Mod-2-Cohomology of group number 241004 of order 1920

About the group Ring generators Ring relations Completion information Restriction maps

General information on the group

  • The group order factors as 27 · 3 · 5.
  • It is non-abelian.
  • It has 2-Rank 4.
  • The centre of a Sylow 2-subgroup has rank 1.
  • Its Sylow 2-subgroup has 2 conjugacy classes of maximal elementary abelian subgroups, which are of rank 2 and 4, respectively.

Structure of the cohomology ring

The computation was based on 5 stability conditions for H*(Syl2(J2); GF(2)).

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    (1  −  t  +  t2) · (1  −  t  +  t2  +  2·t4  +  t9)
    (1  +  t) · ( − 1  +  t)4 · (1  +  t  +  t2) · (1  +  t2)2 · (1  +  t4)
  • The a-invariants are -∞,-∞,-5,-8,-4. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
  • 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

Ring generators

The cohomology ring has 21 minimal generators of maximal degree 10:

  1. b_2_0, an element of degree 2
  2. a_3_2, a nilpotent element of degree 3
  3. b_3_1, an element of degree 3
  4. b_3_0, an element of degree 3
  5. b_4_3, an element of degree 4
  6. b_4_1, an element of degree 4
  7. b_4_0, an element of degree 4
  8. a_5_4, a nilpotent element of degree 5
  9. b_5_1, an element of degree 5
  10. b_5_0, an element of degree 5
  11. b_6_1, an element of degree 6
  12. b_6_0, an element of degree 6
  13. a_7_10, a nilpotent element of degree 7
  14. b_7_4, an element of degree 7
  15. b_7_0, an element of degree 7
  16. c_8_2, a Duflot element of degree 8
  17. b_8_1, an element of degree 8
  18. b_8_0, an element of degree 8
  19. b_9_1, an element of degree 9
  20. b_9_0, an element of degree 9
  21. b_10_15, an element of degree 10

About the group Ring generators Ring relations Completion information Restriction maps

Ring relations

There are 158 minimal relations of maximal degree 20:

