·b_5_15 + a_8_21·b_5_14 + b_4_102·a_5_13
       + b_2_4·b_4_10·b_1_24·a_3_6 + b_2_42·b_1_26·a_3_6 + b_2_42·b_4_10·b_1_22·a_3_6
       + b_2_44·a_5_13 + b_2_44·b_1_22·a_3_6 + b_2_45·a_3_6 + b_2_3·b_4_10·a_7_20
       + b_2_3·b_2_4·b_4_10·a_5_13 + b_2_3·b_2_43·a_5_13 + b_2_3·b_2_43·b_1_22·a_3_6
       + b_2_32·b_4_10·a_5_13 + b_2_32·b_4_10·b_1_22·a_3_6 + b_2_32·b_2_4·b_1_24·a_3_6
       + b_2_32·b_2_42·a_5_13 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_32·b_2_43·a_3_6
       + b_2_33·b_1_24·a_3_6 + b_2_34·a_5_13 + c_8_44·b_1_22·a_3_6 + b_2_3·c_8_44·a_3_6
       + b_2_32·c_8_44·a_1_0
  108. a_8_22·b_5_15 + b_4_102·a_5_13 + b_2_42·b_1_26·a_3_6 + b_2_42·b_4_10·a_5_13
       + b_2_42·b_4_10·b_1_22·a_3_6 + b_2_44·b_1_22·a_3_6 + b_2_3·b_4_10·b_1_24·a_3_6
       + b_2_3·b_4_102·a_3_6 + b_2_3·b_2_4·b_4_10·a_5_13 + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6
       + b_2_3·b_2_42·a_7_15 + b_2_3·b_2_43·a_5_13 + b_2_32·b_4_10·a_5_13
       + b_2_32·b_4_10·b_1_22·a_3_6 + b_2_32·b_2_4·a_7_15 + b_2_32·b_2_4·b_4_10·a_3_6
       + b_2_32·b_2_42·a_5_13 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_32·b_2_43·a_3_6
       + b_2_33·a_7_20 + b_2_33·b_4_10·a_3_6 + b_2_34·a_5_13 + b_2_34·b_1_22·a_3_6
       + b_2_34·b_2_4·a_3_6 + b_2_35·a_3_6 + b_2_36·a_1_1 + b_2_36·a_1_0
       + c_8_44·b_1_22·a_3_6 + b_2_4·c_8_44·a_3_6 + b_2_32·c_8_44·a_1_1
  109. a_8_22·a_5_13
  110. b_8_43·b_5_14 + b_2_42·b_4_10·b_5_15 + b_2_42·b_4_10·b_1_25
       + b_2_42·b_4_102·b_1_2 + b_2_43·b_4_10·b_1_23 + b_2_44·b_5_15
       + b_2_3·b_4_102·b_1_23 + b_2_3·b_2_42·b_1_22·b_5_15 + b_2_3·b_2_42·b_1_27
       + b_2_3·b_2_42·b_4_10·b_1_23 + b_2_3·b_2_43·b_5_16 + b_2_3·b_2_43·b_5_15
       + b_2_3·b_2_43·b_4_10·b_1_2 + b_2_3·b_2_44·b_1_23 + b_2_32·b_4_10·b_1_25
       + b_2_32·b_4_102·b_1_2 + b_2_32·b_2_4·b_1_22·b_5_15 + b_2_32·b_2_42·b_1_25
       + b_2_32·b_2_42·b_4_10·b_1_2 + b_2_33·b_4_10·b_1_23 + b_2_33·b_2_4·b_5_15
       + b_2_33·b_2_4·b_4_10·b_1_2 + b_2_33·b_2_43·b_1_2 + b_2_34·b_5_16
       + b_2_34·b_2_4·b_1_23 + b_2_35·b_1_23 + b_2_35·b_2_4·b_1_2 + b_2_36·b_1_2
       + b_4_102·b_1_22·a_3_6 + b_2_42·b_1_26·a_3_6 + b_2_42·b_4_10·a_5_13
       + b_2_42·b_4_10·b_1_22·a_3_6 + b_2_43·a_7_20 + b_2_43·b_1_24·a_3_6
       + b_2_44·b_1_22·a_3_6 + b_2_45·a_3_6 + b_2_3·b_4_10·b_1_24·a_3_6
       + b_2_3·b_2_4·b_4_10·a_5_13 + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_42·a_7_20
       + b_2_3·b_2_42·b_1_24·a_3_6 + b_2_3·b_2_44·a_3_6 + b_2_32·b_1_26·a_3_6
       + b_2_32·b_4_10·a_5_13 + b_2_32·b_4_10·b_1_22·a_3_6 + b_2_32·b_2_4·a_7_20
       + b_2_32·b_2_4·b_1_24·a_3_6 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_32·b_2_43·a_3_6
       + b_2_33·b_2_4·b_1_22·a_3_6 + b_2_33·b_2_42·a_3_6 + b_2_34·b_2_4·a_3_6
       + b_2_36·a_1_1 + b_2_3·c_8_44·b_1_23 + c_8_44·b_1_22·a_3_6
  111. b_8_43·b_5_15 + b_4_102·b_1_25 + b_4_103·b_1_2 + b_2_4·b_4_10·b_1_22·b_5_15
       + b_2_4·b_4_10·b_1_27 + b_2_4·b_4_102·b_1_23 + b_2_42·b_1_29
       + b_2_42·b_4_10·b_1_25 + b_2_43·b_1_27 + b_2_43·b_4_10·b_1_23 + b_2_44·b_5_15
       + b_2_44·b_4_10·b_1_2 + b_2_3·b_4_10·b_1_22·b_5_15 + b_2_3·b_4_10·b_1_27
       + b_2_3·b_4_102·b_1_23 + b_2_3·b_2_4·b_4_10·b_5_15 + b_2_3·b_2_4·b_4_10·b_1_25
       + b_2_3·b_2_4·b_4_102·b_1_2 + b_2_3·b_2_42·b_1_27 + b_2_3·b_2_42·b_4_10·b_1_23
       + b_2_3·b_2_43·b_5_15 + b_2_3·b_2_44·b_1_23 + b_2_3·b_2_45·b_1_2
       + b_2_32·b_4_10·b_1_25 + b_2_32·b_2_4·b_1_22·b_5_15 + b_2_32·b_2_4·b_1_27
       + b_2_32·b_2_42·b_5_16 + b_2_32·b_2_42·b_5_15 + b_2_32·b_2_42·b_1_25
