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 A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2

Last change: 25.08.2009