  1. b_2_0·a_3_2
  2. a_3_22
  3. a_3_2·b_3_0
  4. a_3_2·b_3_1
  5. b_3_12 + b_3_0·b_3_1 + b_3_02 + b_2_03
  6. b_2_0·a_5_4
  7. b_4_1·a_3_2
  8. b_4_3·a_3_2 + b_4_0·a_3_2
  9. b_4_3·b_3_0 + b_4_1·b_3_1 + b_4_0·b_3_0 + b_2_0·b_5_0
  10. b_4_3·b_3_1 + b_4_1·b_3_1 + b_4_1·b_3_0 + b_4_0·b_3_1 + b_2_0·b_5_1 + b_2_02·b_3_1
  11. a_3_2·a_5_4
  12. a_3_2·b_5_0
  13. a_3_2·b_5_1
  14. b_3_0·a_5_4
  15. b_3_1·a_5_4
  16. b_4_32 + b_4_1·b_4_3 + b_4_12 + b_4_0·b_4_1 + b_4_02 + b_2_0·b_3_0·b_3_1
       + b_2_0·b_3_02 + b_2_0·b_6_1 + b_2_0·b_6_0 + b_2_04
  17. b_3_0·b_5_0 + b_4_1·b_4_3 + b_4_0·b_4_1 + b_2_0·b_3_0·b_3_1 + b_2_0·b_3_02 + b_2_0·b_6_0
       + b_2_02·b_4_0 + b_2_04
  18. b_3_0·b_5_1 + b_4_1·b_4_3 + b_4_12 + b_4_0·b_4_1 + b_2_0·b_3_02 + b_2_0·b_6_0
       + b_2_02·b_4_1 + b_2_04
  19. b_3_1·b_5_0 + b_4_1·b_4_3 + b_4_12 + b_4_0·b_4_1 + b_2_0·b_3_0·b_3_1 + b_2_0·b_3_02
       + b_2_0·b_6_0 + b_2_04
  20. b_3_1·b_5_1 + b_4_12 + b_2_0·b_3_0·b_3_1 + b_2_0·b_3_02 + b_2_02·b_4_3 + b_2_04
  21. b_2_0·a_7_10
  22. b_4_1·a_5_4
  23. b_4_3·a_5_4 + b_4_0·a_5_4
  24. b_6_0·a_3_2
  25. b_6_1·a_3_2
  26. b_4_3·b_5_0 + b_4_1·b_5_1 + b_4_0·b_5_0 + b_2_0·b_7_0 + b_2_0·b_4_0·b_3_0 + b_2_02·b_5_0
  27. b_4_3·b_5_1 + b_4_1·b_5_1 + b_4_1·b_5_0 + b_4_0·b_5_1 + b_2_0·b_7_4 + b_2_0·b_4_1·b_3_0
       + b_2_02·b_5_1 + b_2_03·b_3_1
  28. b_6_1·b_3_0 + b_2_0·b_7_0 + b_2_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_3_1
  29. b_6_1·b_3_1 + b_2_0·b_7_4 + b_2_0·b_4_0·b_3_0 + b_2_02·b_5_0
  30. b_3_03 + b_6_0·b_3_1 + b_4_1·b_5_1 + b_2_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_3_0
       + b_2_02·b_5_0 + b_2_03·b_3_1 + b_2_03·b_3_0
  31. b_3_02·b_3_1 + b_6_0·b_3_1 + b_6_0·b_3_0 + b_4_1·b_5_1 + b_4_1·b_5_0 + b_2_0·b_4_1·b_3_1
       + b_2_0·b_4_0·b_3_1 + b_2_03·b_3_1
  32. a_3_2·a_7_10
  33. a_5_42
  34. a_3_2·b_7_0
  35. a_3_2·b_7_4
  36. b_3_0·a_7_10
  37. b_3_1·a_7_10
  38. a_5_4·b_5_0
  39. a_5_4·b_5_1
  40. b_4_1·b_6_1 + b_2_0·b_8_1 + b_2_0·b_8_0 + b_2_0·b_4_1·b_4_3 + b_2_0·b_4_12
       + b_2_0·b_4_0·b_4_3 + b_2_0·b_4_02 + b_2_02·b_3_0·b_3_1 + b_2_02·b_3_02
       + b_2_02·b_6_0 + b_2_05
  41. b_4_3·b_6_1 + b_4_0·b_6_1 + b_2_0·b_8_0 + b_2_0·b_4_1·b_4_3 + b_2_0·b_4_0·b_4_3
       + b_2_0·b_4_0·b_4_1 + b_2_02·b_6_1 + b_2_02·b_6_0
  42. b_3_0·b_7_0 + b_4_3·b_6_0 + b_4_1·b_3_0·b_3_1 + b_4_1·b_3_02 + b_4_0·b_3_02
       + b_4_0·b_6_0 + b_2_0·b_8_1 + b_2_0·b_8_0 + b_2_0·b_4_12 + b_2_0·b_4_0·b_4_1
       + b_2_03·b_4_3 + b_2_03·b_4_1 + b_2_03·b_4_0
  43. b_3_0·b_7_4 + b_4_3·b_6_0 + b_4_1·b_3_0·b_3_1 + b_4_1·b_6_0 + b_4_0·b_6_0 + b_2_0·b_8_1
       + b_2_0·b_8_0 + b_2_0·b_4_12 + b_2_0·b_4_0·b_4_3 + b_2_0·b_4_02 + b_2_02·b_3_0·b_3_1
       + b_2_02·b_3_02 + b_2_02·b_6_0 + b_2_03·b_4_3 + b_2_05
  44. b_3_1·b_7_0 + b_4_3·b_6_0 + b_4_1·b_3_02 + b_4_1·b_6_0 + b_4_0·b_3_0·b_3_1 + b_4_0·b_6_0
       + b_2_0·b_8_1 + b_2_0·b_8_0 + b_2_0·b_4_1·b_4_3 + b_2_0·b_4_12 + b_2_0·b_4_0·b_4_3
       + b_2_0·b_4_0·b_4_1 + b_2_0·b_4_02 + b_2_03·b_4_3 + b_2_03·b_4_1
  45. b_3_1·b_7_4 + b_4_1·b_3_0·b_3_1 + b_4_1·b_3_02 + b_4_1·b_6_0 + b_2_0·b_4_12
       + b_2_0·b_4_0·b_4_3 + b_2_0·b_4_0·b_4_1 + b_2_0·b_4_02 + b_2_02·b_3_0·b_3_1
       + b_2_02·b_3_02 + b_2_02·b_6_1 + b_2_02·b_6_0 + b_2_03·b_4_1 + b_2_05
  46. b_5_02 + b_4_3·b_6_0 + b_4_1·b_3_02 + b_4_0·b_6_0 + b_2_0·b_8_1 + b_2_0·b_8_0
       + b_2_0·b_4_1·b_4_3 + b_2_02·b_3_0·b_3_1 + b_2_02·b_3_02 + b_2_02·b_6_0
       + b_2_03·b_4_3 + b_2_03·b_4_1 + b_2_05
  47. b_5_0·b_5_1 + b_4_3·b_6_0 + b_4_1·b_3_0·b_3_1 + b_4_1·b_6_0 + b_4_0·b_6_0 + b_2_0·b_8_1
       + b_2_0·b_8_0 + b_2_0·b_4_12 + b_2_0·b_4_0·b_4_3 + b_2_0·b_4_02 + b_2_03·b_4_3
  48. b_5_12 + b_4_1·b_3_0·b_3_1 + b_4_1·b_3_02 + b_4_1·b_6_0 + b_2_0·b_4_0·b_4_3
       + b_2_0·b_4_0·b_4_1 + b_2_0·b_4_02 + b_2_02·b_6_1 + b_2_02·b_6_0 + b_2_03·b_4_1
  49. b_4_1·a_7_10
  50. b_4_3·a_7_10 + b_4_0·a_7_10
  51. b_6_0·a_5_4
  52. b_6_1·a_5_4
  53. b_8_0·a_3_2 + b_4_02·a_3_2
  54. b_8_1·a_3_2 + b_4_02·a_3_2
  55. b_4_3·b_7_0 + b_4_1·b_7_4 + b_4_12·b_3_1 + b_4_12·b_3_0 + b_4_0·b_7_0
       + b_4_0·b_4_1·b_3_1 + b_2_0·b_9_0 + b_2_0·b_4_1·b_5_0 + b_2_0·b_4_0·b_5_1
       + b_2_0·b_4_0·b_5_0 + b_2_02·b_7_0 + b_2_02·b_4_1·b_3_1 + b_2_02·b_4_0·b_3_1
       + b_2_02·b_4_0·b_3_0 + b_2_03·b_5_0
  56. b_4_3·b_7_4 + b_4_1·b_7_4 + b_4_1·b_7_0 + b_4_12·b_3_1 + b_4_0·b_7_4 + b_4_0·b_4_1·b_3_0
       + b_2_0·b_9_1 + b_2_0·b_6_0·b_3_0 + b_2_0·b_4_1·b_5_1 + b_2_02·b_4_1·b_3_0
       + b_2_02·b_4_0·b_3_0 + b_2_03·b_5_1 + b_2_03·b_5_0 + b_2_04·b_3_1
  57. b_6_0·b_5_0 + b_4_1·b_7_0 + b_4_12·b_3_1 + b_4_12·b_3_0 + b_4_0·b_4_1·b_3_0
       + b_2_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_5_1 + b_2_0·b_4_0·b_5_0 + b_2_02·b_7_0
       + b_2_02·b_4_0·b_3_1
  58. b_6_0·b_5_1 + b_4_1·b_7_4 + b_4_12·b_3_1 + b_2_0·b_6_0·b_3_1 + b_2_0·b_4_1·b_5_1
       + b_2_0·b_4_0·b_5_0 + b_2_02·b_7_0 + b_2_02·b_4_1·b_3_1 + b_2_02·b_4_1·b_3_0
       + b_2_02·b_4_0·b_3_1 + b_2_02·b_4_0·b_3_0 + b_2_03·b_5_1 + b_2_03·b_5_0
       + b_2_04·b_3_1
  59. b_6_1·b_5_0 + b_2_0·b_9_0 + b_2_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_5_0 + b_2_02·b_7_0
       + b_2_02·b_4_0·b_3_0 + b_2_03·b_5_0
  60. b_6_1·b_5_1 + b_2_0·b_9_1 + b_2_0·b_6_0·b_3_0 + b_2_0·b_4_1·b_5_0 + b_2_0·b_4_0·b_5_0
       + b_2_02·b_7_4 + b_2_02·b_7_0 + b_2_02·b_4_1·b_3_0 + b_2_02·b_4_0·b_3_0
       + b_2_03·b_5_1 + b_2_03·b_5_0 + b_2_04·b_3_1
  61. b_8_0·b_3_0 + b_4_1·b_7_4 + b_4_12·b_3_1 + b_4_0·b_4_1·b_3_1 + b_4_0·b_4_1·b_3_0
       + b_4_02·b_3_0 + b_2_0·b_9_0 + b_2_0·b_6_0·b_3_0 + b_2_0·b_4_1·b_5_1
       + b_2_02·b_4_1·b_3_1 + b_2_02·b_4_0·b_3_1 + b_2_02·b_4_0·b_3_0 + b_2_03·b_5_0
  62. b_8_0·b_3_1 + b_4_1·b_7_4 + b_4_1·b_7_0 + b_4_12·b_3_0 + b_4_02·b_3_1 + b_2_0·b_9_1
       + b_2_0·b_6_0·b_3_1 + b_2_0·b_6_0·b_3_0 + b_2_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_5_1
       + b_2_0·b_4_0·b_5_0 + b_2_02·b_7_4 + b_2_02·b_7_0 + b_2_02·b_4_1·b_3_1
       + b_2_02·b_4_1·b_3_0 + b_2_02·b_4_0·b_3_1 + b_2_02·b_4_0·b_3_0 + b_2_03·b_5_1
       + b_2_03·b_5_0 + b_2_04·b_3_1
  63. b_8_1·b_3_0 + b_4_1·b_7_4 + b_4_1·b_7_0 + b_4_12·b_3_1 + b_4_12·b_3_0
       + b_4_0·b_4_1·b_3_1 + b_4_02·b_3_0 + b_2_0·b_9_0 + b_2_0·b_6_0·b_3_0 + b_2_0·b_4_1·b_5_1
       + b_2_0·b_4_0·b_5_0 + b_2_02·b_4_1·b_3_1
  64. b_8_1·b_3_1 + b_4_1·b_7_0 + b_4_02·b_3_1 + b_2_0·b_9_1 + b_2_0·b_6_0·b_3_1
       + b_2_0·b_6_0·b_3_0 + b_2_0·b_4_1·b_5_1 + b_2_0·b_4_1·b_5_0 + b_2_0·b_4_0·b_5_0
       + b_2_02·b_7_4 + b_2_02·b_7_0 + b_2_02·b_4_1·b_3_1 + b_2_02·b_4_1·b_3_0
       + b_2_03·b_5_1 + b_2_04·b_3_1
  65. a_5_4·a_7_10
  66. a_3_2·b_9_0
  67. a_3_2·b_9_1
  68. a_5_4·b_7_0
  69. a_5_4·b_7_4
  70. b_5_0·a_7_10
  71. b_5_1·a_7_10
  72. b_4_3·b_8_0 + b_4_1·b_8_1 + b_4_12·b_4_3 + b_4_0·b_8_0 + b_4_0·b_4_1·b_4_3
       + b_4_0·b_4_12 + b_4_02·b_4_3 + b_4_03 + b_2_0·b_10_15 + b_2_0·b_4_3·b_6_0
       + b_2_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_1·b_6_0
       + b_2_0·b_4_0·b_3_0·b_3_1 + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1 + b_2_02·b_4_02
       + b_2_03·b_6_0 + b_2_04·b_4_1 + b_2_02·c_8_2
  73. b_4_3·b_8_1 + b_4_1·b_8_1 + b_4_1·b_8_0 + b_4_13 + b_4_0·b_8_1 + b_4_0·b_4_12
       + b_4_02·b_4_3 + b_4_03 + b_2_0·b_10_15 + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_1·b_6_0
       + b_2_0·b_4_0·b_3_02 + b_2_0·b_4_0·b_6_1 + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1
       + b_2_02·b_4_12 + b_2_02·b_4_02 + b_2_03·b_6_0 + b_2_04·b_4_3 + b_2_04·b_4_1
       + b_2_04·b_4_0 + b_2_02·c_8_2
  74. b_6_0·b_6_1 + b_2_0·b_10_15 + b_2_0·b_4_1·b_6_0 + b_2_0·b_4_0·b_3_0·b_3_1
       + b_2_0·b_4_0·b_3_02 + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1 + b_2_02·b_4_1·b_4_3
       + b_2_02·b_4_12 + b_2_02·b_4_0·b_4_1 + b_2_02·b_4_02 + b_2_03·b_3_0·b_3_1
       + b_2_03·b_3_02 + b_2_04·b_4_0 + b_2_06
  75. b_6_0·b_3_0·b_3_1 + b_6_0·b_3_02 + b_6_02 + b_4_1·b_8_1 + b_4_1·b_8_0 + b_4_12·b_4_3
       + b_4_0·b_4_12 + b_2_0·b_4_3·b_6_0 + b_2_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_1·b_6_0
       + b_2_0·b_4_0·b_3_02 + b_2_02·b_8_1 + b_2_02·b_8_0 + b_2_02·b_4_1·b_4_3
       + b_2_02·b_4_12 + b_2_02·b_4_0·b_4_1 + b_2_02·b_4_02 + b_2_03·b_6_0
       + b_2_04·b_4_3 + b_2_04·b_4_0
  76. b_6_12 + b_2_0·b_4_0·b_6_1 + b_2_02·b_8_0 + b_2_02·b_4_1·b_4_3 + b_2_02·b_4_12
       + b_2_02·b_4_02 + b_2_03·b_3_0·b_3_1 + b_2_03·b_3_02 + b_2_06 + b_2_02·c_8_2
  77. b_3_0·b_9_0 + b_4_1·b_8_0 + b_4_13 + b_4_02·b_4_1 + b_2_0·b_10_15 + b_2_0·b_4_3·b_6_0
       + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_0·b_3_0·b_3_1 + b_2_0·b_4_0·b_6_1
       + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1 + b_2_02·b_4_0·b_4_1 + b_2_03·b_3_0·b_3_1
       + b_2_03·b_3_02 + b_2_03·b_6_1 + b_2_04·b_4_3 + b_2_04·b_4_1 + b_2_06
  78. b_3_0·b_9_1 + b_6_0·b_3_02 + b_4_1·b_8_1 + b_4_12·b_4_3 + b_4_13 + b_4_0·b_4_1·b_4_3
       + b_2_0·b_10_15 + b_2_0·b_4_3·b_6_0 + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_1·b_6_0
       + b_2_0·b_4_0·b_3_0·b_3_1 + b_2_0·b_4_0·b_3_02 + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_0
       + b_2_02·b_4_1·b_4_3 + b_2_02·b_4_12 + b_2_02·b_4_0·b_4_3 + b_2_02·b_4_02
       + b_2_03·b_6_1 + b_2_03·b_6_0 + b_2_04·b_4_3 + b_2_04·b_4_1 + b_2_04·b_4_0
  79. b_3_1·b_9_0 + b_4_1·b_8_1 + b_4_0·b_4_1·b_4_3 + b_2_0·b_10_15 + b_2_0·b_4_3·b_6_0
       + b_2_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_1·b_6_0 + b_2_0·b_4_0·b_3_0·b_3_1
       + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1 + b_2_02·b_4_0·b_4_3 + b_2_02·b_4_0·b_4_1
       + b_2_03·b_3_0·b_3_1 + b_2_03·b_3_02 + b_2_03·b_6_1 + b_2_04·b_4_3 + b_2_06
  80. b_3_1·b_9_1 + b_6_0·b_3_02 + b_6_02 + b_4_12·b_4_3 + b_4_0·b_4_12
       + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_0·b_6_1 + b_2_02·b_8_0 + b_2_02·b_4_1·b_4_3
       + b_2_02·b_4_12 + b_2_02·b_4_0·b_4_1 + b_2_03·b_6_1 + b_2_04·b_4_3 + b_2_04·b_4_1
  81. b_5_0·b_7_0 + b_4_1·b_8_0 + b_4_13 + b_4_0·b_4_12 + b_4_02·b_4_1 + b_2_0·b_10_15
       + b_2_0·b_4_0·b_3_0·b_3_1 + b_2_0·b_4_0·b_6_1 + b_2_02·b_8_0 + b_2_02·b_4_1·b_4_3
       + b_2_02·b_4_0·b_4_1 + b_2_02·b_4_02 + b_2_03·b_6_1 + b_2_03·b_6_0
  82. b_5_0·b_7_4 + b_4_1·b_8_1 + b_4_13 + b_4_0·b_4_1·b_4_3 + b_4_0·b_4_12 + b_2_0·b_10_15
       + b_2_0·b_4_3·b_6_0 + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_0·b_3_0·b_3_1
       + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1 + b_2_02·b_4_0·b_4_1 + b_2_03·b_3_0·b_3_1
       + b_2_03·b_3_02 + b_2_03·b_6_1 + b_2_04·b_4_3 + b_2_04·b_4_1 + b_2_06
  83. b_5_1·b_7_0 + b_4_1·b_8_1 + b_4_02·b_4_1 + b_2_0·b_10_15 + b_2_0·b_4_3·b_6_0
       + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_1·b_6_0 + b_2_0·b_4_0·b_3_0·b_3_1
       + b_2_0·b_4_0·b_3_02 + b_2_02·b_8_0 + b_2_02·b_4_0·b_4_3 + b_2_02·b_4_02