       + b_2_32·b_2_42·b_4_10·b_1_2 + b_2_32·b_2_43·b_1_23 + b_2_33·b_1_22·b_5_15
       + b_2_33·b_4_10·b_1_23 + b_2_33·b_2_4·b_4_10·b_1_2 + b_2_33·b_2_42·b_1_23
       + b_2_34·b_5_16 + b_2_34·b_1_25 + b_2_35·b_2_4·b_1_2 + b_2_36·b_1_2
       + b_4_10·b_1_26·a_3_6 + b_4_102·b_1_22·a_3_6 + b_2_43·a_7_20
       + b_2_44·b_1_22·a_3_6 + b_2_45·a_3_6 + b_2_3·b_1_28·a_3_6 + b_2_3·b_4_10·a_7_20
       + b_2_3·b_4_10·b_1_24·a_3_6 + b_2_3·b_2_4·b_1_26·a_3_6
       + b_2_3·b_2_42·b_1_24·a_3_6 + b_2_3·b_2_42·b_4_10·a_3_6 + b_2_3·b_2_43·a_5_13
       + b_2_32·b_1_26·a_3_6 + b_2_32·b_4_10·a_5_13 + b_2_32·b_2_4·a_7_20
       + b_2_32·b_2_4·b_4_10·a_3_6 + b_2_33·b_4_10·a_3_6 + b_2_33·b_2_4·a_5_13
       + b_2_33·b_2_4·b_1_22·a_3_6 + b_2_36·a_1_1 + b_2_36·a_1_0 + c_8_44·b_1_25
       + b_4_10·c_8_44·b_1_2 + b_2_42·c_8_44·b_1_2 + b_2_3·b_2_4·c_8_44·b_1_2
       + b_2_32·c_8_44·b_1_2 + b_2_4·c_8_44·a_3_6 + b_2_32·c_8_44·a_1_1
  112. b_8_43·a_5_13 + b_4_102·b_1_22·a_3_6 + b_2_4·b_4_10·a_7_20
       + b_2_4·b_4_10·b_1_24·a_3_6 + b_2_42·b_1_26·a_3_6 + b_2_42·b_4_10·a_5_13
       + b_2_43·a_7_20 + b_2_43·b_1_24·a_3_6 + b_2_43·b_4_10·a_3_6 + b_2_45·a_3_6
       + b_2_3·b_4_10·b_1_24·a_3_6 + b_2_3·b_4_102·a_3_6 + b_2_3·b_2_42·b_1_24·a_3_6
       + b_2_3·b_2_43·a_5_13 + b_2_3·b_2_43·b_1_22·a_3_6 + b_2_32·b_4_10·b_1_22·a_3_6
       + b_2_32·b_2_4·b_1_24·a_3_6 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_32·b_2_43·a_3_6
       + b_2_34·b_1_22·a_3_6 + b_2_34·b_2_4·a_3_6 + b_2_35·a_3_6 + c_8_44·b_1_22·a_3_6
  113. b_8_43·b_5_16 + b_2_4·b_4_102·b_1_23 + b_2_42·b_4_10·b_5_15
       + b_2_42·b_4_10·b_1_25 + b_2_42·b_4_102·b_1_2 + b_2_43·b_1_22·b_5_15
       + b_2_43·b_1_27 + b_2_44·b_5_16 + b_2_44·b_5_15 + b_2_44·b_1_25
       + b_2_44·b_4_10·b_1_2 + b_2_45·b_1_23 + b_2_3·b_2_4·b_4_10·b_1_25
       + b_2_3·b_2_4·b_4_102·b_1_2 + b_2_3·b_2_42·b_1_22·b_5_15 + b_2_3·b_2_43·b_1_25
       + b_2_3·b_2_44·b_1_23 + b_2_32·b_2_4·b_4_10·b_1_23 + b_2_32·b_2_42·b_1_25
       + b_2_32·b_2_43·b_1_23 + b_2_32·b_2_44·b_1_2 + b_2_33·b_2_4·b_5_16
       + b_2_33·b_2_42·b_1_23 + b_2_34·b_2_4·b_1_23 + b_2_34·b_2_42·b_1_2
       + b_2_35·b_2_4·b_1_2 + b_2_4·b_4_10·a_7_20 + b_2_4·b_4_10·b_1_24·a_3_6
       + b_2_4·b_4_102·a_3_6 + b_2_42·b_4_10·b_1_22·a_3_6 + b_2_44·a_5_13 + b_2_45·a_3_6
       + b_2_3·b_2_4·b_1_26·a_3_6 + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_42·a_7_20
       + b_2_3·b_2_42·b_1_24·a_3_6 + b_2_3·b_2_42·b_4_10·a_3_6 + b_2_3·b_2_43·a_5_13
       + b_2_3·b_2_43·b_1_22·a_3_6 + b_2_32·b_2_4·a_7_20 + b_2_32·b_2_4·b_1_24·a_3_6
       + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_33·b_2_4·a_5_13 + b_2_33·b_2_42·a_3_6
       + b_2_34·b_2_4·a_3_6 + b_2_36·a_1_1 + b_2_4·c_8_44·b_1_23
  114. a_8_21·b_5_14 + b_2_42·b_4_10·a_5_13 + b_2_43·b_4_10·a_3_6 + b_2_44·a_5_13
       + b_2_44·b_1_22·a_3_6 + b_2_3·b_4_10·a_7_20 + b_2_3·b_2_4·b_4_10·a_5_13
       + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_42·b_1_24·a_3_6
       + b_2_3·b_2_44·a_3_6 + b_2_32·a_9_25 + b_2_32·b_4_10·b_1_22·a_3_6
       + b_2_32·b_2_4·a_7_15 + b_2_32·b_2_4·a_7_20 + b_2_32·b_2_4·b_1_24·a_3_6
       + b_2_32·b_2_42·a_5_13 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_33·a_7_15
       + b_2_33·b_4_10·a_3_6 + b_2_33·b_2_4·b_1_22·a_3_6 + b_2_33·b_2_42·a_3_6
       + b_2_34·a_5_13 + b_2_34·b_1_22·a_3_6 + b_2_34·b_2_4·a_3_6 + b_2_35·a_3_6
       + b_2_36·a_1_1
  115. a_4_6·a_9_25
  116. a_8_21·b_5_15 + a_8_21·b_5_14 + b_4_102·a_5_13 + b_2_4·b_4_10·b_1_24·a_3_6
       + b_2_42·b_1_26·a_3_6 + b_2_42·b_4_10·a_5_13 + b_2_42·b_4_10·b_1_22·a_3_6