       + b_2_03·b_3_0·b_3_1 + b_2_03·b_3_02 + b_2_03·b_6_1 + b_2_04·b_4_3 + b_2_04·b_4_1
       + b_2_04·b_4_0 + b_2_06
  84. b_5_1·b_7_4 + b_4_1·b_8_1 + b_4_1·b_8_0 + b_4_12·b_4_3 + b_4_13 + b_4_0·b_4_12
       + b_2_0·b_4_3·b_6_0 + b_2_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_1·b_6_0
       + b_2_0·b_4_0·b_3_0·b_3_1 + b_2_0·b_4_0·b_3_02 + b_2_0·b_4_0·b_6_1 + b_2_02·b_8_1
       + b_2_02·b_4_12 + b_2_02·b_4_0·b_4_3 + b_2_03·b_6_0 + b_2_04·b_4_3 + b_2_04·b_4_0
  85. b_6_0·a_7_10
  86. b_6_1·a_7_10
  87. b_8_0·a_5_4 + b_4_02·a_5_4
  88. b_8_1·a_5_4 + b_4_02·a_5_4
  89. b_10_15·a_3_2
  90. b_4_3·b_9_0 + b_4_1·b_9_1 + b_4_1·b_6_0·b_3_0 + b_4_12·b_5_1 + b_4_0·b_9_0
       + b_4_0·b_4_1·b_5_1 + b_4_0·b_4_1·b_5_0 + b_2_0·b_4_1·b_7_4 + b_2_0·b_4_1·b_7_0
       + b_2_0·b_4_12·b_3_1 + b_2_0·b_4_0·b_7_4 + b_2_0·b_4_0·b_7_0 + b_2_0·b_4_0·b_4_1·b_3_1
       + b_2_02·b_9_0 + b_2_02·b_4_1·b_5_1 + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_1
       + b_2_02·b_4_0·b_5_0 + b_2_03·b_7_0 + b_2_03·b_4_0·b_3_1 + b_2_03·b_4_0·b_3_0
       + b_2_04·b_5_0 + b_2_0·c_8_2·b_3_0
  91. b_4_3·b_9_1 + b_4_1·b_9_1 + b_4_1·b_9_0 + b_4_1·b_6_0·b_3_1 + b_4_1·b_6_0·b_3_0
       + b_4_12·b_5_0 + b_4_0·b_9_1 + b_4_0·b_4_1·b_5_1 + b_2_0·b_4_1·b_7_0
       + b_2_0·b_4_12·b_3_1 + b_2_0·b_4_12·b_3_0 + b_2_0·b_4_0·b_7_4
       + b_2_0·b_4_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_1
       + b_2_02·b_9_1 + b_2_02·b_6_0·b_3_0 + b_2_02·b_4_1·b_5_1 + b_2_02·b_4_1·b_5_0
       + b_2_02·b_4_0·b_5_1 + b_2_03·b_4_1·b_3_0 + b_2_03·b_4_0·b_3_1 + b_2_04·b_5_1
       + b_2_05·b_3_1 + b_2_0·c_8_2·b_3_1
  92. b_6_0·b_7_0 + b_4_1·b_9_0 + b_4_1·b_6_0·b_3_1 + b_4_12·b_5_1 + b_4_12·b_5_0
       + b_4_0·b_6_0·b_3_0 + b_4_0·b_4_1·b_5_1 + b_2_0·b_4_1·b_7_0 + b_2_0·b_4_12·b_3_1
       + b_2_0·b_4_0·b_7_4 + b_2_0·b_4_0·b_7_0 + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_0
       + b_2_02·b_9_0 + b_2_02·b_4_1·b_5_1 + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_0
       + b_2_03·b_4_1·b_3_1 + b_2_03·b_4_0·b_3_0 + b_2_04·b_5_0
  93. b_6_0·b_7_4 + b_4_1·b_9_1 + b_4_1·b_6_0·b_3_0 + b_4_12·b_5_1 + b_4_12·b_5_0
       + b_2_0·b_4_12·b_3_1 + b_2_0·b_4_12·b_3_0 + b_2_0·b_4_0·b_7_0
       + b_2_0·b_4_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_0
       + b_2_02·b_9_0 + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_0 + b_2_03·b_7_4
  94. b_6_1·b_7_0 + b_2_0·b_4_12·b_3_0 + b_2_0·b_4_0·b_7_4 + b_2_0·b_4_0·b_7_0
       + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_1 + b_2_0·b_4_02·b_3_0 + b_2_02·b_9_0
       + b_2_02·b_4_1·b_5_1 + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_0 + b_2_03·b_4_1·b_3_1
       + b_2_0·c_8_2·b_3_0
  95. b_6_1·b_7_4 + b_2_0·b_4_1·b_7_4 + b_2_0·b_4_1·b_7_0 + b_2_0·b_4_0·b_7_4
       + b_2_0·b_4_0·b_7_0 + b_2_0·b_4_02·b_3_1 + b_2_0·b_4_02·b_3_0 + b_2_02·b_9_1
       + b_2_02·b_9_0 + b_2_02·b_6_0·b_3_0 + b_2_02·b_4_0·b_5_1 + b_2_02·b_4_0·b_5_0
       + b_2_03·b_7_4 + b_2_03·b_4_1·b_3_1 + b_2_03·b_4_1·b_3_0 + b_2_03·b_4_0·b_3_1
       + b_2_03·b_4_0·b_3_0 + b_2_04·b_5_1 + b_2_04·b_5_0 + b_2_05·b_3_1 + b_2_0·c_8_2·b_3_1
  96. b_8_0·b_5_0 + b_4_1·b_9_1 + b_4_1·b_6_0·b_3_0 + b_4_12·b_5_1 + b_4_12·b_5_0
       + b_4_0·b_4_1·b_5_1 + b_4_0·b_4_1·b_5_0 + b_4_02·b_5_0 + b_2_0·b_4_1·b_7_4
       + b_2_0·b_4_1·b_7_0 + b_2_0·b_4_12·b_3_1 + b_2_0·b_4_12·b_3_0 + b_2_0·b_4_0·b_7_4
       + b_2_0·b_4_0·b_7_0 + b_2_0·b_4_0·b_4_1·b_3_1 + b_2_02·b_9_0 + b_2_02·b_4_1·b_5_1
       + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_1 + b_2_02·b_4_0·b_5_0 + b_2_03·b_7_0
       + b_2_03·b_4_0·b_3_1 + b_2_0·c_8_2·b_3_0
  97. b_8_0·b_5_1 + b_4_1·b_9_1 + b_4_1·b_9_0 + b_4_1·b_6_0·b_3_0 + b_4_0·b_4_1·b_5_1
       + b_4_0·b_4_1·b_5_0 + b_4_02·b_5_1 + b_2_0·b_4_0·b_7_0 + b_2_0·b_4_0·b_4_1·b_3_1
       + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_1 + b_2_0·b_4_02·b_3_0 + b_2_02·b_9_1
       + b_2_02·b_9_0 + b_2_02·b_6_0·b_3_1 + b_2_02·b_6_0·b_3_0 + b_2_02·b_4_1·b_5_1
       + b_2_03·b_7_0 + b_2_03·b_4_0·b_3_1 + b_2_03·b_4_0·b_3_0 + b_2_04·b_5_0
       + b_2_0·c_8_2·b_3_1
  98. b_8_1·b_5_0 + b_4_1·b_9_1 + b_4_1·b_9_0 + b_4_1·b_6_0·b_3_0 + b_4_12·b_5_1
       + b_4_0·b_4_1·b_5_0 + b_4_02·b_5_0 + b_2_0·b_4_1·b_7_4 + b_2_0·b_4_12·b_3_0
       + b_2_0·b_4_0·b_7_4 + b_2_0·b_4_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_4_1·b_3_0
       + b_2_0·b_4_02·b_3_0 + b_2_02·b_9_0 + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_0
       + b_2_03·b_4_0·b_3_0 + b_2_04·b_5_0 + b_2_0·c_8_2·b_3_0
  99. b_8_1·b_5_1 + b_4_1·b_9_0 + b_4_0·b_4_1·b_5_1 + b_4_0·b_4_1·b_5_0 + b_4_02·b_5_1
       + b_2_0·b_4_1·b_7_4 + b_2_0·b_4_1·b_7_0 + b_2_0·b_4_0·b_7_4 + b_2_0·b_4_0·b_7_0
       + b_2_0·b_4_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_1
       + b_2_0·b_4_02·b_3_0 + b_2_02·b_9_1 + b_2_02·b_9_0 + b_2_02·b_6_0·b_3_1
       + b_2_02·b_6_0·b_3_0 + b_2_02·b_4_1·b_5_1 + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_1
       + b_2_02·b_4_0·b_5_0 + b_2_03·b_4_1·b_3_1 + b_2_03·b_4_0·b_3_0 + b_2_04·b_5_0
       + b_2_0·c_8_2·b_3_1
  100. b_10_15·b_3_0 + b_4_1·b_9_0 + b_4_1·b_6_0·b_3_0 + b_4_12·b_5_1 + b_4_12·b_5_0
       + b_4_0·b_6_0·b_3_1 + b_4_0·b_6_0·b_3_0 + b_4_0·b_4_1·b_5_1 + b_4_0·b_4_1·b_5_0
       + b_2_0·b_4_1·b_7_4 + b_2_0·b_4_12·b_3_1 + b_2_0·b_4_0·b_7_4 + b_2_0·b_4_0·b_7_0
       + b_2_0·b_4_0·b_4_1·b_3_1 + b_2_0·b_4_0·b_4_1·b_3_0 + b_2_0·b_4_02·b_3_1
       + b_2_02·b_4_1·b_5_0 + b_2_02·b_4_0·b_5_0 + b_2_03·b_4_0·b_3_1
  101. b_10_15·b_3_1 + b_4_1·b_9_1 + b_4_1·b_6_0·b_3_1 + b_4_1·b_6_0·b_3_0 + b_4_12·b_5_1
       + b_4_12·b_5_0 + b_4_0·b_6_0·b_3_0 + b_4_0·b_4_1·b_5_1 + b_2_0·b_4_12·b_3_0
       + b_2_0·b_4_0·b_7_0 + b_2_02·b_9_1 + b_2_02·b_9_0 + b_2_02·b_6_0·b_3_0
       + b_2_02·b_4_0·b_5_1 + b_2_03·b_4_1·b_3_1 + b_2_03·b_4_1·b_3_0 + b_2_03·b_4_0·b_3_1
       + b_2_03·b_4_0·b_3_0 + b_2_04·b_5_1 + b_2_04·b_5_0 + b_2_05·b_3_1
  102. a_7_102
  103. a_5_4·b_9_0
  104. a_5_4·b_9_1
  105. a_7_10·b_7_0
  106. a_7_10·b_7_4
  107. b_4_1·b_10_15 + b_4_1·b_4_3·b_6_0 + b_4_12·b_3_02 + b_4_0·b_4_3·b_6_0
       + b_4_0·b_4_1·b_3_02 + b_4_02·b_3_0·b_3_1 + b_4_02·b_3_02 + b_4_02·b_6_0
       + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_0·b_8_0 + b_2_0·b_4_0·b_4_1·b_4_3
       + b_2_0·b_4_02·b_4_1 + b_2_0·b_4_03 + b_2_02·b_4_1·b_3_0·b_3_1
       + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_1·b_6_0 + b_2_02·b_4_0·b_3_0·b_3_1
       + b_2_02·b_4_0·b_3_02 + b_2_03·b_8_1 + b_2_03·b_8_0 + b_2_03·b_4_1·b_4_3
       + b_2_03·b_4_0·b_4_3 + b_2_03·b_4_0·b_4_1 + b_2_04·b_3_0·b_3_1 + b_2_04·b_3_02
       + b_2_04·b_6_0 + b_2_05·b_4_1 + b_2_05·b_4_0 + b_2_07 + c_8_2·b_3_0·b_3_1
       + c_8_2·b_3_02
  108. b_4_3·b_10_15 + b_4_1·b_4_3·b_6_0 + b_4_12·b_3_0·b_3_1 + b_4_12·b_6_0 + b_4_0·b_10_15
       + b_4_0·b_4_1·b_3_0·b_3_1 + b_4_02·b_3_02 + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_12·b_4_3
       + b_2_0·b_4_13 + b_2_0·b_4_0·b_8_0 + b_2_0·b_4_0·b_4_1·b_4_3 + b_2_0·b_4_0·b_4_12
       + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_02·b_10_15 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_0·b_3_1 + b_2_02·b_4_1·b_6_0 + b_2_02·b_4_0·b_3_02
       + b_2_02·b_4_0·b_6_1 + b_2_02·b_4_0·b_6_0 + b_2_03·b_4_0·b_4_3 + b_2_03·b_4_0·b_4_1
       + b_2_03·b_4_02 + b_2_04·b_3_0·b_3_1 + b_2_04·b_3_02 + b_2_04·b_6_1
       + b_2_04·b_6_0 + b_2_05·b_4_3 + b_2_05·b_4_0 + b_2_07 + c_8_2·b_3_02
       + b_2_0·b_4_1·c_8_2 + b_2_03·c_8_2
  109. b_6_0·b_8_0 + b_4_1·b_4_3·b_6_0 + b_4_12·b_3_0·b_3_1 + b_4_12·b_6_0
       + b_4_0·b_4_1·b_3_0·b_3_1 + b_4_0·b_4_1·b_3_02 + b_4_02·b_3_02 + b_4_02·b_6_0
       + b_2_0·b_6_02 + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_12·b_4_3 + b_2_0·b_4_13
       + b_2_0·b_4_0·b_8_0 + b_2_0·b_4_0·b_4_1·b_4_3 + b_2_0·b_4_0·b_4_12
       + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_02·b_10_15 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_0·b_3_0·b_3_1 + b_2_02·b_4_0·b_3_02
       + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1 + b_2_03·b_8_0 + b_2_03·b_4_0·b_4_3
       + b_2_03·b_4_0·b_4_1 + b_2_04·b_3_0·b_3_1 + b_2_04·b_3_02 + b_2_04·b_6_1
       + b_2_04·b_6_0 + b_2_05·b_4_3 + b_2_05·b_4_1 + b_2_05·b_4_0 + b_2_07 + c_8_2·b_3_02
       + b_2_0·b_4_1·c_8_2
  110. b_6_0·b_8_1 + b_4_1·b_4_3·b_6_0 + b_4_12·b_3_0·b_3_1 + b_4_12·b_3_02 + b_4_12·b_6_0
       + b_4_0·b_4_1·b_3_02 + b_4_0·b_4_1·b_6_0 + b_4_02·b_3_0·b_3_1 + b_4_02·b_6_0
       + b_2_0·b_6_02 + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_12·b_4_3
       + b_2_0·b_4_0·b_4_12 + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_0·b_4_03
       + b_2_02·b_10_15 + b_2_02·b_4_1·b_3_0·b_3_1 + b_2_02·b_4_1·b_3_02
       + b_2_02·b_4_0·b_3_02 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1 + b_2_03·b_8_0
       + b_2_03·b_4_12 + b_2_03·b_4_02 + b_2_04·b_6_1 + b_2_05·b_4_1 + b_2_05·b_4_0
       + c_8_2·b_3_0·b_3_1 + b_2_0·b_4_1·c_8_2
  111. b_6_1·b_8_0 + b_4_02·b_6_1 + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_13
       + b_2_0·b_4_0·b_4_1·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_0·b_3_02 + b_2_02·b_4_0·b_6_1 + b_2_03·b_8_0
       + b_2_03·b_4_12 + b_2_03·b_4_0·b_4_1 + b_2_03·b_4_02 + b_2_04·b_6_0
       + b_2_05·b_4_3 + b_2_05·b_4_1 + b_2_05·b_4_0 + b_2_0·b_4_3·c_8_2 + b_2_0·b_4_0·c_8_2
  112. b_6_1·b_8_1 + b_4_02·b_6_1 + b_2_0·b_4_12·b_4_3 + b_2_0·b_4_13 + b_2_0·b_4_0·b_8_0
       + b_2_0·b_4_0·b_4_12 + b_2_0·b_4_02·b_4_3 + b_2_02·b_10_15 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_0·b_3_1 + b_2_03·b_4_1·b_4_3 + b_2_03·b_4_12 + b_2_04·b_6_1
       + b_2_05·b_4_3 + b_2_0·b_4_3·c_8_2 + b_2_0·b_4_1·c_8_2 + b_2_0·b_4_0·c_8_2
  113. b_5_0·b_9_0 + b_4_12·b_3_02 + b_4_0·b_4_1·b_3_02 + b_4_0·b_4_1·b_6_0
       + b_4_02·b_3_02 + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_12·b_4_3 + b_2_0·b_4_0·b_4_1·b_4_3
       + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_0·b_4_03 + b_2_02·b_10_15
       + b_2_02·b_4_0·b_3_02 + b_2_02·b_4_0·b_6_1 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_0
       + b_2_03·b_4_1·b_4_3 + b_2_03·b_4_12 + b_2_04·b_6_1 + b_2_04·b_6_0 + b_2_05·b_4_0
       + c_8_2·b_3_02
  114. b_5_0·b_9_1 + b_4_12·b_6_0 + b_4_0·b_4_3·b_6_0 + b_4_0·b_4_1·b_3_02
       + b_4_0·b_4_1·b_6_0 + b_4_02·b_3_0·b_3_1 + b_4_02·b_6_0 + b_2_0·b_4_0·b_8_1
       + b_2_0·b_4_0·b_8_0 + b_2_0·b_4_0·b_4_1·b_4_3 + b_2_0·b_4_02·b_4_3
       + b_2_0·b_4_02·b_4_1 + b_2_0·b_4_03 + b_2_02·b_10_15 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_1·b_6_0 + b_2_02·b_4_0·b_3_0·b_3_1
       + b_2_02·b_4_0·b_3_02 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1 + b_2_03·b_4_12
       + b_2_03·b_4_0·b_4_3 + b_2_03·b_4_0·b_4_1 + b_2_04·b_6_1 + b_2_04·b_6_0
       + b_2_05·b_4_3 + b_2_05·b_4_1 + b_2_05·b_4_0 + c_8_2·b_3_0·b_3_1