       + b_2_43·a_7_20 + b_2_43·b_1_24·a_3_6 + b_2_44·b_1_22·a_3_6 + b_2_3·b_2_4·a_9_25
       + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_42·b_1_24·a_3_6
       + b_2_3·b_2_42·b_4_10·a_3_6 + b_2_3·b_2_43·a_5_13 + b_2_3·b_2_43·b_1_22·a_3_6
       + b_2_3·b_2_44·a_3_6 + b_2_32·b_2_4·a_7_20 + b_2_32·b_2_4·b_1_24·a_3_6
       + b_2_32·b_2_4·b_4_10·a_3_6 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_33·a_7_20
       + b_2_33·b_1_24·a_3_6 + b_2_33·b_4_10·a_3_6 + b_2_33·b_2_4·b_1_22·a_3_6
       + b_2_33·b_2_42·a_3_6 + b_2_34·a_5_13 + b_2_34·b_1_22·a_3_6 + b_2_35·a_3_6
       + b_2_36·a_1_1 + c_8_44·b_1_22·a_3_6 + b_2_3·c_8_44·a_3_6 + b_2_32·c_8_44·a_1_0
  117. a_8_22·b_5_16 + b_2_4·b_4_10·a_7_20 + b_2_42·a_9_25 + b_2_42·b_4_10·b_1_22·a_3_6
       + b_2_43·a_7_20 + b_2_43·b_4_10·a_3_6 + b_2_44·a_5_13 + b_2_3·b_2_4·b_4_10·a_5_13
       + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_42·a_7_20
       + b_2_3·b_2_42·b_4_10·a_3_6 + b_2_32·b_2_4·a_7_20 + b_2_32·b_2_4·b_4_10·a_3_6
       + b_2_32·b_2_42·a_5_13 + b_2_32·b_2_42·b_1_22·a_3_6 + b_2_32·b_2_43·a_3_6
       + b_2_33·b_2_4·b_1_22·a_3_6 + b_2_33·b_2_42·a_3_6 + b_2_34·b_2_4·a_3_6
       + b_2_36·a_1_1
  118. a_8_22·b_5_16 + a_8_21·b_5_15 + b_4_10·a_9_25 + b_4_102·b_1_22·a_3_6
       + b_2_4·b_4_102·a_3_6 + b_2_43·a_7_20 + b_2_43·b_4_10·a_3_6 + b_2_44·a_5_13
       + b_2_3·b_4_10·a_7_20 + b_2_3·b_4_10·b_1_24·a_3_6 + b_2_3·b_4_102·a_3_6
       + b_2_3·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_3·b_2_42·a_7_20
       + b_2_3·b_2_42·b_1_24·a_3_6 + b_2_3·b_2_42·b_4_10·a_3_6 + b_2_3·b_2_43·a_5_13
       + b_2_3·b_2_44·a_3_6 + b_2_32·b_4_10·b_1_22·a_3_6 + b_2_32·b_2_4·a_7_15
       + b_2_32·b_2_4·a_7_20 + b_2_32·b_2_4·b_1_24·a_3_6 + b_2_32·b_2_42·b_1_22·a_3_6
       + b_2_33·a_7_15 + b_2_33·a_7_20 + b_2_33·b_1_24·a_3_6 + b_2_33·b_4_10·a_3_6
       + b_2_33·b_2_4·a_5_13 + b_2_33·b_2_42·a_3_6 + b_2_34·a_5_13 + b_2_34·b_2_4·a_3_6
       + b_2_36·a_1_1 + b_2_3·c_8_44·a_3_6 + b_2_32·c_8_44·a_1_0
  119. a_4_7·a_9_25
  120. a_7_202
  121. a_7_20·a_7_15
  122. a_7_152
  123. b_5_15·a_9_25 + b_5_14·a_9_25 + b_4_102·b_1_23·a_3_6 + b_2_4·b_4_10·a_8_21
       + b_2_43·b_1_2·a_7_20 + b_2_43·a_8_21 + b_2_43·b_4_10·b_1_2·a_3_6
       + b_2_45·b_1_2·a_3_6 + b_2_3·b_2_4·b_4_10·b_1_2·a_5_13
       + b_2_3·b_2_4·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_42·b_1_25·a_3_6
       + b_2_3·b_2_43·b_1_2·a_5_13 + b_2_3·b_2_43·b_1_23·a_3_6
       + b_2_3·b_2_44·b_1_2·a_3_6 + b_2_3·b_2_44·a_4_7 + b_2_32·b_2_4·b_1_2·a_7_20
       + b_2_32·b_2_4·b_4_10·b_1_2·a_3_6 + b_2_32·b_2_42·b_1_23·a_3_6
       + b_2_32·b_2_43·a_4_7 + b_2_33·b_1_2·a_7_20 + b_2_33·b_2_4·b_1_2·a_5_13
       + b_2_33·b_2_42·b_1_2·a_3_6 + b_2_34·b_1_2·a_5_13 + b_2_34·b_1_23·a_3_6
       + b_2_34·a_1_0·b_5_15 + b_2_34·b_2_4·b_1_2·a_3_6 + b_2_34·b_2_4·a_4_7
       + b_2_34·b_2_4·a_4_6 + b_2_35·a_4_7 + b_2_35·a_4_6 + c_8_44·b_1_2·a_5_13
       + b_2_3·c_8_44·b_1_2·a_3_6
  124. b_5_14·a_9_25 + b_2_42·b_1_2·a_9_25 + b_2_3·b_4_10·a_8_21
       + b_2_3·b_4_102·b_1_2·a_3_6 + b_2_3·b_2_4·b_4_10·b_1_2·a_5_13
       + b_2_3·b_2_42·b_1_25·a_3_6 + b_2_3·b_2_42·a_8_21 + b_2_3·b_2_43·b_1_2·a_5_13
       + b_2_3·b_2_43·b_1_23·a_3_6 + b_2_3·b_2_44·b_1_2·a_3_6 + b_2_32·b_1_2·a_9_25
       + b_2_32·b_4_10·b_1_23·a_3_6 + b_2_32·b_2_4·b_1_2·a_7_20 + b_2_32·b_2_4·a_8_22
       + b_2_32·b_2_4·a_8_21 + b_2_32·b_2_42·b_1_23·a_3_6 + b_2_32·b_2_43·a_4_7
       + b_2_33·a_8_22 + b_2_33·a_8_21 + b_2_33·b_4_10·b_1_2·a_3_6
       + b_2_33·b_2_4·b_1_2·a_5_13 + b_2_33·b_2_4·b_1_23·a_3_6
       + b_2_33·b_2_42·b_1_2·a_3_6 + b_2_33·b_2_42·a_4_7 + b_2_34·b_1_2·a_5_13