  115. b_5_1·b_9_0 + b_4_12·b_3_0·b_3_1 + b_4_0·b_4_3·b_6_0 + b_4_0·b_4_1·b_3_0·b_3_1
       + b_4_02·b_3_0·b_3_1 + b_4_02·b_6_0 + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_12·b_4_3
       + b_2_0·b_4_0·b_8_1 + b_2_0·b_4_0·b_8_0 + b_2_0·b_4_0·b_4_12 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_0·b_3_1 + b_2_02·b_4_0·b_6_1 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1
       + b_2_03·b_8_0 + b_2_03·b_4_0·b_4_3 + b_2_03·b_4_02 + b_2_04·b_3_0·b_3_1
       + b_2_04·b_3_02 + b_2_04·b_6_0 + b_2_05·b_4_3 + b_2_07 + c_8_2·b_3_0·b_3_1
  116. b_5_1·b_9_1 + b_4_1·b_4_3·b_6_0 + b_4_0·b_4_1·b_3_0·b_3_1 + b_4_02·b_3_0·b_3_1
       + b_4_02·b_3_02 + b_2_0·b_6_0·b_3_02 + b_2_0·b_6_02 + b_2_0·b_4_1·b_8_1
       + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_0·b_4_03
       + b_2_02·b_4_3·b_6_0 + b_2_02·b_4_1·b_3_0·b_3_1 + b_2_02·b_4_1·b_3_02
       + b_2_02·b_4_0·b_3_0·b_3_1 + b_2_02·b_4_0·b_6_1 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1
       + b_2_03·b_8_0 + b_2_03·b_4_1·b_4_3 + b_2_03·b_4_0·b_4_3 + b_2_03·b_4_0·b_4_1
       + b_2_04·b_6_0 + b_2_05·b_4_1 + c_8_2·b_3_0·b_3_1 + c_8_2·b_3_02 + b_2_03·c_8_2
  117. b_7_02 + b_4_1·b_4_3·b_6_0 + b_4_12·b_6_0 + b_4_0·b_4_3·b_6_0
       + b_4_0·b_4_1·b_3_0·b_3_1 + b_4_0·b_4_1·b_3_02 + b_4_0·b_4_1·b_6_0 + b_4_02·b_6_0
       + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_12·b_4_3 + b_2_0·b_4_13 + b_2_0·b_4_0·b_8_1
       + b_2_0·b_4_0·b_8_0 + b_2_0·b_4_0·b_4_1·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_02·b_10_15
       + b_2_02·b_4_3·b_6_0 + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_0·b_3_0·b_3_1
       + b_2_02·b_4_0·b_6_1 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1 + b_2_03·b_4_1·b_4_3
       + b_2_03·b_4_0·b_4_3 + b_2_04·b_3_0·b_3_1 + b_2_04·b_3_02 + b_2_04·b_6_1
       + b_2_05·b_4_3 + b_2_05·b_4_1 + b_2_07 + c_8_2·b_3_02
  118. b_7_0·b_7_4 + b_4_12·b_3_0·b_3_1 + b_4_0·b_4_1·b_3_0·b_3_1 + b_4_0·b_4_1·b_3_02
       + b_4_02·b_3_0·b_3_1 + b_2_0·b_4_1·b_8_1 + b_2_0·b_4_1·b_8_0 + b_2_0·b_4_12·b_4_3
       + b_2_0·b_4_13 + b_2_0·b_4_0·b_4_1·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_1 + b_2_03·b_8_0
       + b_2_03·b_4_0·b_4_3 + b_2_03·b_4_0·b_4_1 + b_2_03·b_4_02 + b_2_04·b_3_0·b_3_1
       + b_2_04·b_3_02 + b_2_04·b_6_0 + b_2_05·b_4_3 + b_2_05·b_4_1 + b_2_07
       + c_8_2·b_3_0·b_3_1
  119. b_7_42 + b_4_1·b_4_3·b_6_0 + b_4_12·b_3_0·b_3_1 + b_4_0·b_4_1·b_3_0·b_3_1
       + b_4_02·b_3_0·b_3_1 + b_4_02·b_3_02 + b_2_0·b_4_12·b_4_3 + b_2_0·b_4_13
       + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1 + b_2_0·b_4_03 + b_2_02·b_4_3·b_6_0
       + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_0·b_6_0 + b_2_03·b_8_0 + b_2_03·b_4_1·b_4_3
       + b_2_04·b_3_0·b_3_1 + b_2_04·b_3_02 + b_2_05·b_4_3 + b_2_05·b_4_1 + b_2_07
       + c_8_2·b_3_0·b_3_1 + c_8_2·b_3_02 + b_2_03·c_8_2
  120. b_8_0·a_7_10 + b_4_02·a_7_10
  121. b_8_1·a_7_10 + b_4_02·a_7_10
  122. b_10_15·a_5_4
  123. b_6_0·b_9_0 + b_4_12·b_7_0 + b_4_13·b_3_0 + b_4_0·b_4_1·b_7_4 + b_4_0·b_4_1·b_7_0
       + b_4_0·b_4_12·b_3_1 + b_4_0·b_4_12·b_3_0 + b_2_0·b_4_1·b_9_1
       + b_2_0·b_4_1·b_6_0·b_3_0 + b_2_0·b_4_12·b_5_1 + b_2_0·b_4_0·b_9_1 + b_2_0·b_4_0·b_9_0
       + b_2_0·b_4_0·b_6_0·b_3_0 + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_0·b_4_02·b_5_1
       + b_2_0·b_4_02·b_5_0 + b_2_02·b_4_1·b_7_4 + b_2_02·b_4_0·b_7_0
       + b_2_02·b_4_0·b_4_1·b_3_1 + b_2_02·b_4_02·b_3_0 + b_2_03·b_4_1·b_5_1
       + b_2_04·b_7_0 + b_2_04·b_4_0·b_3_0 + b_2_05·b_5_0 + b_4_1·c_8_2·b_3_0
       + b_2_02·c_8_2·b_3_0
  124. b_6_0·b_9_1 + b_6_02·b_3_0 + b_4_13·b_3_1 + b_4_13·b_3_0 + b_4_0·b_4_1·b_7_4
       + b_4_0·b_4_12·b_3_1 + b_4_0·b_4_12·b_3_0 + b_4_02·b_4_1·b_3_1
       + b_2_0·b_4_1·b_6_0·b_3_1 + b_2_0·b_4_1·b_6_0·b_3_0 + b_2_0·b_4_12·b_5_0
       + b_2_0·b_4_0·b_9_0 + b_2_0·b_4_0·b_6_0·b_3_0 + b_2_0·b_4_0·b_4_1·b_5_1
       + b_2_0·b_4_0·b_4_1·b_5_0 + b_2_0·b_4_02·b_5_1 + b_2_02·b_4_12·b_3_0
       + b_2_02·b_4_0·b_7_4 + b_2_02·b_4_0·b_7_0 + b_2_02·b_4_0·b_4_1·b_3_0
       + b_2_02·b_4_02·b_3_1 + b_2_03·b_9_1 + b_2_03·b_9_0 + b_2_03·b_6_0·b_3_0
       + b_2_03·b_4_0·b_5_0 + b_2_04·b_7_0 + b_2_04·b_4_1·b_3_1 + b_2_04·b_4_0·b_3_1
       + b_2_04·b_4_0·b_3_0 + b_2_05·b_5_0 + b_4_1·c_8_2·b_3_1 + b_2_02·c_8_2·b_3_0
  125. b_6_1·b_9_0 + b_2_0·b_4_12·b_5_0 + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_4_1·b_5_0
       + b_2_02·b_4_1·b_7_0 + b_2_02·b_4_12·b_3_1 + b_2_02·b_4_0·b_7_0
       + b_2_02·b_4_0·b_4_1·b_3_0 + b_2_02·b_4_02·b_3_0 + b_2_03·b_9_0
       + b_2_03·b_4_0·b_5_1 + b_2_03·b_4_0·b_5_0 + b_2_04·b_4_0·b_3_1 + b_2_0·c_8_2·b_5_0
  126. b_6_1·b_9_1 + b_2_0·b_4_1·b_9_1 + b_2_0·b_4_1·b_9_0 + b_2_0·b_4_1·b_6_0·b_3_0
       + b_2_0·b_4_0·b_9_1 + b_2_0·b_4_0·b_9_0 + b_2_0·b_4_0·b_6_0·b_3_1
       + b_2_0·b_4_0·b_4_1·b_5_0 + b_2_02·b_4_12·b_3_1 + b_2_02·b_4_0·b_7_0
       + b_2_02·b_4_0·b_4_1·b_3_1 + b_2_02·b_4_0·b_4_1·b_3_0 + b_2_03·b_9_1 + b_2_03·b_9_0
       + b_2_03·b_6_0·b_3_0 + b_2_03·b_4_0·b_5_0 + b_2_04·b_7_4 + b_2_04·b_7_0
       + b_2_04·b_4_1·b_3_0 + b_2_04·b_4_0·b_3_0 + b_2_05·b_5_1 + b_2_05·b_5_0
       + b_2_06·b_3_1 + b_2_0·c_8_2·b_5_1 + b_2_02·c_8_2·b_3_0
  127. b_8_0·b_7_0 + b_4_12·b_7_4 + b_4_13·b_3_0 + b_4_0·b_4_1·b_7_4 + b_4_0·b_4_1·b_7_0
       + b_4_0·b_4_12·b_3_1 + b_4_02·b_7_0 + b_2_0·b_4_1·b_9_1 + b_2_0·b_4_1·b_6_0·b_3_1
       + b_2_0·b_4_1·b_6_0·b_3_0 + b_2_0·b_4_0·b_9_1 + b_2_0·b_4_0·b_4_1·b_5_1
       + b_2_0·b_4_0·b_4_1·b_5_0 + b_2_0·b_4_02·b_5_1 + b_2_0·b_4_02·b_5_0
       + b_2_02·b_4_12·b_3_0 + b_2_02·b_4_0·b_7_4 + b_2_02·b_4_0·b_4_1·b_3_0
       + b_2_03·b_9_0 + b_2_03·b_4_1·b_5_1 + b_2_03·b_4_1·b_5_0 + b_2_03·b_4_0·b_5_0
       + b_2_04·b_7_0 + b_4_1·c_8_2·b_3_1 + b_2_0·c_8_2·b_5_0
  128. b_8_0·b_7_4 + b_4_12·b_7_4 + b_4_13·b_3_1 + b_4_13·b_3_0 + b_4_0·b_4_1·b_7_4
       + b_4_0·b_4_12·b_3_0 + b_4_02·b_7_4 + b_4_02·b_4_1·b_3_1 + b_4_02·b_4_1·b_3_0
       + b_2_0·b_4_1·b_9_1 + b_2_0·b_4_1·b_6_0·b_3_0 + b_2_0·b_4_12·b_5_0 + b_2_0·b_4_0·b_9_0
       + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_02·b_4_1·b_7_4 + b_2_02·b_4_0·b_7_0
       + b_2_02·b_4_0·b_4_1·b_3_1 + b_2_02·b_4_0·b_4_1·b_3_0 + b_2_03·b_9_1 + b_2_03·b_9_0
       + b_2_03·b_6_0·b_3_0 + b_2_03·b_4_1·b_5_1 + b_2_03·b_4_0·b_5_0 + b_2_04·b_7_4
       + b_2_04·b_7_0 + b_2_04·b_4_1·b_3_1 + b_2_04·b_4_1·b_3_0 + b_2_05·b_5_1
       + b_2_06·b_3_1 + b_4_1·c_8_2·b_3_1 + b_4_1·c_8_2·b_3_0 + b_2_0·c_8_2·b_5_1
       + b_2_02·c_8_2·b_3_1 + b_2_02·c_8_2·b_3_0
  129. b_8_1·b_7_0 + b_4_12·b_7_0 + b_4_13·b_3_1 + b_4_13·b_3_0 + b_4_0·b_4_1·b_7_4
       + b_4_0·b_4_1·b_7_0 + b_4_0·b_4_12·b_3_1 + b_4_02·b_7_0 + b_4_02·b_4_1·b_3_0
       + b_2_0·b_4_1·b_9_1 + b_2_0·b_4_1·b_9_0 + b_2_0·b_4_1·b_6_0·b_3_1
       + b_2_0·b_4_1·b_6_0·b_3_0 + b_2_0·b_4_12·b_5_1 + b_2_0·b_4_0·b_9_1 + b_2_0·b_4_0·b_9_0
       + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_4_1·b_5_0 + b_2_02·b_4_12·b_3_1
       + b_2_02·b_4_12·b_3_0 + b_2_02·b_4_02·b_3_0 + b_2_03·b_4_0·b_5_0
       + b_2_04·b_4_0·b_3_0 + b_2_05·b_5_0 + b_4_1·c_8_2·b_3_1 + b_4_1·c_8_2·b_3_0
       + b_2_0·c_8_2·b_5_0
  130. b_8_1·b_7_4 + b_4_13·b_3_0 + b_4_0·b_4_12·b_3_1 + b_4_02·b_7_4 + b_4_02·b_4_1·b_3_0
       + b_2_0·b_4_1·b_9_0 + b_2_0·b_4_12·b_5_1 + b_2_0·b_4_0·b_9_1 + b_2_0·b_4_0·b_9_0
       + b_2_0·b_4_0·b_6_0·b_3_0 + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_4_1·b_5_0
       + b_2_02·b_4_12·b_3_0 + b_2_02·b_4_0·b_4_1·b_3_1 + b_2_02·b_4_0·b_4_1·b_3_0
       + b_2_03·b_9_1 + b_2_03·b_6_0·b_3_0 + b_2_03·b_4_0·b_5_0 + b_2_04·b_7_4
       + b_2_04·b_7_0 + b_2_04·b_4_1·b_3_0 + b_2_05·b_5_1 + b_2_06·b_3_1 + b_4_1·c_8_2·b_3_0
       + b_2_0·c_8_2·b_5_1 + b_2_02·c_8_2·b_3_1 + b_2_02·c_8_2·b_3_0
  131. b_10_15·b_5_0 + b_4_12·b_7_4 + b_4_0·b_4_1·b_7_4 + b_4_0·b_4_1·b_7_0
       + b_4_0·b_4_12·b_3_1 + b_4_0·b_4_12·b_3_0 + b_2_0·b_4_0·b_9_1 + b_2_0·b_4_0·b_9_0
       + b_2_0·b_4_0·b_6_0·b_3_0 + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_0·b_4_0·b_4_1·b_5_0
       + b_2_0·b_4_02·b_5_1 + b_2_0·b_4_02·b_5_0 + b_2_02·b_4_1·b_7_0
       + b_2_02·b_4_12·b_3_1 + b_2_02·b_4_0·b_4_1·b_3_0 + b_2_03·b_4_0·b_5_1
       + b_2_04·b_4_0·b_3_1 + b_4_1·c_8_2·b_3_0
  132. b_10_15·b_5_1 + b_4_12·b_7_4 + b_4_12·b_7_0 + b_4_13·b_3_1 + b_4_0·b_4_1·b_7_0
       + b_4_0·b_4_12·b_3_0 + b_4_02·b_4_1·b_3_1 + b_4_02·b_4_1·b_3_0 + b_2_0·b_4_1·b_9_1
       + b_2_0·b_4_1·b_6_0·b_3_1 + b_2_0·b_4_1·b_6_0·b_3_0 + b_2_0·b_4_0·b_9_0
       + b_2_0·b_4_0·b_6_0·b_3_0 + b_2_0·b_4_0·b_4_1·b_5_1 + b_2_02·b_4_1·b_7_4
       + b_2_02·b_4_1·b_7_0 + b_2_02·b_4_12·b_3_0 + b_2_02·b_4_0·b_7_4
       + b_2_02·b_4_0·b_4_1·b_3_1 + b_2_02·b_4_02·b_3_1 + b_2_02·b_4_02·b_3_0
       + b_2_03·b_4_1·b_5_1 + b_2_04·b_7_4 + b_2_04·b_7_0 + b_2_04·b_4_0·b_3_0
       + b_2_05·b_5_0 + b_4_1·c_8_2·b_3_1 + b_2_02·c_8_2·b_3_1 + b_2_02·c_8_2·b_3_0
  133. a_7_10·b_9_0
  134. a_7_10·b_9_1
  135. b_6_0·b_10_15 + b_4_1·b_6_02 + b_4_12·b_8_0 + b_4_13·b_4_3 + b_4_0·b_6_0·b_3_02
       + b_4_0·b_6_02 + b_4_0·b_4_1·b_8_0 + b_4_0·b_4_13 + b_4_02·b_4_1·b_4_3
       + b_4_02·b_4_12 + b_2_0·b_4_1·b_4_3·b_6_0 + b_2_0·b_4_12·b_3_0·b_3_1
       + b_2_0·b_4_12·b_6_0 + b_2_0·b_4_0·b_10_15 + b_2_0·b_4_0·b_4_3·b_6_0
       + b_2_0·b_4_0·b_4_1·b_3_02 + b_2_0·b_4_02·b_3_0·b_3_1 + b_2_0·b_4_02·b_3_02
       + b_2_0·b_4_02·b_6_1 + b_2_02·b_4_12·b_4_3 + b_2_02·b_4_0·b_8_1
       + b_2_02·b_4_02·b_4_1 + b_2_02·b_4_03 + b_2_03·b_10_15 + b_2_03·b_4_1·b_6_0
       + b_2_03·b_4_0·b_3_0·b_3_1 + b_2_03·b_4_0·b_6_1 + b_2_04·b_8_1 + b_2_04·b_8_0
       + b_2_04·b_4_1·b_4_3 + b_2_04·b_4_12 + b_2_04·b_4_0·b_4_3 + b_2_04·b_4_0·b_4_1
       + b_2_04·b_4_02 + b_2_05·b_3_0·b_3_1 + b_2_05·b_3_02 + b_2_05·b_6_0 + b_2_08
       + b_4_12·c_8_2 + b_2_0·c_8_2·b_3_0·b_3_1 + b_2_0·c_8_2·b_3_02 + b_2_02·b_4_1·c_8_2
  136. b_6_1·b_10_15 + b_2_0·b_4_1·b_4_3·b_6_0 + b_2_0·b_4_12·b_3_0·b_3_1
       + b_2_0·b_4_12·b_3_02 + b_2_0·b_4_12·b_6_0 + b_2_0·b_4_0·b_4_3·b_6_0
       + b_2_0·b_4_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_02·b_6_0 + b_2_02·b_4_1·b_8_0
       + b_2_02·b_4_0·b_8_0 + b_2_02·b_4_0·b_4_1·b_4_3 + b_2_02·b_4_0·b_4_12
       + b_2_02·b_4_02·b_4_3 + b_2_03·b_4_3·b_6_0 + b_2_03·b_4_1·b_3_02
       + b_2_03·b_4_1·b_6_0 + b_2_03·b_4_0·b_3_0·b_3_1 + b_2_03·b_4_0·b_3_02
       + b_2_03·b_4_0·b_6_1 + b_2_03·b_4_0·b_6_0 + b_2_04·b_4_1·b_4_3 + b_2_04·b_4_12
       + b_2_04·b_4_0·b_4_1 + b_2_04·b_4_02 + b_2_05·b_3_0·b_3_1 + b_2_05·b_3_02
       + b_2_05·b_6_1 + b_2_05·b_6_0 + b_2_06·b_4_3 + b_2_06·b_4_1 + b_2_06·b_4_0 + b_2_08
       + b_2_0·c_8_2·b_3_0·b_3_1 + b_2_0·b_6_0·c_8_2 + b_2_02·b_4_3·c_8_2
       + b_2_02·b_4_0·c_8_2
  137. b_8_02 + b_4_12·b_8_1 + b_4_12·b_8_0 + b_4_13·b_4_3 + b_4_14 + b_4_0·b_4_1·b_8_1