       + b_2_34·b_1_23·a_3_6 + b_2_34·b_2_4·a_4_6 + b_2_35·a_4_6
       + b_2_3·c_8_44·b_1_2·a_3_6
  125. a_5_13·a_9_25
  126. b_5_16·a_9_25 + b_5_14·a_9_25 + b_2_4·b_4_10·a_8_21 + b_2_4·b_4_102·b_1_2·a_3_6
       + b_2_42·b_4_10·b_1_2·a_5_13 + b_2_43·b_1_25·a_3_6 + b_2_43·a_8_21
       + b_2_44·b_1_2·a_5_13 + b_2_44·b_1_23·a_3_6 + b_2_45·b_1_2·a_3_6
       + b_2_3·b_4_10·a_8_21 + b_2_3·b_4_102·b_1_2·a_3_6 + b_2_3·b_2_4·b_1_2·a_9_25
       + b_2_3·b_2_4·b_4_10·b_1_2·a_5_13 + b_2_3·b_2_4·b_4_10·b_1_23·a_3_6
       + b_2_3·b_2_42·b_1_2·a_7_20 + b_2_3·b_2_42·b_1_25·a_3_6 + b_2_3·b_2_42·a_8_22
       + b_2_3·b_2_43·b_1_2·a_5_13 + b_2_3·b_2_44·b_1_2·a_3_6 + b_2_3·b_2_44·a_4_7
       + b_2_32·b_1_2·a_9_25 + b_2_32·b_4_10·b_1_23·a_3_6 + b_2_32·b_2_4·b_1_2·a_7_20
       + b_2_32·b_2_4·b_4_10·b_1_2·a_3_6 + b_2_32·b_2_42·b_1_2·a_5_13
       + b_2_32·b_2_43·b_1_2·a_3_6 + b_2_33·a_8_22 + b_2_33·a_8_21
       + b_2_33·b_4_10·b_1_2·a_3_6 + b_2_33·b_2_42·b_1_2·a_3_6 + b_2_33·b_2_42·a_4_7
       + b_2_34·b_1_2·a_5_13 + b_2_34·b_1_23·a_3_6 + b_2_34·a_1_0·b_5_15
       + b_2_34·b_2_4·a_4_7 + b_2_35·a_4_7 + b_2_4·c_8_44·b_1_2·a_3_6
       + b_2_3·c_8_44·b_1_2·a_3_6
  127. a_8_21·a_7_20
  128. a_8_21·a_7_15
  129. a_8_22·a_7_20
  130. a_8_22·a_7_15
  131. b_8_43·a_7_20 + b_4_103·a_3_6 + b_2_4·b_4_10·b_1_26·a_3_6 + b_2_4·b_4_102·a_5_13
       + b_2_42·b_4_10·a_7_20 + b_2_43·b_4_10·a_5_13 + b_2_43·b_4_10·b_1_22·a_3_6
       + b_2_44·b_1_24·a_3_6 + b_2_44·b_4_10·a_3_6 + b_2_45·b_1_22·a_3_6
       + b_2_3·b_4_10·b_1_26·a_3_6 + b_2_3·b_2_4·b_4_102·a_3_6
       + b_2_3·b_2_42·b_4_10·a_5_13 + b_2_3·b_2_42·b_4_10·b_1_22·a_3_6
       + b_2_3·b_2_43·a_7_20 + b_2_32·b_4_10·a_7_20 + b_2_32·b_4_102·a_3_6
       + b_2_32·b_2_4·b_4_10·a_5_13 + b_2_32·b_2_42·a_7_20
       + b_2_32·b_2_42·b_1_24·a_3_6 + b_2_32·b_2_42·b_4_10·a_3_6
       + b_2_32·b_2_43·a_5_13 + b_2_32·b_2_43·b_1_22·a_3_6 + b_2_32·b_2_44·a_3_6
       + b_2_33·b_1_26·a_3_6 + b_2_33·b_4_10·a_5_13 + b_2_33·b_2_4·a_7_20
       + b_2_33·b_2_4·b_1_24·a_3_6 + b_2_33·b_2_42·b_1_22·a_3_6 + b_2_34·a_7_20
       + b_2_34·b_1_24·a_3_6 + b_2_34·b_2_4·a_5_13 + b_2_34·b_2_4·b_1_22·a_3_6
       + b_2_34·b_2_42·a_3_6 + b_2_35·a_5_13 + b_2_35·b_1_22·a_3_6 + b_2_35·b_2_4·a_3_6
       + b_4_10·c_8_44·a_3_6 + b_2_42·c_8_44·a_3_6 + b_2_3·c_8_44·b_1_22·a_3_6
       + b_2_3·b_2_4·c_8_44·a_3_6 + b_2_32·c_8_44·a_3_6
  132. b_8_43·a_7_15 + b_4_102·b_1_24·a_3_6 + b_2_4·b_4_102·b_1_22·a_3_6
       + b_2_42·b_1_28·a_3_6 + b_2_42·b_4_10·a_7_20 + b_2_42·b_4_10·b_1_24·a_3_6
       + b_2_42·b_4_102·a_3_6 + b_2_43·b_4_10·a_5_13 + b_2_44·a_7_15 + b_2_44·a_7_20
       + b_2_44·b_4_10·a_3_6 + b_2_45·a_5_13 + b_2_3·b_4_10·b_1_26·a_3_6
       + b_2_3·b_4_102·b_1_22·a_3_6 + b_2_3·b_2_4·b_4_10·a_7_20
       + b_2_3·b_2_4·b_4_10·b_1_24·a_3_6 + b_2_3·b_2_42·a_9_25 + b_2_3·b_2_43·a_7_20
       + b_2_3·b_2_43·b_1_24·a_3_6 + b_2_3·b_2_43·b_4_10·a_3_6
       + b_2_3·b_2_44·b_1_22·a_3_6 + b_2_32·b_4_10·b_1_24·a_3_6 + b_2_32·b_2_4·a_9_25
       + b_2_32·b_2_4·b_4_10·a_5_13 + b_2_32·b_2_42·a_7_20
       + b_2_32·b_2_43·b_1_22·a_3_6 + b_2_32·b_2_44·a_3_6 + b_2_33·b_2_4·a_7_15
       + b_2_33·b_2_4·a_7_20 + b_2_33·b_2_4·b_1_24·a_3_6 + b_2_33·b_2_42·b_1_22·a_3_6
       + b_2_33·b_2_43·a_3_6 + b_2_34·b_1_24·a_3_6 + b_2_34·b_2_4·a_5_13
       + b_2_34·b_2_4·b_1_22·a_3_6 + b_2_35·b_1_22·a_3_6 + b_2_35·b_2_4·a_3_6
       + c_8_44·b_1_24·a_3_6 + b_2_4·c_8_44·b_1_22·a_3_6
  133. a_8_212
  134. a_8_222
  135. a_8_21·a_8_22
  136. a_7_20·a_9_25
  137. b_8_432 + b_4_102·b_1_28 + b_2_4·b_4_103·b_1_22 + b_2_42·b_4_10·b_1_28
       + b_2_42·b_4_102·b_1_24 + b_2_43·b_1_210 + b_2_44·b_1_28 + b_2_45·b_1_26
       + b_2_45·b_4_10·b_1_22 + b_2_48 + b_2_3·b_4_103·b_1_22 + b_2_3·b_2_4·b_4_103
       + b_2_3·b_2_42·b_1_210 + b_2_3·b_2_42·b_4_10·b_1_2·b_5_15
       + b_2_3·b_2_42·b_4_102·b_1_22 + b_2_3·b_2_43·b_1_28
       + b_2_3·b_2_43·b_4_10·b_1_24 + b_2_3·b_2_43·b_4_102
       + b_2_3·b_2_44·b_1_2·b_5_15 + b_2_3·b_2_44·b_1_26 + b_2_3·b_2_45·b_4_10
       + b_2_3·b_2_47 + b_2_32·b_4_10·b_1_28 + b_2_32·b_4_102·b_1_24
       + b_2_32·b_4_103 + b_2_32·b_2_4·b_4_10·b_1_2·b_5_15
       + b_2_32·b_2_42·b_4_10·b_1_24 + b_2_32·b_2_43·b_4_10·b_1_22
       + b_2_32·b_2_46 + b_2_33·b_2_4·b_1_28 + b_2_33·b_2_4·b_4_10·b_1_24
       + b_2_33·b_2_42·b_1_26 + b_2_33·b_2_42·b_4_10·b_1_22 + b_2_33·b_2_43·b_4_10
       + b_2_33·b_2_44·b_1_22 + b_2_33·b_2_45 + b_2_34·b_1_28
       + b_2_34·b_4_10·b_1_24 + b_2_34·b_2_4·b_1_2·b_5_15 + b_2_34·b_2_4·b_1_26
       + b_2_34·b_2_44 + b_2_35·b_4_10·b_1_22 + b_2_35·b_2_4·b_1_24
       + b_2_35·b_2_4·b_4_10 + b_2_35·b_2_42·b_1_22 + b_2_35·b_2_43 + b_2_36·b_1_24
       + b_2_36·b_4_10 + b_2_36·b_2_4·b_1_22 + b_2_36·b_2_42 + a_8_22·b_8_43
       + b_2_4·b_4_102·b_1_2·a_5_13 + b_2_4·b_4_102·b_1_23·a_3_6
       + b_2_43·b_4_10·b_1_23·a_3_6 + b_2_44·b_1_2·a_7_20 + b_2_44·a_8_22
       + b_2_45·b_1_2·a_5_13 + b_2_45·b_1_23·a_3_6 + b_2_46·b_1_2·a_3_6
       + b_2_3·b_4_10·b_1_27·a_3_6 + b_2_3·b_2_4·b_1_29·a_3_6 + b_2_3·b_2_4·b_4_10·a_8_21
       + b_2_3·b_2_4·b_4_102·b_1_2·a_3_6 + b_2_3·b_2_43·b_1_2·a_7_20
       + b_2_3·b_2_43·b_4_10·b_1_2·a_3_6 + b_2_3·b_2_44·b_1_23·a_3_6
       + b_2_3·b_2_45·b_1_2·a_3_6 + b_2_3·b_2_45·a_4_7 + b_2_32·b_1_29·a_3_6
       + b_2_32·b_4_102·b_1_2·a_3_6 + b_2_32·b_2_4·b_4_10·b_1_2·a_5_13
       + b_2_32·b_2_4·b_4_10·b_1_23·a_3_6 + b_2_32·b_2_42·b_1_25·a_3_6
       + b_2_32·b_2_42·a_8_22 + b_2_32·b_2_43·b_1_2·a_5_13 + b_2_32·b_2_44·b_1_2·a_3_6
       + b_2_33·b_1_2·a_9_25 + b_2_33·b_2_4·a_8_21 + b_2_33·b_2_42·b_1_23·a_3_6
       + b_2_33·b_2_43·b_1_2·a_3_6 + b_2_33·b_2_43·a_4_7 + b_2_34·b_1_25·a_3_6
       + b_2_34·b_4_10·b_1_2·a_3_6 + b_2_34·b_2_42·b_1_2·a_3_6 + b_2_34·b_2_42·a_4_7
       + b_2_35·b_2_4·a_4_7 + b_2_36·b_1_2·a_3_6 + b_4_102·c_8_44 + b_2_4·c_8_44·b_1_26
       + b_2_44·c_8_44 + b_2_3·c_8_44·b_1_26 + b_2_3·b_2_4·c_8_44·b_1_24
       + b_2_32·c_8_44·b_1_24 + b_2_32·b_2_42·c_8_44 + b_2_34·c_8_44
       + b_4_10·c_8_44·b_1_2·a_3_6 + b_2_4·c_8_44·b_1_2·a_5_13 + b_2_42·c_8_44·b_1_2·a_3_6
       + b_2_3·b_2_4·c_8_44·b_1_2·a_3_6 + b_2_32·c_8_44·b_1_2·a_3_6
  138. b_8_432 + b_4_102·b_1_28 + b_2_4·b_4_103·b_1_22 + b_2_42·b_4_10·b_1_28
       + b_2_42·b_4_102·b_1_24 + b_2_43·b_1_210 + b_2_44·b_1_28 + b_2_45·b_1_26
       + b_2_45·b_4_10·b_1_22 + b_2_48 + b_2_3·b_4_103·b_1_22 + b_2_3·b_2_4·b_4_103
       + b_2_3·b_2_42·b_1_210 + b_2_3·b_2_42·b_4_10·b_1_2·b_5_15
       + b_2_3·b_2_42·b_4_102·b_1_22 + b_2_3·b_2_43·b_1_28
       + b_2_3·b_2_43·b_4_10·b_1_24 + b_2_3·b_2_43·b_4_102
       + b_2_3·b_2_44·b_1_2·b_5_15 + b_2_3·b_2_44·b_1_26 + b_2_3·b_2_45·b_4_10
       + b_2_3·b_2_47 + b_2_32·b_4_10·b_1_28 + b_2_32·b_4_102·b_1_24
       + b_2_32·b_4_103 + b_2_32·b_2_4·b_4_10·b_1_2·b_5_15
       + b_2_32·b_2_42·b_4_10·b_1_24 + b_2_32·b_2_43·b_4_10·b_1_22
       + b_2_32·b_2_46 + b_2_33·b_2_4·b_1_28 + b_2_33·b_2_4·b_4_10·b_1_24
       + b_2_33·b_2_42·b_1_26 + b_2_33·b_2_42·b_4_10·b_1_22 + b_2_33·b_2_43·b_4_10
       + b_2_33·b_2_44·b_1_22 + b_2_33·b_2_45 + b_2_34·b_1_28
       + b_2_34·b_4_10·b_1_24 + b_2_34·b_2_4·b_1_2·b_5_15 + b_2_34·b_2_4·b_1_26
       + b_2_34·b_2_44 + b_2_35·b_4_10·b_1_22 + b_2_35·b_2_4·b_1_24