       + b_4_0·b_4_13 + b_4_02·b_4_1·b_4_3 + b_4_04 + b_2_0·b_4_1·b_4_3·b_6_0
       + b_2_0·b_4_12·b_6_0 + b_2_0·b_4_0·b_10_15 + b_2_0·b_4_0·b_4_3·b_6_0
       + b_2_0·b_4_0·b_4_1·b_3_02 + b_2_0·b_4_02·b_6_0 + b_2_02·b_6_02
       + b_2_02·b_4_1·b_8_1 + b_2_02·b_4_12·b_4_3 + b_2_02·b_4_13 + b_2_02·b_4_0·b_8_1
       + b_2_02·b_4_0·b_8_0 + b_2_02·b_4_0·b_4_1·b_4_3 + b_2_02·b_4_0·b_4_12
       + b_2_02·b_4_02·b_4_1 + b_2_03·b_10_15 + b_2_03·b_4_3·b_6_0
       + b_2_03·b_4_1·b_3_02 + b_2_03·b_4_0·b_3_0·b_3_1 + b_2_03·b_4_0·b_6_0
       + b_2_04·b_8_1 + b_2_04·b_4_12 + b_2_04·b_4_0·b_4_1 + b_2_04·b_4_02
       + b_2_05·b_6_0 + b_2_06·b_4_3 + b_2_06·b_4_1 + b_4_1·b_4_3·c_8_2 + b_4_12·c_8_2
       + b_4_0·b_4_1·c_8_2 + b_2_0·c_8_2·b_3_02 + b_2_0·b_6_1·c_8_2 + b_2_0·b_6_0·c_8_2
       + b_2_02·b_4_3·c_8_2
  138. b_8_0·b_8_1 + b_4_12·b_8_1 + b_4_12·b_8_0 + b_4_0·b_4_1·b_8_0 + b_4_0·b_4_12·b_4_3
       + b_4_02·b_8_1 + b_4_02·b_8_0 + b_4_02·b_4_12 + b_4_03·b_4_1 + b_4_04
       + b_2_0·b_4_12·b_3_02 + b_2_0·b_4_12·b_6_0 + b_2_0·b_4_0·b_4_3·b_6_0
       + b_2_0·b_4_0·b_4_1·b_3_02 + b_2_0·b_4_0·b_4_1·b_6_0 + b_2_0·b_4_02·b_6_0
       + b_2_02·b_6_02 + b_2_02·b_4_0·b_8_1 + b_2_02·b_4_0·b_4_1·b_4_3
       + b_2_02·b_4_0·b_4_12 + b_2_02·b_4_03 + b_2_03·b_4_3·b_6_0
       + b_2_03·b_4_1·b_3_02 + b_2_03·b_4_0·b_3_0·b_3_1 + b_2_03·b_4_0·b_6_1
       + b_2_04·b_8_1 + b_2_04·b_8_0 + b_2_04·b_4_12 + b_2_04·b_4_0·b_4_1
       + b_2_05·b_3_0·b_3_1 + b_2_05·b_3_02 + b_2_05·b_6_1 + b_2_05·b_6_0 + b_2_06·b_4_3
       + b_2_06·b_4_1 + b_2_08 + b_4_12·c_8_2 + b_2_0·c_8_2·b_3_0·b_3_1
       + b_2_0·c_8_2·b_3_02 + b_2_0·b_6_1·c_8_2 + b_2_0·b_6_0·c_8_2 + b_2_02·b_4_3·c_8_2
       + b_2_02·b_4_0·c_8_2
  139. b_8_12 + b_4_12·b_8_1 + b_4_13·b_4_3 + b_4_0·b_4_1·b_8_0 + b_4_0·b_4_12·b_4_3
       + b_4_0·b_4_13 + b_4_02·b_4_1·b_4_3 + b_4_02·b_4_12 + b_4_04
       + b_2_0·b_4_1·b_4_3·b_6_0 + b_2_0·b_4_0·b_10_15 + b_2_0·b_4_0·b_4_3·b_6_0
       + b_2_0·b_4_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_0·b_4_1·b_6_0 + b_2_0·b_4_02·b_3_0·b_3_1
       + b_2_0·b_4_02·b_3_02 + b_2_0·b_4_02·b_6_1 + b_2_02·b_6_02 + b_2_02·b_4_1·b_8_1
       + b_2_02·b_4_12·b_4_3 + b_2_02·b_4_13 + b_2_02·b_4_0·b_8_1 + b_2_02·b_4_0·b_8_0
       + b_2_03·b_10_15 + b_2_03·b_4_0·b_3_02 + b_2_03·b_4_0·b_6_0 + b_2_04·b_8_0
       + b_2_04·b_4_1·b_4_3 + b_2_04·b_4_12 + b_2_04·b_4_02 + b_2_05·b_3_0·b_3_1
       + b_2_05·b_3_02 + b_2_06·b_4_0 + b_2_08 + b_4_1·b_4_3·c_8_2 + b_4_0·b_4_1·c_8_2
       + b_2_0·c_8_2·b_3_02 + b_2_0·b_6_1·c_8_2 + b_2_0·b_6_0·c_8_2 + b_2_02·b_4_3·c_8_2
  140. b_7_0·b_9_0 + b_4_12·b_8_1 + b_4_13·b_4_3 + b_4_0·b_4_1·b_8_1 + b_4_0·b_4_12·b_4_3
       + b_4_02·b_4_1·b_4_3 + b_2_0·b_4_1·b_4_3·b_6_0 + b_2_0·b_4_12·b_3_02
       + b_2_0·b_4_0·b_10_15 + b_2_0·b_4_0·b_4_3·b_6_0 + b_2_0·b_4_0·b_4_1·b_6_0
       + b_2_0·b_4_02·b_3_02 + b_2_0·b_4_02·b_6_0 + b_2_02·b_4_1·b_8_1
       + b_2_02·b_4_1·b_8_0 + b_2_02·b_4_02·b_4_3 + b_2_02·b_4_02·b_4_1
       + b_2_02·b_4_03 + b_2_03·b_10_15 + b_2_03·b_4_3·b_6_0 + b_2_03·b_4_1·b_3_02
       + b_2_03·b_4_1·b_6_0 + b_2_03·b_4_0·b_3_0·b_3_1 + b_2_03·b_4_0·b_6_0 + b_2_04·b_8_1
       + b_2_04·b_4_12 + b_2_04·b_4_0·b_4_1 + b_2_04·b_4_02 + b_2_05·b_3_0·b_3_1
       + b_2_05·b_3_02 + b_2_05·b_6_1 + b_2_06·b_4_3 + b_2_06·b_4_1 + b_2_08
       + b_4_1·b_4_3·c_8_2 + b_4_0·b_4_1·c_8_2 + b_2_0·b_6_0·c_8_2 + b_2_02·b_4_0·c_8_2
       + b_2_04·c_8_2
  141. b_7_0·b_9_1 + b_4_1·b_6_0·b_3_02 + b_4_1·b_6_02 + b_4_12·b_8_1 + b_4_12·b_8_0
       + b_4_0·b_6_0·b_3_02 + b_4_0·b_4_12·b_4_3 + b_4_0·b_4_13 + b_4_02·b_4_1·b_4_3
       + b_4_03·b_4_1 + b_2_0·b_4_12·b_3_0·b_3_1 + b_2_0·b_4_12·b_3_02
       + b_2_0·b_4_12·b_6_0 + b_2_0·b_4_0·b_4_1·b_3_02 + b_2_0·b_4_0·b_4_1·b_6_0
       + b_2_0·b_4_02·b_3_02 + b_2_0·b_4_02·b_6_0 + b_2_02·b_4_1·b_8_0
       + b_2_02·b_4_12·b_4_3 + b_2_02·b_4_0·b_8_1 + b_2_02·b_4_02·b_4_3
       + b_2_03·b_4_1·b_3_0·b_3_1 + b_2_03·b_4_1·b_3_02 + b_2_03·b_4_1·b_6_0
       + b_2_03·b_4_0·b_3_02 + b_2_03·b_4_0·b_6_0 + b_2_04·b_4_1·b_4_3 + b_2_04·b_4_02
       + b_2_05·b_3_0·b_3_1 + b_2_05·b_3_02 + b_2_05·b_6_0 + b_2_06·b_4_1 + b_2_06·b_4_0
       + b_2_08 + b_4_1·b_4_3·c_8_2 + b_4_12·c_8_2 + b_4_0·b_4_1·c_8_2 + b_2_0·b_6_0·c_8_2
       + b_2_02·b_4_1·c_8_2 + b_2_04·c_8_2
  142. b_7_4·b_9_0 + b_4_13·b_4_3 + b_4_14 + b_4_0·b_4_1·b_8_0 + b_4_0·b_4_12·b_4_3
       + b_4_02·b_4_12 + b_4_03·b_4_1 + b_2_0·b_4_1·b_4_3·b_6_0 + b_2_0·b_4_0·b_10_15
       + b_2_0·b_4_0·b_4_1·b_3_02 + b_2_0·b_4_02·b_3_0·b_3_1 + b_2_0·b_4_02·b_3_02
       + b_2_0·b_4_02·b_6_1 + b_2_02·b_4_1·b_8_1 + b_2_02·b_4_1·b_8_0 + b_2_02·b_4_13
       + b_2_02·b_4_0·b_8_0 + b_2_02·b_4_02·b_4_1 + b_2_03·b_4_3·b_6_0
       + b_2_03·b_4_1·b_3_0·b_3_1 + b_2_03·b_4_1·b_6_0 + b_2_03·b_4_0·b_3_0·b_3_1
       + b_2_03·b_4_0·b_3_02 + b_2_03·b_4_0·b_6_0 + b_2_04·b_8_1 + b_2_04·b_8_0
       + b_2_04·b_4_0·b_4_1 + b_2_05·b_3_0·b_3_1 + b_2_05·b_3_02 + b_2_05·b_6_0
       + b_2_06·b_4_3 + b_2_06·b_4_0 + b_2_08 + b_4_1·b_4_3·c_8_2 + b_4_12·c_8_2
       + b_4_0·b_4_1·c_8_2 + b_2_0·c_8_2·b_3_0·b_3_1 + b_2_0·b_6_0·c_8_2 + b_2_04·c_8_2
  143. b_7_4·b_9_1 + b_4_12·b_8_0 + b_4_0·b_4_1·b_8_1 + b_4_0·b_4_1·b_8_0
       + b_4_0·b_4_12·b_4_3 + b_4_02·b_4_12 + b_2_0·b_4_1·b_4_3·b_6_0
       + b_2_0·b_4_12·b_3_0·b_3_1 + b_2_0·b_4_12·b_3_02 + b_2_0·b_4_12·b_6_0
       + b_2_0·b_4_0·b_4_1·b_6_0 + b_2_0·b_4_02·b_3_0·b_3_1 + b_2_0·b_4_02·b_3_02
       + b_2_0·b_4_02·b_6_1 + b_2_0·b_4_02·b_6_0 + b_2_02·b_4_1·b_8_1 + b_2_02·b_4_0·b_8_1
       + b_2_02·b_4_0·b_8_0 + b_2_02·b_4_0·b_4_12 + b_2_02·b_4_02·b_4_3
       + b_2_03·b_4_1·b_6_0 + b_2_04·b_8_1 + b_2_04·b_4_12 + b_2_04·b_4_02
       + b_2_05·b_6_0 + b_4_12·c_8_2 + b_2_02·b_4_3·c_8_2 + b_2_04·c_8_2
  144. b_10_15·a_7_10
  145. b_8_0·b_9_0 + b_4_12·b_6_0·b_3_1 + b_4_0·b_4_1·b_9_1 + b_4_0·b_4_1·b_6_0·b_3_1
       + b_4_0·b_4_12·b_5_0 + b_4_02·b_9_0 + b_4_02·b_6_0·b_3_1 + b_4_02·b_4_1·b_5_0
       + b_2_0·b_4_12·b_7_0 + b_2_0·b_4_13·b_3_1 + b_2_0·b_4_13·b_3_0
       + b_2_0·b_4_0·b_4_1·b_7_4 + b_2_0·b_4_02·b_7_4 + b_2_0·b_4_02·b_7_0
       + b_2_0·b_4_02·b_4_1·b_3_1 + b_2_0·b_4_02·b_4_1·b_3_0 + b_2_0·b_4_03·b_3_0
       + b_2_02·b_4_1·b_9_1 + b_2_02·b_4_1·b_9_0 + b_2_02·b_4_1·b_6_0·b_3_0
       + b_2_02·b_4_12·b_5_0 + b_2_02·b_4_0·b_9_0 + b_2_02·b_4_0·b_4_1·b_5_1
       + b_2_02·b_4_02·b_5_0 + b_2_03·b_4_1·b_7_4 + b_2_03·b_4_1·b_7_0
       + b_2_03·b_4_12·b_3_1 + b_2_03·b_4_0·b_7_4 + b_6_0·c_8_2·b_3_1 + b_2_0·c_8_2·b_7_0
       + b_2_0·b_4_1·c_8_2·b_3_1 + b_2_0·b_4_0·c_8_2·b_3_0 + b_2_02·c_8_2·b_5_0
       + b_2_03·c_8_2·b_3_1
  146. b_8_0·b_9_1 + b_4_13·b_5_1 + b_4_0·b_4_1·b_9_1 + b_4_0·b_4_1·b_6_0·b_3_0
       + b_4_0·b_4_12·b_5_1 + b_4_02·b_9_1 + b_4_02·b_6_0·b_3_1 + b_4_02·b_4_1·b_5_0
       + b_2_0·b_6_02·b_3_0 + b_2_0·b_4_12·b_7_4 + b_2_0·b_4_13·b_3_0
       + b_2_0·b_4_0·b_4_1·b_7_4 + b_2_0·b_4_0·b_4_1·b_7_0 + b_2_0·b_4_0·b_4_12·b_3_1
       + b_2_0·b_4_02·b_7_4 + b_2_0·b_4_02·b_7_0 + b_2_0·b_4_02·b_4_1·b_3_1
       + b_2_0·b_4_02·b_4_1·b_3_0 + b_2_0·b_4_03·b_3_0 + b_2_02·b_4_1·b_6_0·b_3_1
       + b_2_02·b_4_1·b_6_0·b_3_0 + b_2_02·b_4_0·b_6_0·b_3_1 + b_2_02·b_4_0·b_4_1·b_5_1
       + b_2_03·b_4_1·b_7_0 + b_2_03·b_4_12·b_3_1 + b_2_03·b_4_0·b_7_0
       + b_2_03·b_4_0·b_4_1·b_3_1 + b_2_03·b_4_02·b_3_1 + b_2_03·b_4_02·b_3_0
       + b_2_04·b_4_1·b_5_0 + b_2_04·b_4_0·b_5_1 + b_2_04·b_4_0·b_5_0 + b_2_05·b_4_1·b_3_1
       + b_2_05·b_4_1·b_3_0 + b_2_06·b_5_1 + b_2_07·b_3_1 + b_6_0·c_8_2·b_3_1
       + b_4_1·c_8_2·b_5_0 + b_2_0·c_8_2·b_7_4 + b_2_0·b_4_1·c_8_2·b_3_1 + b_2_03·c_8_2·b_3_1
       + b_2_03·c_8_2·b_3_0
  147. b_8_1·b_9_0 + b_4_12·b_6_0·b_3_0 + b_4_13·b_5_1 + b_4_0·b_4_1·b_9_0
       + b_4_0·b_4_1·b_6_0·b_3_1 + b_4_0·b_4_12·b_5_1 + b_4_0·b_4_12·b_5_0 + b_4_02·b_9_0
       + b_4_02·b_6_0·b_3_0 + b_4_02·b_4_1·b_5_0 + b_2_0·b_4_12·b_7_0
       + b_2_0·b_4_0·b_4_12·b_3_1 + b_2_0·b_4_02·b_4_1·b_3_0 + b_2_0·b_4_03·b_3_1
       + b_2_0·b_4_03·b_3_0 + b_2_02·b_4_1·b_9_1 + b_2_02·b_4_1·b_6_0·b_3_0
       + b_2_02·b_4_12·b_5_1 + b_2_02·b_4_12·b_5_0 + b_2_03·b_4_1·b_7_4
       + b_2_03·b_4_1·b_7_0 + b_2_03·b_4_0·b_4_1·b_3_1 + b_2_03·b_4_02·b_3_1
       + b_2_04·b_9_0 + b_2_04·b_4_1·b_5_1 + b_2_04·b_4_0·b_5_0 + b_2_05·b_7_0
       + b_2_05·b_4_0·b_3_0 + b_2_06·b_5_0 + b_6_0·c_8_2·b_3_0 + b_4_1·c_8_2·b_5_1
       + b_2_0·c_8_2·b_7_0 + b_2_0·b_4_0·c_8_2·b_3_1 + b_2_02·c_8_2·b_5_0
  148. b_8_1·b_9_1 + b_4_12·b_6_0·b_3_0 + b_4_13·b_5_1 + b_4_13·b_5_0
       + b_4_0·b_4_1·b_6_0·b_3_1 + b_4_0·b_4_1·b_6_0·b_3_0 + b_4_0·b_4_12·b_5_0
       + b_4_02·b_9_1 + b_4_02·b_4_1·b_5_0 + b_2_0·b_6_02·b_3_0 + b_2_0·b_4_13·b_3_0
       + b_2_0·b_4_0·b_4_1·b_7_4 + b_2_0·b_4_0·b_4_1·b_7_0 + b_2_0·b_4_0·b_4_12·b_3_1
       + b_2_0·b_4_0·b_4_12·b_3_0 + b_2_0·b_4_02·b_7_0 + b_2_0·b_4_03·b_3_1
       + b_2_02·b_4_1·b_9_1 + b_2_02·b_4_1·b_6_0·b_3_1 + b_2_02·b_4_12·b_5_1
       + b_2_02·b_4_0·b_9_0 + b_2_02·b_4_0·b_6_0·b_3_0 + b_2_02·b_4_0·b_4_1·b_5_1
       + b_2_02·b_4_02·b_5_1 + b_2_02·b_4_02·b_5_0 + b_2_03·b_4_1·b_7_4
       + b_2_03·b_4_12·b_3_1 + b_2_03·b_4_0·b_7_4 + b_2_03·b_4_0·b_4_1·b_3_0
       + b_2_03·b_4_02·b_3_0 + b_2_04·b_9_0 + b_2_04·b_4_1·b_5_1 + b_2_04·b_4_0·b_5_1
       + b_2_04·b_4_0·b_5_0 + b_2_05·b_4_1·b_3_0 + b_2_05·b_4_0·b_3_0 + b_2_06·b_5_1
       + b_2_06·b_5_0 + b_2_07·b_3_1 + b_4_1·c_8_2·b_5_0 + b_2_0·c_8_2·b_7_4
       + b_2_0·b_4_1·c_8_2·b_3_0 + b_2_0·b_4_0·c_8_2·b_3_1 + b_2_0·b_4_0·c_8_2·b_3_0
       + b_2_02·c_8_2·b_5_0
  149. b_10_15·b_7_0 + b_4_12·b_6_0·b_3_1 + b_4_13·b_5_1 + b_4_0·b_4_1·b_9_1
       + b_4_0·b_4_1·b_6_0·b_3_0 + b_4_0·b_4_12·b_5_1 + b_4_0·b_4_12·b_5_0
       + b_4_02·b_6_0·b_3_1 + b_4_02·b_6_0·b_3_0 + b_2_0·b_4_12·b_7_4 + b_2_0·b_4_12·b_7_0
       + b_2_0·b_4_0·b_4_1·b_7_4 + b_2_0·b_4_02·b_7_0 + b_2_0·b_4_02·b_4_1·b_3_1
       + b_2_0·b_4_03·b_3_0 + b_2_02·b_4_1·b_9_0 + b_2_02·b_4_12·b_5_1
       + b_2_02·b_4_02·b_5_1 + b_2_02·b_4_02·b_5_0 + b_2_03·b_4_1·b_7_4
       + b_2_03·b_4_1·b_7_0 + b_2_03·b_4_0·b_7_4 + b_2_03·b_4_02·b_3_1
       + b_2_03·b_4_02·b_3_0 + b_2_04·b_4_0·b_5_0 + b_4_1·c_8_2·b_5_0
       + b_2_0·b_4_1·c_8_2·b_3_1 + b_2_0·b_4_0·c_8_2·b_3_1 + b_2_0·b_4_0·c_8_2·b_3_0
  150. b_10_15·b_7_4 + b_4_12·b_6_0·b_3_1 + b_4_12·b_6_0·b_3_0 + b_4_13·b_5_1
       + b_4_0·b_4_1·b_9_0 + b_4_0·b_4_1·b_6_0·b_3_0 + b_4_0·b_4_12·b_5_1
       + b_4_02·b_6_0·b_3_1 + b_4_02·b_6_0·b_3_0 + b_4_02·b_4_1·b_5_1 + b_4_02·b_4_1·b_5_0
       + b_2_0·b_4_12·b_7_4 + b_2_0·b_4_12·b_7_0 + b_2_0·b_4_13·b_3_0
       + b_2_0·b_4_0·b_4_12·b_3_1 + b_2_0·b_4_02·b_7_4 + b_2_0·b_4_02·b_7_0
       + b_2_0·b_4_02·b_4_1·b_3_1 + b_2_0·b_4_02·b_4_1·b_3_0 + b_2_0·b_4_03·b_3_1
       + b_2_02·b_4_1·b_9_1 + b_2_02·b_4_1·b_6_0·b_3_0 + b_2_02·b_4_12·b_5_1
       + b_2_02·b_4_0·b_9_0 + b_2_02·b_4_0·b_4_1·b_5_0 + b_2_02·b_4_02·b_5_1
       + b_2_03·b_4_1·b_7_0 + b_2_03·b_4_12·b_3_0 + b_2_03·b_4_0·b_4_1·b_3_1
       + b_2_03·b_4_0·b_4_1·b_3_0 + b_2_03·b_4_02·b_3_1 + b_2_04·b_4_1·b_5_1
       + b_2_04·b_4_0·b_5_1 + b_2_04·b_4_0·b_5_0 + b_2_05·b_7_4 + b_2_05·b_7_0
       + b_2_05·b_4_0·b_3_1 + b_2_05·b_4_0·b_3_0 + b_2_06·b_5_0 + b_6_0·c_8_2·b_3_1
       + b_6_0·c_8_2·b_3_0 + b_4_1·c_8_2·b_5_0 + b_2_0·b_4_1·c_8_2·b_3_1
       + b_2_0·b_4_0·c_8_2·b_3_1 + b_2_0·b_4_0·c_8_2·b_3_0 + b_2_02·c_8_2·b_5_1
       + b_2_02·c_8_2·b_5_0 + b_2_03·c_8_2·b_3_1
  151. b_8_0·b_10_15 + b_4_12·b_4_3·b_6_0 + b_4_13·b_3_0·b_3_1 + b_4_13·b_3_02
       + b_4_0·b_4_1·b_4_3·b_6_0 + b_4_0·b_4_12·b_3_0·b_3_1 + b_4_0·b_4_12·b_3_02
       + b_4_02·b_10_15 + b_4_02·b_4_1·b_3_0·b_3_1 + b_4_02·b_4_1·b_3_02
       + b_4_03·b_3_02 + b_2_0·b_4_1·b_6_02 + b_2_0·b_4_12·b_8_1
       + b_2_0·b_4_0·b_6_0·b_3_02 + b_2_0·b_4_0·b_6_02 + b_2_0·b_4_0·b_4_1·b_8_1
       + b_2_0·b_4_0·b_4_1·b_8_0 + b_2_0·b_4_0·b_4_13 + b_2_0·b_4_02·b_8_0
       + b_2_0·b_4_02·b_4_1·b_4_3 + b_2_0·b_4_02·b_4_12 + b_2_0·b_4_03·b_4_3
       + b_2_02·b_4_12·b_3_02 + b_2_02·b_4_12·b_6_0 + b_2_02·b_4_0·b_4_1·b_3_02
       + b_2_02·b_4_0·b_4_1·b_6_0 + b_2_02·b_4_02·b_3_0·b_3_1 + b_2_02·b_4_02·b_6_1
       + b_2_03·b_4_1·b_8_1 + b_2_03·b_4_12·b_4_3 + b_2_03·b_4_0·b_4_12
       + b_2_03·b_4_03 + b_2_04·b_4_3·b_6_0 + b_2_04·b_4_1·b_3_02 + b_2_04·b_4_1·b_6_0
       + b_2_05·b_4_12 + b_2_05·b_4_0·b_4_3 + b_2_05·b_4_02 + b_2_06·b_3_0·b_3_1
       + b_2_06·b_3_02 + b_2_06·b_6_1 + b_2_06·b_6_0 + b_2_07·b_4_3 + b_2_07·b_4_1
       + b_2_09 + b_4_3·b_6_0·c_8_2 + b_4_1·c_8_2·b_3_0·b_3_1 + b_4_0·c_8_2·b_3_02
       + b_4_0·b_6_0·c_8_2 + b_2_0·b_4_0·b_4_1·c_8_2 + b_2_02·c_8_2·b_3_0·b_3_1
       + b_2_02·b_6_1·c_8_2 + b_2_02·b_6_0·c_8_2 + b_2_03·b_4_3·c_8_2 + b_2_03·b_4_0·c_8_2
  152. b_8_1·b_10_15 + b_4_13·b_3_0·b_3_1 + b_4_13·b_3_02 + b_4_0·b_4_1·b_4_3·b_6_0
       + b_4_0·b_4_12·b_3_02 + b_4_0·b_4_12·b_6_0 + b_4_02·b_10_15 + b_4_02·b_4_3·b_6_0
       + b_4_02·b_4_1·b_3_0·b_3_1 + b_4_03·b_3_0·b_3_1 + b_4_03·b_3_02 + b_4_03·b_6_0
       + b_2_0·b_4_1·b_6_02 + b_2_0·b_4_12·b_8_1 + b_2_0·b_4_12·b_8_0 + b_2_0·b_4_14
       + b_2_0·b_4_0·b_6_0·b_3_02 + b_2_0·b_4_0·b_6_02 + b_2_0·b_4_0·b_4_1·b_8_0
       + b_2_0·b_4_0·b_4_12·b_4_3 + b_2_0·b_4_02·b_8_0 + b_2_0·b_4_03·b_4_1
       + b_2_0·b_4_04 + b_2_02·b_4_12·b_3_02 + b_2_02·b_4_0·b_4_3·b_6_0
       + b_2_02·b_4_0·b_4_1·b_3_02 + b_2_02·b_4_0·b_4_1·b_6_0
       + b_2_02·b_4_02·b_3_0·b_3_1 + b_2_02·b_4_02·b_3_02 + b_2_02·b_4_02·b_6_1
       + b_2_02·b_4_02·b_6_0 + b_2_03·b_4_1·b_8_1 + b_2_03·b_4_0·b_8_1
       + b_2_03·b_4_0·b_8_0 + b_2_03·b_4_0·b_4_1·b_4_3 + b_2_03·b_4_0·b_4_12
       + b_2_03·b_4_03 + b_2_04·b_4_3·b_6_0 + b_2_04·b_4_1·b_3_02 + b_2_04·b_4_1·b_6_0
       + b_2_04·b_4_0·b_3_0·b_3_1 + b_2_04·b_4_0·b_3_02 + b_2_04·b_4_0·b_6_1
       + b_2_04·b_4_0·b_6_0 + b_2_05·b_8_1 + b_2_05·b_8_0 + b_2_05·b_4_1·b_4_3
       + b_2_05·b_4_0·b_4_3 + b_2_05·b_4_02 + b_2_06·b_6_1 + b_2_07·b_4_3 + b_2_07·b_4_1
       + b_2_07·b_4_0 + b_4_3·b_6_0·c_8_2 + b_4_1·c_8_2·b_3_0·b_3_1 + b_4_1·b_6_0·c_8_2
       + b_4_0·c_8_2·b_3_0·b_3_1 + b_4_0·c_8_2·b_3_02 + b_4_0·b_6_0·c_8_2
       + b_2_0·b_4_1·b_4_3·c_8_2 + b_2_0·b_4_0·b_4_1·c_8_2 + b_2_02·c_8_2·b_3_0·b_3_1
       + b_2_02·b_6_1·c_8_2 + b_2_02·b_6_0·c_8_2 + b_2_03·b_4_3·c_8_2
  153. b_9_02 + b_4_12·b_4_3·b_6_0 + b_4_13·b_3_0·b_3_1 + b_4_13·b_3_02
       + b_4_0·b_4_1·b_4_3·b_6_0 + b_4_02·b_4_1·b_3_0·b_3_1 + b_4_02·b_4_1·b_3_02
       + b_4_03·b_3_02 + b_2_0·b_4_12·b_8_0 + b_2_0·b_4_0·b_4_1·b_8_1
       + b_2_0·b_4_0·b_4_1·b_8_0 + b_2_0·b_4_02·b_4_12 + b_2_0·b_4_03·b_4_3
       + b_2_0·b_4_03·b_4_1 + b_2_0·b_4_04 + b_2_02·b_4_1·b_4_3·b_6_0
       + b_2_02·b_4_12·b_3_0·b_3_1 + b_2_02·b_4_0·b_4_3·b_6_0
       + b_2_02·b_4_0·b_4_1·b_3_02 + b_2_02·b_4_0·b_4_1·b_6_0 + b_2_02·b_4_02·b_6_1
       + b_2_02·b_4_02·b_6_0 + b_2_03·b_4_1·b_8_1 + b_2_03·b_4_13 + b_2_03·b_4_0·b_8_1
       + b_2_03·b_4_0·b_8_0 + b_2_03·b_4_0·b_4_12 + b_2_03·b_4_03 + b_2_04·b_10_15
       + b_2_04·b_4_3·b_6_0 + b_2_04·b_4_1·b_3_02 + b_2_04·b_4_0·b_3_0·b_3_1
       + b_2_04·b_4_0·b_6_1 + b_2_04·b_4_0·b_6_0 + b_2_05·b_8_1 + b_2_05·b_4_1·b_4_3
       + b_2_05·b_4_0·b_4_3 + b_2_06·b_3_0·b_3_1 + b_2_06·b_3_02 + b_2_06·b_6_1
       + b_2_07·b_4_3 + b_2_07·b_4_1 + b_2_09 + b_4_3·b_6_0·c_8_2 + b_4_1·c_8_2·b_3_0·b_3_1
       + b_4_1·c_8_2·b_3_02 + b_4_0·c_8_2·b_3_02 + b_4_0·b_6_0·c_8_2 + b_2_0·b_8_1·c_8_2
       + b_2_0·b_8_0·c_8_2 + b_2_0·b_4_0·b_4_1·c_8_2 + b_2_03·b_4_3·c_8_2
       + b_2_03·b_4_1·c_8_2 + b_2_03·b_4_0·c_8_2
  154. b_9_0·b_9_1 + b_4_13·b_3_02 + b_4_13·b_6_0 + b_4_0·b_4_1·b_4_3·b_6_0
       + b_4_0·b_4_12·b_3_0·b_3_1 + b_4_02·b_4_1·b_3_02 + b_4_03·b_3_02
       + b_2_0·b_4_12·b_8_0 + b_2_0·b_4_13·b_4_3 + b_2_0·b_4_14 + b_2_0·b_4_0·b_4_1·b_8_1
       + b_2_0·b_4_0·b_4_12·b_4_3 + b_2_0·b_4_02·b_4_12 + b_2_0·b_4_03·b_4_3
       + b_2_0·b_4_04 + b_2_02·b_4_12·b_3_02 + b_2_02·b_4_0·b_10_15
       + b_2_02·b_4_0·b_4_3·b_6_0 + b_2_02·b_4_02·b_3_02 + b_2_03·b_4_12·b_4_3
       + b_2_03·b_4_13 + b_2_03·b_4_0·b_8_1 + b_2_03·b_4_0·b_8_0
       + b_2_03·b_4_0·b_4_1·b_4_3 + b_2_03·b_4_0·b_4_12 + b_2_03·b_4_02·b_4_3
       + b_2_03·b_4_02·b_4_1 + b_2_04·b_10_15 + b_2_04·b_4_1·b_6_0
       + b_2_04·b_4_0·b_3_02 + b_2_04·b_4_0·b_6_1 + b_2_04·b_4_0·b_6_0 + b_2_05·b_8_0
       + b_2_05·b_4_12 + b_2_05·b_4_0·b_4_1 + b_2_06·b_6_1 + b_2_06·b_6_0 + b_2_07·b_4_0
       + b_4_3·b_6_0·c_8_2 + b_4_1·c_8_2·b_3_0·b_3_1 + b_4_1·b_6_0·c_8_2
       + b_4_0·c_8_2·b_3_02 + b_4_0·b_6_0·c_8_2 + b_2_0·b_8_1·c_8_2 + b_2_0·b_8_0·c_8_2
       + b_2_0·b_4_0·b_4_3·c_8_2 + b_2_0·b_4_02·c_8_2 + b_2_02·c_8_2·b_3_0·b_3_1
       + b_2_03·b_4_3·c_8_2 + b_2_03·b_4_0·c_8_2
  155. b_9_12 + b_6_02·b_3_02 + b_4_13·b_3_02 + b_4_0·b_4_1·b_4_3·b_6_0
       + b_4_02·b_4_1·b_6_0 + b_4_03·b_3_0·b_3_1 + b_4_03·b_3_02 + b_2_0·b_4_12·b_8_0
       + b_2_0·b_4_0·b_4_1·b_8_1 + b_2_0·b_4_0·b_4_1·b_8_0 + b_2_0·b_4_0·b_4_13
       + b_2_0·b_4_02·b_4_12 + b_2_02·b_4_1·b_4_3·b_6_0 + b_2_02·b_4_12·b_6_0
       + b_2_02·b_4_0·b_4_3·b_6_0 + b_2_02·b_4_0·b_4_1·b_3_0·b_3_1
       + b_2_02·b_4_0·b_4_1·b_3_02 + b_2_02·b_4_02·b_3_0·b_3_1 + b_2_02·b_4_02·b_6_0
       + b_2_03·b_4_13 + b_2_03·b_4_0·b_8_0 + b_2_03·b_4_02·b_4_1 + b_2_03·b_4_03
       + b_2_04·b_4_0·b_3_0·b_3_1 + b_2_04·b_4_0·b_3_02 + b_2_05·b_8_1
       + b_2_05·b_4_0·b_4_1 + b_2_06·b_6_0 + b_2_07·b_4_0 + b_4_1·c_8_2·b_3_0·b_3_1
       + b_4_1·b_6_0·c_8_2 + b_4_0·c_8_2·b_3_0·b_3_1 + b_4_0·c_8_2·b_3_02
       + b_2_0·b_4_12·c_8_2 + b_2_0·b_4_0·b_4_3·c_8_2 + b_2_0·b_4_0·b_4_1·c_8_2
       + b_2_0·b_4_02·c_8_2 + b_2_02·b_6_1·c_8_2 + b_2_02·b_6_0·c_8_2 + b_2_03·b_4_3·c_8_2
       + b_2_03·b_4_0·c_8_2 + b_2_05·c_8_2
  156. b_10_15·b_9_0 + b_4_14·b_3_1 + b_4_0·b_4_13·b_3_1 + b_4_02·b_4_1·b_7_4
       + b_4_02·b_4_1·b_7_0 + b_4_02·b_4_12·b_3_0 + b_2_0·b_4_12·b_6_0·b_3_0
       + b_2_0·b_4_13·b_5_1 + b_2_0·b_4_13·b_5_0 + b_2_0·b_4_0·b_4_1·b_9_0
       + b_2_0·b_4_0·b_4_1·b_6_0·b_3_1 + b_2_0·b_4_0·b_4_12·b_5_1
       + b_2_0·b_4_0·b_4_12·b_5_0 + b_2_0·b_4_02·b_9_1 + b_2_0·b_4_02·b_9_0
       + b_2_0·b_4_03·b_5_1 + b_2_0·b_4_03·b_5_0 + b_2_02·b_4_13·b_3_0
       + b_2_02·b_4_0·b_4_1·b_7_4 + b_2_02·b_4_0·b_4_12·b_3_0 + b_2_02·b_4_02·b_7_4
       + b_2_02·b_4_02·b_7_0 + b_2_02·b_4_02·b_4_1·b_3_1 + b_2_03·b_4_12·b_5_1
       + b_2_03·b_4_0·b_9_1 + b_2_03·b_4_0·b_9_0 + b_2_03·b_4_0·b_6_0·b_3_0
       + b_2_03·b_4_0·b_4_1·b_5_1 + b_2_03·b_4_02·b_5_0 + b_2_04·b_4_1·b_7_0
       + b_2_04·b_4_12·b_3_1 + b_2_04·b_4_0·b_7_0 + b_2_04·b_4_02·b_3_0
       + b_2_05·b_4_1·b_5_0 + b_2_05·b_4_0·b_5_1 + b_2_05·b_4_0·b_5_0 + b_2_06·b_4_0·b_3_1
       + b_4_1·c_8_2·b_7_0 + b_4_12·c_8_2·b_3_1 + b_2_0·b_6_0·c_8_2·b_3_0
       + b_2_0·b_4_0·c_8_2·b_5_1 + b_2_0·b_4_0·c_8_2·b_5_0 + b_2_02·b_4_1·c_8_2·b_3_0
       + b_2_02·b_4_0·c_8_2·b_3_0 + b_2_03·c_8_2·b_5_0 + b_2_04·c_8_2·b_3_0
  157. b_10_15·b_9_1 + b_4_1·b_6_02·b_3_0 + b_4_13·b_7_0 + b_4_14·b_3_0
       + b_4_0·b_6_02·b_3_1 + b_4_0·b_6_02·b_3_0 + b_4_0·b_4_13·b_3_1 + b_4_0·b_4_13·b_3_0
       + b_4_02·b_4_1·b_7_4 + b_4_02·b_4_1·b_7_0 + b_4_02·b_4_12·b_3_1
       + b_4_02·b_4_12·b_3_0 + b_2_0·b_4_12·b_6_0·b_3_1 + b_2_0·b_4_12·b_6_0·b_3_0
       + b_2_0·b_4_13·b_5_0 + b_2_0·b_4_0·b_4_12·b_5_1 + b_2_0·b_4_0·b_4_12·b_5_0
       + b_2_0·b_4_02·b_9_1 + b_2_0·b_4_02·b_9_0 + b_2_0·b_4_02·b_6_0·b_3_0
       + b_2_0·b_4_03·b_5_1 + b_2_0·b_4_03·b_5_0 + b_2_02·b_4_12·b_7_4
       + b_2_02·b_4_12·b_7_0 + b_2_02·b_4_0·b_4_1·b_7_0 + b_2_02·b_4_0·b_4_12·b_3_1
       + b_2_02·b_4_02·b_7_0 + b_2_02·b_4_02·b_4_1·b_3_1 + b_2_02·b_4_02·b_4_1·b_3_0
       + b_2_02·b_4_03·b_3_1 + b_2_02·b_4_03·b_3_0 + b_2_03·b_4_1·b_9_1
       + b_2_03·b_4_1·b_6_0·b_3_0 + b_2_03·b_4_12·b_5_1 + b_2_03·b_4_12·b_5_0
       + b_2_03·b_4_0·b_9_1 + b_2_03·b_4_0·b_9_0 + b_2_03·b_4_0·b_6_0·b_3_1
       + b_2_03·b_4_0·b_6_0·b_3_0 + b_2_03·b_4_0·b_4_1·b_5_1 + b_2_03·b_4_02·b_5_1
       + b_2_03·b_4_02·b_5_0 + b_2_04·b_4_1·b_7_4 + b_2_04·b_4_1·b_7_0
       + b_2_04·b_4_12·b_3_1 + b_2_04·b_4_12·b_3_0 + b_2_04·b_4_0·b_7_4
       + b_2_04·b_4_0·b_4_1·b_3_1 + b_2_05·b_4_1·b_5_1 + b_2_05·b_4_1·b_5_0
       + b_2_05·b_4_0·b_5_1 + b_2_05·b_4_0·b_5_0 + b_2_06·b_7_4 + b_2_06·b_7_0
       + b_2_06·b_4_0·b_3_1 + b_2_06·b_4_0·b_3_0 + b_2_07·b_5_0 + b_4_1·c_8_2·b_7_4
       + b_4_12·c_8_2·b_3_1 + b_4_12·c_8_2·b_3_0 + b_4_0·b_4_1·c_8_2·b_3_0
       + b_2_0·b_4_0·c_8_2·b_5_0 + b_2_02·c_8_2·b_7_4 + b_2_02·c_8_2·b_7_0
       + b_2_02·b_4_0·c_8_2·b_3_1 + b_2_02·b_4_0·c_8_2·b_3_0 + b_2_03·c_8_2·b_5_1
       + b_2_04·c_8_2·b_3_0
  158. b_10_152 + b_4_13·b_8_1 + b_4_15 + b_4_0·b_4_1·b_6_0·b_3_02 + b_4_0·b_4_12·b_8_0
       + b_4_02·b_6_0·b_3_02 + b_4_02·b_6_02 + b_4_02·b_4_1·b_8_0
       + b_4_02·b_4_12·b_4_3 + b_4_03·b_4_1·b_4_3 + b_2_0·b_4_12·b_4_3·b_6_0
       + b_2_0·b_4_13·b_3_0·b_3_1 + b_2_0·b_4_13·b_6_0 + b_2_0·b_4_02·b_10_15
       + b_2_0·b_4_03·b_3_02 + b_2_0·b_4_03·b_6_1 + b_2_0·b_4_03·b_6_0
       + b_2_02·b_4_12·b_8_1 + b_2_02·b_4_14 + b_2_02·b_4_0·b_4_1·b_8_0
       + b_2_02·b_4_02·b_8_1 + b_2_02·b_4_02·b_8_0 + b_2_03·b_4_1·b_4_3·b_6_0
       + b_2_03·b_4_12·b_6_0 + b_2_03·b_4_0·b_4_3·b_6_0 + b_2_03·b_4_0·b_4_1·b_3_02
       + b_2_03·b_4_0·b_4_1·b_6_0 + b_2_04·b_4_1·b_8_1 + b_2_04·b_4_12·b_4_3
       + b_2_04·b_4_13 + b_2_04·b_4_0·b_8_1 + b_2_04·b_4_0·b_4_1·b_4_3
       + b_2_04·b_4_0·b_4_12 + b_2_05·b_10_15 + b_2_05·b_4_0·b_3_0·b_3_1
       + b_2_05·b_4_0·b_6_0 + b_2_06·b_4_0·b_4_1 + b_2_06·b_4_02 + b_6_02·c_8_2
       + b_4_12·b_4_3·c_8_2 + b_2_0·b_4_1·c_8_2·b_3_0·b_3_1 + b_2_0·b_4_0·c_8_2·b_3_0·b_3_1
       + b_2_0·b_4_0·c_8_2·b_3_02 + b_2_03·c_8_2·b_3_0·b_3_1 + b_2_03·c_8_2·b_3_02
       + b_2_03·b_6_1·c_8_2 + b_2_04·b_4_3·c_8_2 + b_2_04·b_4_0·c_8_2 + b_2_06·c_8_2