       + b_2_35·b_2_4·b_4_10 + b_2_35·b_2_42·b_1_22 + b_2_35·b_2_43 + b_2_36·b_1_24
       + b_2_36·b_4_10 + b_2_36·b_2_4·b_1_22 + b_2_36·b_2_42 + b_4_103·b_1_2·a_3_6
       + b_2_4·b_4_10·b_1_27·a_3_6 + b_2_4·b_4_102·b_1_2·a_5_13 + b_2_42·b_4_10·a_8_21
       + b_2_43·b_1_27·a_3_6 + b_2_43·b_4_10·b_1_23·a_3_6 + b_2_44·a_8_21
       + b_2_46·b_1_2·a_3_6 + b_2_3·b_4_10·b_1_27·a_3_6 + b_2_3·b_4_102·b_1_2·a_5_13
       + b_2_3·b_4_102·b_1_23·a_3_6 + b_2_3·b_2_4·b_1_29·a_3_6
       + b_2_3·b_2_4·b_4_102·b_1_2·a_3_6 + b_2_3·b_2_42·b_1_2·a_9_25
       + b_2_3·b_2_42·b_1_27·a_3_6 + b_2_3·b_2_42·b_4_10·b_1_2·a_5_13
       + b_2_3·b_2_42·b_4_10·b_1_23·a_3_6 + b_2_3·b_2_43·b_1_2·a_7_20
       + b_2_3·b_2_43·b_1_25·a_3_6 + b_2_3·b_2_43·a_8_21 + b_2_3·b_2_44·b_1_2·a_5_13
       + b_2_3·b_2_44·b_1_23·a_3_6 + b_2_3·b_2_45·b_1_2·a_3_6 + b_2_32·b_1_29·a_3_6
       + b_2_32·b_4_102·b_1_2·a_3_6 + b_2_32·b_2_4·b_1_27·a_3_6
       + b_2_32·b_2_4·b_4_10·b_1_23·a_3_6 + b_2_32·b_2_42·b_1_2·a_7_20
       + b_2_32·b_2_42·a_8_21 + b_2_32·b_2_42·b_4_10·b_1_2·a_3_6
       + b_2_32·b_2_43·b_1_23·a_3_6 + b_2_33·b_4_10·b_1_2·a_5_13
       + b_2_33·b_4_10·b_1_23·a_3_6 + b_2_33·b_2_4·b_1_25·a_3_6 + b_2_34·b_1_25·a_3_6
       + b_2_34·b_4_10·b_1_2·a_3_6 + b_2_34·b_2_4·b_1_23·a_3_6
       + b_2_34·b_2_42·b_1_2·a_3_6 + b_2_35·b_1_23·a_3_6 + b_2_35·b_2_4·b_1_2·a_3_6
       + b_2_36·b_1_2·a_3_6 + b_4_102·c_8_44 + b_2_4·c_8_44·b_1_26 + b_2_44·c_8_44
       + b_2_3·c_8_44·b_1_26 + b_2_3·b_2_4·c_8_44·b_1_24 + b_2_32·c_8_44·b_1_24
       + b_2_32·b_2_42·c_8_44 + b_2_34·c_8_44 + b_2_4·c_8_44·b_1_23·a_3_6
  139. b_8_432 + b_4_102·b_1_28 + b_2_4·b_4_103·b_1_22 + b_2_42·b_4_10·b_1_28
       + b_2_42·b_4_102·b_1_24 + b_2_43·b_1_210 + b_2_44·b_1_28 + b_2_45·b_1_26
       + b_2_45·b_4_10·b_1_22 + b_2_48 + b_2_3·b_4_103·b_1_22 + b_2_3·b_2_4·b_4_103
       + b_2_3·b_2_42·b_1_210 + b_2_3·b_2_42·b_4_10·b_1_2·b_5_15
       + b_2_3·b_2_42·b_4_102·b_1_22 + b_2_3·b_2_43·b_1_28
       + b_2_3·b_2_43·b_4_10·b_1_24 + b_2_3·b_2_43·b_4_102
       + b_2_3·b_2_44·b_1_2·b_5_15 + b_2_3·b_2_44·b_1_26 + b_2_3·b_2_45·b_4_10
       + b_2_3·b_2_47 + b_2_32·b_4_10·b_1_28 + b_2_32·b_4_102·b_1_24
       + b_2_32·b_4_103 + b_2_32·b_2_4·b_4_10·b_1_2·b_5_15
       + b_2_32·b_2_42·b_4_10·b_1_24 + b_2_32·b_2_43·b_4_10·b_1_22
       + b_2_32·b_2_46 + b_2_33·b_2_4·b_1_28 + b_2_33·b_2_4·b_4_10·b_1_24
       + b_2_33·b_2_42·b_1_26 + b_2_33·b_2_42·b_4_10·b_1_22 + b_2_33·b_2_43·b_4_10
       + b_2_33·b_2_44·b_1_22 + b_2_33·b_2_45 + b_2_34·b_1_28
       + b_2_34·b_4_10·b_1_24 + b_2_34·b_2_4·b_1_2·b_5_15 + b_2_34·b_2_4·b_1_26
       + b_2_34·b_2_44 + b_2_35·b_4_10·b_1_22 + b_2_35·b_2_4·b_1_24
       + b_2_35·b_2_4·b_4_10 + b_2_35·b_2_42·b_1_22 + b_2_35·b_2_43 + b_2_36·b_1_24
       + b_2_36·b_4_10 + b_2_36·b_2_4·b_1_22 + b_2_36·b_2_42 + a_8_22·b_8_43
       + a_8_21·b_8_43 + b_4_103·b_1_2·a_3_6 + b_2_4·b_4_102·b_1_2·a_5_13
       + b_2_4·b_4_102·b_1_23·a_3_6 + b_2_42·b_4_102·b_1_2·a_3_6 + b_2_43·b_1_2·a_9_25
       + b_2_43·b_4_10·b_1_23·a_3_6 + b_2_44·b_1_2·a_7_20 + b_2_44·b_1_25·a_3_6
       + b_2_44·a_8_22 + b_2_44·a_8_21 + b_2_44·b_4_10·b_1_2·a_3_6
       + b_2_3·b_4_102·b_1_2·a_5_13 + b_2_3·b_4_102·b_1_23·a_3_6
       + b_2_3·b_2_4·b_1_29·a_3_6 + b_2_3·b_2_4·b_4_10·a_8_21
       + b_2_3·b_2_4·b_4_102·b_1_2·a_3_6 + b_2_3·b_2_42·b_4_10·b_1_2·a_5_13
       + b_2_3·b_2_43·b_1_2·a_7_20 + b_2_3·b_2_43·b_1_25·a_3_6
       + b_2_3·b_2_44·b_1_2·a_5_13 + b_2_3·b_2_44·b_1_23·a_3_6
       + b_2_3·b_2_45·b_1_2·a_3_6 + b_2_3·b_2_45·a_4_7 + b_2_32·b_1_29·a_3_6
       + b_2_32·b_4_10·b_1_25·a_3_6 + b_2_32·b_4_102·b_1_2·a_3_6
       + b_2_32·b_2_4·b_1_27·a_3_6 + b_2_32·b_2_42·b_1_2·a_7_20
       + b_2_32·b_2_42·b_1_25·a_3_6 + b_2_32·b_2_42·a_8_21
       + b_2_32·b_2_43·b_1_2·a_5_13 + b_2_32·b_2_44·a_4_7 + b_2_33·b_1_27·a_3_6
       + b_2_33·b_4_10·b_1_2·a_5_13 + b_2_33·b_4_10·b_1_23·a_3_6
       + b_2_33·b_2_4·b_1_2·a_7_20 + b_2_33·b_2_4·b_1_25·a_3_6 + b_2_33·b_2_4·a_8_22
       + b_2_33·b_2_4·a_8_21 + b_2_33·b_2_4·b_4_10·b_1_2·a_3_6
       + b_2_33·b_2_42·b_1_23·a_3_6 + b_2_34·b_2_42·a_4_7 + b_2_35·b_1_2·a_5_13
       + b_2_35·b_2_4·a_4_7 + b_2_36·b_1_2·a_3_6 + b_4_102·c_8_44 + b_2_4·c_8_44·b_1_26
       + b_2_44·c_8_44 + b_2_3·c_8_44·b_1_26 + b_2_3·b_2_4·c_8_44·b_1_24
       + b_2_32·c_8_44·b_1_24 + b_2_32·b_2_42·c_8_44 + b_2_34·c_8_44
       + b_2_4·c_8_44·b_1_2·a_5_13 + b_2_3·c_8_44·b_1_2·a_5_13
       + b_2_3·b_2_4·c_8_44·b_1_2·a_3_6 + b_2_32·c_8_44·b_1_2·a_3_6
  140. a_7_15·a_9_25
  141. a_8_22·a_9_25
  142. b_8_43·a_9_25 + b_4_102·b_1_26·a_3_6 + b_4_103·b_1_22·a_3_6 + b_2_4·b_4_103·a_3_6
       + b_2_42·b_4_102·a_5_13 + b_2_42·b_4_102·b_1_22·a_3_6 + b_2_43·b_1_28·a_3_6
       + b_2_43·b_4_10·a_7_20 + b_2_44·a_9_25 + b_2_44·b_1_26·a_3_6
       + b_2_44·b_4_10·a_5_13 + b_2_44·b_4_10·b_1_22·a_3_6 + b_2_45·a_7_20
       + b_2_45·b_1_24·a_3_6 + b_2_46·b_1_22·a_3_6 + b_2_47·a_3_6
       + b_2_3·b_4_102·b_1_24·a_3_6 + b_2_3·b_2_42·b_1_28·a_3_6
       + b_2_3·b_2_42·b_4_10·a_7_20 + b_2_3·b_2_42·b_4_10·b_1_24·a_3_6
       + b_2_3·b_2_44·a_7_20 + b_2_3·b_2_44·b_1_24·a_3_6 + b_2_3·b_2_44·b_4_10·a_3_6
       + b_2_3·b_2_45·a_5_13 + b_2_3·b_2_45·b_1_22·a_3_6 + b_2_32·b_4_102·b_1_22·a_3_6
       + b_2_32·b_2_4·b_4_102·a_3_6 + b_2_32·b_2_42·b_1_26·a_3_6
       + b_2_32·b_2_42·b_4_10·a_5_13 + b_2_32·b_2_43·a_7_15 + b_2_32·b_2_43·a_7_20
       + b_2_32·b_2_43·b_1_24·a_3_6 + b_2_32·b_2_43·b_4_10·a_3_6
       + b_2_33·b_4_10·a_7_20 + b_2_33·b_4_102·a_3_6 + b_2_33·b_2_4·a_9_25
       + b_2_33·b_2_4·b_4_10·b_1_22·a_3_6 + b_2_33·b_2_43·b_1_22·a_3_6
       + b_2_33·b_2_44·a_3_6 + b_2_34·b_4_10·b_1_22·a_3_6 + b_2_34·b_2_4·a_7_15
       + b_2_34·b_2_4·a_7_20 + b_2_34·b_2_4·b_1_24·a_3_6 + b_2_35·a_7_20
       + b_2_35·b_1_24·a_3_6 + b_2_37·a_3_6 + b_4_10·c_8_44·a_5_13
       + b_4_10·c_8_44·b_1_22·a_3_6 + b_2_4·c_8_44·b_1_24·a_3_6 + b_2_42·c_8_44·a_5_13
       + b_2_3·c_8_44·b_1_24·a_3_6 + b_2_3·b_2_4·c_8_44·a_5_13 + b_2_32·c_8_44·a_5_13
  143. a_8_21·a_9_25
  144. a_9_252

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 18.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_8_44, a Duflot regular element of degree 8
    2. b_1_24 + b_2_42 + b_2_3·b_2_4 + b_2_32, an element of degree 4
    3. b_2_42·b_1_22 + b_2_3·b_2_4·b_1_22 + b_2_3·b_2_42 + b_2_32·b_1_22
         + b_2_32·b_2_4, an element of degree 6
    4. b_1_22, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, 4, 8, 14, 16].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_3 → 0, an element of degree 2
  5. b_2_4 → 0, an element of degree 2
  6. a_3_6 → 0, an element of degree 3
  7. a_4_6 → 0, an element of degree 4
  8. a_4_7 → 0, an element of degree 4
  9. b_4_10 → 0, an element of degree 4
  10. a_5_13 → 0, an element of degree 5
  11. b_5_14 → 0, an element of degree 5
  12. b_5_15 → 0, an element of degree 5
  13. b_5_16 → 0, an element of degree 5
  14. a_7_20 → 0, an element of degree 7
  15. a_7_15 → 0, an element of degree 7
  16. a_8_21 → 0, an element of degree 8
  17. a_8_22 → 0, an element of degree 8
  18. b_8_43 → 0, an element of degree 8
  19. c_8_44 → c_1_08, an element of degree 8
  20. a_9_25 → 0, an element of degree 9