About the group Ring generators Ring relations Completion information Restriction maps

Data used for the Hilbert-Poincaré test

  • We proved completion in degree 20 using the Hilbert-Poincaré criterion.
  • 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. b_4_1·b_4_3 + b_4_0·b_4_3 + b_2_04 + c_8_2, an element of degree 8
    2. b_6_02 + b_4_1·b_8_1 + b_4_1·b_8_0 + b_4_13 + b_4_02·b_4_3 + b_4_02·b_4_1 + b_4_03
         + b_2_0·b_4_1·b_3_0·b_3_1 + b_2_0·b_4_1·b_3_02 + b_2_0·b_4_1·b_6_0
         + b_2_0·b_4_0·b_3_0·b_3_1 + b_2_0·b_4_0·b_3_02 + b_2_0·b_4_0·b_6_0 + b_2_02·b_8_1
         + b_2_02·b_4_1·b_4_3 + b_2_02·b_4_12 + b_2_02·b_4_0·b_4_1 + b_2_02·b_4_02
         + b_2_03·b_3_0·b_3_1 + b_2_03·b_3_02 + b_2_03·b_6_1 + b_2_04·b_4_1 + b_2_04·b_4_0
         + b_2_06 + b_4_3·c_8_2 + b_2_02·c_8_2, an element of degree 12
    3. b_4_12·b_3_02 + b_4_0·b_4_1·b_3_0·b_3_1 + b_4_02·b_3_0·b_3_1 + b_4_02·b_3_02
         + b_2_0·b_4_12·b_4_3 + b_2_0·b_4_13 + b_2_0·b_4_02·b_4_3 + b_2_0·b_4_02·b_4_1
         + b_2_0·b_4_03 + b_2_02·b_4_3·b_6_0 + b_2_02·b_4_1·b_3_02 + b_2_02·b_4_0·b_6_0
         + b_2_03·b_8_0 + b_2_03·b_4_0·b_4_1 + b_2_03·b_4_02 + b_2_04·b_6_1 + b_2_04·b_6_0
         + b_2_05·b_4_3 + b_2_05·b_4_1 + c_8_2·b_3_0·b_3_1 + c_8_2·b_3_02 + b_2_0·b_4_3·c_8_2
         + b_2_03·c_8_2, an element of degree 14
    4. b_3_0, an element of degree 3
  • A Duflot regular sequence is given by c_8_2.
  • The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, 15, 26, 33].
  • Modifying the above filter regular HSOP, we obtained the following parameters:
    1. b_4_1·b_4_3 + b_4_0·b_4_3 + b_2_04 + c_8_2, an element of degree 8
    2. b_4_0 + b_2_02, an element of degree 4
    3. b_2_0, an element of degree 2
    4. b_3_0, an element of degree 3

About the group Ring generators Ring relations Completion information Restriction maps

Restriction maps

Expressing the generators as elements of H*(Syl2(J2); GF(2))