Restriction map to a maximal el. ab. subgp. of rank 4

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_1, an element of degree 1
  4. b_2_3 → c_1_22 + c_1_1·c_1_2, an element of degree 2
  5. b_2_4 → c_1_32 + c_1_1·c_1_3, an element of degree 2
  6. a_3_6 → 0, an element of degree 3
  7. a_4_6 → 0, an element of degree 4
  8. a_4_7 → 0, an element of degree 4
  9. b_4_10 → c_1_34 + c_1_22·c_1_32 + c_1_24 + c_1_12·c_1_32 + c_1_12·c_1_22
       + c_1_02·c_1_12, an element of degree 4
  10. a_5_13 → 0, an element of degree 5
  11. b_5_14 → c_1_23·c_1_32 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_12·c_1_2·c_1_32
       + c_1_13·c_1_32 + c_1_13·c_1_2·c_1_3 + c_1_02·c_1_1·c_1_22
       + c_1_02·c_1_12·c_1_2, an element of degree 5
  12. b_5_15 → c_1_22·c_1_33 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_12·c_1_2·c_1_32
       + c_1_13·c_1_32 + c_1_13·c_1_2·c_1_3 + c_1_02·c_1_1·c_1_32
       + c_1_02·c_1_12·c_1_3 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  13. b_5_16 → c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32
       + c_1_02·c_1_1·c_1_32 + c_1_02·c_1_12·c_1_3, an element of degree 5
  14. a_7_20 → 0, an element of degree 7
  15. a_7_15 → 0, an element of degree 7
  16. a_8_21 → 0, an element of degree 8
  17. a_8_22 → 0, an element of degree 8
  18. b_8_43 → c_1_38 + c_1_23·c_1_35 + c_1_24·c_1_34 + c_1_25·c_1_33 + c_1_1·c_1_2·c_1_36
       + c_1_1·c_1_22·c_1_35 + c_1_1·c_1_23·c_1_34 + c_1_1·c_1_25·c_1_32
       + c_1_12·c_1_36 + c_1_12·c_1_2·c_1_35 + c_1_12·c_1_22·c_1_34
       + c_1_12·c_1_23·c_1_33 + c_1_13·c_1_35 + c_1_13·c_1_2·c_1_34
       + c_1_13·c_1_23·c_1_32 + c_1_14·c_1_34 + c_1_14·c_1_2·c_1_33
       + c_1_15·c_1_33 + c_1_15·c_1_2·c_1_32 + c_1_15·c_1_22·c_1_3 + c_1_16·c_1_32
       + c_1_16·c_1_2·c_1_3 + c_1_02·c_1_1·c_1_2·c_1_34 + c_1_02·c_1_1·c_1_24·c_1_3
       + c_1_02·c_1_12·c_1_34 + c_1_02·c_1_12·c_1_22·c_1_32
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_13·c_1_2·c_1_32
       + c_1_02·c_1_13·c_1_22·c_1_3 + c_1_02·c_1_14·c_1_22 + c_1_02·c_1_15·c_1_3
       + c_1_02·c_1_16 + c_1_04·c_1_1·c_1_2·c_1_32 + c_1_04·c_1_1·c_1_22·c_1_3
       + c_1_04·c_1_12·c_1_32 + c_1_04·c_1_12·c_1_2·c_1_3 + c_1_04·c_1_13·c_1_3
       + c_1_06·c_1_12, an element of degree 8
  19. c_8_44 → c_1_38 + c_1_23·c_1_35 + c_1_24·c_1_34 + c_1_25·c_1_33 + c_1_28
       + c_1_1·c_1_23·c_1_34 + c_1_1·c_1_24·c_1_33 + c_1_1·c_1_25·c_1_32
       + c_1_1·c_1_26·c_1_3 + c_1_12·c_1_22·c_1_34 + c_1_12·c_1_24·c_1_32
       + c_1_12·c_1_25·c_1_3 + c_1_12·c_1_26 + c_1_13·c_1_22·c_1_33
       + c_1_13·c_1_24·c_1_3 + c_1_13·c_1_25 + c_1_14·c_1_23·c_1_3 + c_1_15·c_1_23
       + c_1_16·c_1_32 + c_1_02·c_1_22·c_1_34 + c_1_02·c_1_24·c_1_32
       + c_1_02·c_1_1·c_1_2·c_1_34 + c_1_02·c_1_1·c_1_24·c_1_3
       + c_1_02·c_1_12·c_1_22·c_1_32 + c_1_02·c_1_12·c_1_24
       + c_1_02·c_1_14·c_1_32 + c_1_02·c_1_14·c_1_2·c_1_3 + c_1_02·c_1_15·c_1_3
       + c_1_02·c_1_15·c_1_2 + c_1_04·c_1_34 + c_1_04·c_1_22·c_1_32
       + c_1_04·c_1_24 + c_1_04·c_1_1·c_1_2·c_1_32 + c_1_04·c_1_1·c_1_22·c_1_3
       + c_1_04·c_1_12·c_1_2·c_1_3 + c_1_04·c_1_13·c_1_3 + c_1_04·c_1_13·c_1_2
       + c_1_08, an element of degree 8
  20. a_9_25 → 0, an element of degree 9

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128


Simon King
Department of Mathematics and Computer Science
Friedrich-Schiller-Universität Jena
07737 Jena
GERMANY
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46161
Fax: +49 (0)3641 9-46162
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Last change: 28.02.2009