  1. b_2_0 → b_1_22 + b_1_1·b_1_2 + b_1_12
  2. a_3_2 → a_2_4·b_1_2
  3. b_3_1 → b_1_1·b_1_22 + b_1_12·b_1_2
  4. b_3_0 → b_1_23 + b_1_12·b_1_2 + b_1_13
  5. b_4_3 → b_1_1·b_3_8 + b_1_04 + b_4_14 + a_2_4·b_1_02 + a_2_4·a_2_5
  6. b_4_1 → b_1_2·b_3_8 + b_1_1·b_3_9 + b_1_1·b_1_23 + b_1_12·b_1_22
  7. b_4_0 → b_1_2·b_3_9 + b_1_1·b_3_9 + b_1_12·b_1_22 + b_1_13·b_1_2 + b_1_04 + b_4_14
       + a_2_4·b_1_02 + a_2_4·a_2_5
  8. a_5_4 → a_2_4·b_3_9
  9. b_5_1 → b_1_22·b_3_8 + b_1_12·b_3_9 + b_1_12·b_1_23 + b_1_14·b_1_2
  10. b_5_0 → b_1_22·b_3_9 + b_1_12·b_3_9 + b_1_12·b_3_8 + b_1_13·b_1_22 + b_1_14·b_1_2
  11. b_6_1 → b_1_2·b_5_20 + b_1_1·b_5_21 + b_1_1·b_5_20 + b_1_13·b_3_8 + b_4_14·b_1_22
       + b_4_14·b_1_1·b_1_2 + b_4_14·b_1_12
  12. b_6_0 → b_3_8·b_3_9 + b_1_1·b_5_20 + b_1_12·b_1_2·b_3_9 + b_4_14·b_1_22 + b_4_14·b_1_1·b_1_2
       + a_2_5·b_4_14 + a_2_4·b_4_14 + a_2_4·a_2_5·b_1_02 + a_2_42·b_1_02
  13. a_7_10 → a_2_4·b_5_20 + a_2_42·b_1_03 + a_2_42·a_2_5·b_1_0
  14. b_7_4 → b_1_1·b_1_2·b_5_20 + b_1_12·b_5_20 + b_1_12·b_1_25 + b_1_14·b_3_8
       + b_1_14·b_1_23 + b_4_14·b_1_23 + b_4_14·b_1_1·b_1_22 + b_4_14·b_1_13
  15. b_7_0 → b_1_22·b_5_20 + b_1_12·b_5_21 + b_1_12·b_5_20 + b_1_12·b_1_25 + b_1_13·b_1_24
       + b_1_14·b_3_8 + b_1_14·b_1_23 + b_1_15·b_1_22 + b_4_14·b_1_23
       + b_4_14·b_1_1·b_1_22 + b_4_14·b_1_13
  16. c_8_2 → b_3_8·b_5_20 + b_1_1·b_1_22·b_5_20 + b_1_12·b_1_23·b_3_9 + b_1_13·b_5_20
       + b_1_13·b_1_22·b_3_9 + b_1_14·b_1_2·b_3_9 + b_1_14·b_1_2·b_3_8 + b_1_15·b_3_9
       + b_4_14·b_1_2·b_3_9 + b_4_14·b_1_24 + b_4_14·b_1_14 + b_4_142
       + a_2_4·a_2_5·b_1_04 + c_8_49
  17. b_8_1 → b_3_9·b_5_20 + b_3_8·b_5_21 + b_3_8·b_5_20 + b_1_1·b_1_22·b_5_20 + b_1_13·b_5_20
       + b_1_13·b_1_22·b_3_9 + b_1_14·b_1_2·b_3_9 + b_1_08 + b_4_14·b_1_2·b_3_9
       + b_4_14·b_1_1·b_3_9 + b_4_14·b_1_1·b_3_8 + b_4_14·b_1_12·b_1_22
       + b_4_14·b_1_13·b_1_2 + b_4_142 + a_2_42·b_1_04
  18. b_8_0 → b_3_9·b_5_21 + b_3_9·b_5_20 + b_3_8·b_5_21 + b_1_12·b_1_2·b_5_20
       + b_1_13·b_1_22·b_3_9 + b_1_13·b_1_22·b_3_8 + b_1_13·b_1_25 + b_1_15·b_1_23
       + b_1_08 + b_4_14·b_1_1·b_1_23 + b_4_142 + a_2_42·b_1_04
  19. b_9_1 → b_1_2·b_3_8·b_5_20 + b_1_1·b_3_9·b_5_21 + b_1_12·b_1_22·b_5_20
       + b_1_13·b_1_23·b_3_9 + b_1_13·b_1_23·b_3_8 + b_1_14·b_5_21 + b_1_14·b_1_25
       + b_1_15·b_1_2·b_3_8 + b_1_15·b_1_24 + b_1_16·b_3_8 + b_1_16·b_1_23
       + b_1_17·b_1_22 + b_4_14·b_1_22·b_3_9 + b_4_14·b_1_22·b_3_8 + b_4_14·b_1_25
       + b_4_14·b_1_12·b_3_8 + b_4_14·b_1_14·b_1_2 + b_4_14·b_1_15
  20. b_9_0 → b_1_2·b_3_9·b_5_20 + b_1_1·b_3_9·b_5_21 + b_1_1·b_3_8·b_5_21 + b_1_12·b_1_22·b_5_20
       + b_1_14·b_1_22·b_3_9 + b_1_14·b_1_22·b_3_8 + b_1_15·b_1_2·b_3_8
       + b_4_14·b_1_1·b_1_24 + b_4_14·b_1_14·b_1_2
  21. b_10_15 → b_1_12·b_3_8·b_5_21 + b_1_14·b_1_26 + b_1_15·b_1_22·b_3_9
       + b_1_15·b_1_22·b_3_8 + b_1_15·b_1_25 + b_1_16·b_1_2·b_3_8 + b_1_16·b_1_24
       + b_1_17·b_1_23 + b_10_83 + b_4_14·b_3_8·b_3_9 + b_4_14·b_1_23·b_3_9
       + b_4_14·b_1_23·b_3_8 + b_4_14·b_1_1·b_5_21 + b_4_14·b_1_1·b_1_22·b_3_9
       + b_4_14·b_1_12·b_1_2·b_3_9 + b_4_14·b_1_13·b_3_9 + b_4_14·b_1_13·b_3_8
       + b_4_142·b_1_1·b_1_2 + b_4_142·b_1_12 + a_2_5·b_4_142 + a_2_4·a_2_5·b_1_06
       + c_8_49·b_1_1·b_1_2 + c_8_49·b_1_12 + c_8_49·b_1_02 + a_2_4·c_8_49

Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 1

  1. b_2_0 → 0, an element of degree 2
  2. a_3_2 → 0, an element of degree 3
  3. b_3_1 → 0, an element of degree 3
  4. b_3_0 → 0, an element of degree 3
  5. b_4_3 → 0, an element of degree 4
  6. b_4_1 → 0, an element of degree 4
  7. b_4_0 → 0, an element of degree 4
  8. a_5_4 → 0, an element of degree 5
  9. b_5_1 → 0, an element of degree 5
  10. b_5_0 → 0, an element of degree 5
  11. b_6_1 → 0, an element of degree 6
  12. b_6_0 → 0, an element of degree 6
  13. a_7_10 → 0, an element of degree 7
  14. b_7_4 → 0, an element of degree 7
  15. b_7_0 → 0, an element of degree 7
  16. c_8_2 → c_1_08, an element of degree 8
  17. b_8_1 → 0, an element of degree 8
  18. b_8_0 → 0, an element of degree 8
  19. b_9_1 → 0, an element of degree 9
  20. b_9_0 → 0, an element of degree 9
  21. b_10_15 → 0, an element of degree 10

Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup

  1. b_2_0 → 0, an element of degree 2
  2. a_3_2 → 0, an element of degree 3
  3. b_3_1 → 0, an element of degree 3
  4. b_3_0 → 0, an element of degree 3
  5. b_4_3 → c_1_14, an element of degree 4
  6. b_4_1 → 0, an element of degree 4
  7. b_4_0 → c_1_14, an element of degree 4
  8. a_5_4 → 0, an element of degree 5
  9. b_5_1 → 0, an element of degree 5
  10. b_5_0 → 0, an element of degree 5
  11. b_6_1 → 0, an element of degree 6
  12. b_6_0 → 0, an element of degree 6
  13. a_7_10 → 0, an element of degree 7
  14. b_7_4 → 0, an element of degree 7
  15. b_7_0 → 0, an element of degree 7
  16. c_8_2 → c_1_04·c_1_14 + c_1_08, an element of degree 8
  17. b_8_1 → c_1_18, an element of degree 8
  18. b_8_0 → c_1_18, an element of degree 8
  19. b_9_1 → 0, an element of degree 9
  20. b_9_0 → 0, an element of degree 9
  21. b_10_15 → 0, an element of degree 10

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

  1. b_2_0 → c_1_32 + c_1_2·c_1_3 + c_1_22, an element of degree 2
  2. a_3_2 → 0, an element of degree 3
  3. b_3_1 → c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  4. b_3_0 → c_1_33 + c_1_22·c_1_3 + c_1_23, an element of degree 3
  5. b_4_3 → c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3
       + c_1_12·c_1_22 + c_1_14, an element of degree 4
  6. b_4_1 → c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_1·c_1_33 + c_1_1·c_1_22·c_1_3
       + c_1_1·c_1_23 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22
       + c_1_0·c_1_2·c_1_32 + c_1_0·c_1_22·c_1_3, an element of degree 4
  7. b_4_0 → c_1_22·c_1_32 + c_1_23·c_1_3 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3
       + c_1_12·c_1_22 + c_1_14 + c_1_0·c_1_33 + c_1_0·c_1_2·c_1_32 + c_1_0·c_1_23
       + c_1_02·c_1_32 + c_1_02·c_1_2·c_1_3 + c_1_02·c_1_22, an element of degree 4
  8. a_5_4 → 0, an element of degree 5
  9. b_5_1 → c_1_22·c_1_33 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_1·c_1_22·c_1_32
       + c_1_1·c_1_24 + c_1_12·c_1_33 + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_23
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3, an element of degree 5
  10. b_5_0 → c_1_23·c_1_32 + c_1_24·c_1_3 + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_3
       + c_1_0·c_1_34 + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_24 + c_1_02·c_1_33
       + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_23, an element of degree 5
  11. b_6_1 → c_1_0·c_1_2·c_1_34 + c_1_0·c_1_24·c_1_3 + c_1_02·c_1_34
       + c_1_02·c_1_22·c_1_32 + c_1_02·c_1_24 + c_1_04·c_1_32 + c_1_04·c_1_2·c_1_3
       + c_1_04·c_1_22, an element of degree 6
  12. b_6_0 → c_1_1·c_1_23·c_1_32 + c_1_1·c_1_24·c_1_3 + c_1_12·c_1_34
       + c_1_12·c_1_23·c_1_3 + c_1_12·c_1_24 + c_1_13·c_1_2·c_1_32
       + c_1_13·c_1_22·c_1_3 + c_1_14·c_1_32 + c_1_14·c_1_2·c_1_3 + c_1_14·c_1_22
       + c_1_0·c_1_22·c_1_33 + c_1_0·c_1_24·c_1_3 + c_1_0·c_1_1·c_1_34
       + c_1_0·c_1_1·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_24 + c_1_0·c_1_12·c_1_33
       + c_1_0·c_1_12·c_1_2·c_1_32 + c_1_0·c_1_12·c_1_23 + c_1_02·c_1_2·c_1_33
       + c_1_02·c_1_22·c_1_32 + c_1_02·c_1_1·c_1_33 + c_1_02·c_1_1·c_1_22·c_1_3
       + c_1_02·c_1_1·c_1_23 + c_1_02·c_1_12·c_1_32 + c_1_02·c_1_12·c_1_2·c_1_3
       + c_1_02·c_1_12·c_1_22 + c_1_03·c_1_2·c_1_32 + c_1_03·c_1_22·c_1_3, an element of degree 6
  13. a_7_10 → 0, an element of degree 7
  14. b_7_4 → c_1_22·c_1_35 + c_1_24·c_1_33 + c_1_12·c_1_35 + c_1_12·c_1_24·c_1_3
       + c_1_12·c_1_25 + c_1_14·c_1_33 + c_1_14·c_1_22·c_1_3 + c_1_14·c_1_23
       + c_1_02·c_1_2·c_1_34 + c_1_02·c_1_24·c_1_3 + c_1_04·c_1_2·c_1_32
       + c_1_04·c_1_22·c_1_3, an element of degree 7
  15. b_7_0 → c_1_22·c_1_35 + c_1_23·c_1_34 + c_1_24·c_1_33 + c_1_25·c_1_32
       + c_1_1·c_1_2·c_1_35 + c_1_1·c_1_22·c_1_34 + c_1_1·c_1_23·c_1_33
       + c_1_1·c_1_25·c_1_3 + c_1_14·c_1_2·c_1_32 + c_1_14·c_1_22·c_1_3
       + c_1_02·c_1_35 + c_1_02·c_1_24·c_1_3 + c_1_02·c_1_25 + c_1_04·c_1_33
       + c_1_04·c_1_22·c_1_3 + c_1_04·c_1_23, an element of degree 7
  16. c_8_2 → c_1_1·c_1_22·c_1_35 + 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_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_25 + c_1_14·c_1_34
       + c_1_14·c_1_2·c_1_33 + c_1_14·c_1_22·c_1_32 + c_1_14·c_1_23·c_1_3
       + c_1_14·c_1_24 + c_1_15·c_1_33 + c_1_15·c_1_2·c_1_32 + c_1_15·c_1_23
       + c_1_16·c_1_32 + c_1_16·c_1_2·c_1_3 + c_1_16·c_1_22
       + c_1_0·c_1_1·c_1_2·c_1_35 + c_1_0·c_1_1·c_1_23·c_1_33
       + c_1_0·c_1_1·c_1_24·c_1_32 + c_1_0·c_1_1·c_1_25·c_1_3 + c_1_0·c_1_12·c_1_35
       + c_1_0·c_1_12·c_1_24·c_1_3 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_33
       + c_1_0·c_1_14·c_1_2·c_1_32 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_22·c_1_34
       + c_1_02·c_1_24·c_1_32 + 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_32 + c_1_04·c_1_12·c_1_2·c_1_3 + c_1_04·c_1_12·c_1_22
       + c_1_04·c_1_14 + c_1_08, an element of degree 8
  17. b_8_1 → c_1_1·c_1_22·c_1_35 + c_1_1·c_1_23·c_1_34 + c_1_1·c_1_24·c_1_33
       + c_1_1·c_1_26·c_1_3 + 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_25·c_1_3 + c_1_12·c_1_26
       + c_1_13·c_1_35 + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_25 + c_1_14·c_1_34
       + c_1_14·c_1_2·c_1_33 + c_1_14·c_1_24 + c_1_15·c_1_33 + c_1_15·c_1_22·c_1_3
       + c_1_15·c_1_23 + c_1_16·c_1_32 + c_1_16·c_1_2·c_1_3 + c_1_16·c_1_22 + c_1_18
       + c_1_0·c_1_24·c_1_33 + c_1_0·c_1_26·c_1_3 + c_1_0·c_1_1·c_1_36
       + c_1_0·c_1_1·c_1_22·c_1_34 + c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_35
       + c_1_0·c_1_12·c_1_24·c_1_3 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_2·c_1_32
       + c_1_0·c_1_14·c_1_22·c_1_3 + c_1_02·c_1_2·c_1_35 + c_1_02·c_1_23·c_1_33
       + 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_03·c_1_35
       + c_1_03·c_1_2·c_1_34 + c_1_03·c_1_25 + c_1_04·c_1_34 + c_1_04·c_1_2·c_1_33
       + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_23·c_1_3 + c_1_04·c_1_24
       + c_1_04·c_1_1·c_1_33 + c_1_04·c_1_1·c_1_2·c_1_32 + c_1_04·c_1_1·c_1_23
       + 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_12·c_1_22
       + c_1_05·c_1_33 + c_1_05·c_1_22·c_1_3 + c_1_05·c_1_23 + c_1_06·c_1_32
       + c_1_06·c_1_2·c_1_3 + c_1_06·c_1_22, an element of degree 8
  18. b_8_0 → c_1_23·c_1_35 + c_1_25·c_1_33 + 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_25·c_1_3 + c_1_12·c_1_26 + c_1_13·c_1_2·c_1_34
       + c_1_13·c_1_24·c_1_3 + c_1_14·c_1_22·c_1_32 + c_1_14·c_1_23·c_1_3
       + c_1_15·c_1_2·c_1_32 + c_1_15·c_1_22·c_1_3 + c_1_18 + c_1_0·c_1_23·c_1_34
       + c_1_0·c_1_25·c_1_32 + c_1_0·c_1_1·c_1_2·c_1_35 + c_1_0·c_1_1·c_1_22·c_1_34
       + c_1_0·c_1_1·c_1_23·c_1_33 + c_1_0·c_1_1·c_1_25·c_1_3 + c_1_0·c_1_12·c_1_35
       + c_1_0·c_1_12·c_1_24·c_1_3 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_33
       + c_1_0·c_1_14·c_1_2·c_1_32 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_36
       + c_1_02·c_1_2·c_1_35 + c_1_02·c_1_22·c_1_34 + c_1_02·c_1_23·c_1_33
       + c_1_02·c_1_26 + 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_14·c_1_32 + c_1_02·c_1_14·c_1_2·c_1_3
       + c_1_02·c_1_14·c_1_22 + c_1_03·c_1_35 + c_1_03·c_1_2·c_1_34
       + c_1_03·c_1_25 + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_23·c_1_3
       + 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_05·c_1_33
       + c_1_05·c_1_2·c_1_32 + c_1_05·c_1_23 + c_1_06·c_1_32 + c_1_06·c_1_2·c_1_3
       + c_1_06·c_1_22, an element of degree 8
  19. b_9_1 → c_1_24·c_1_35 + c_1_25·c_1_34 + c_1_26·c_1_33 + c_1_27·c_1_32
       + c_1_1·c_1_22·c_1_36 + c_1_1·c_1_23·c_1_35 + c_1_1·c_1_25·c_1_33
       + c_1_1·c_1_26·c_1_32 + c_1_12·c_1_37 + c_1_12·c_1_2·c_1_36
       + c_1_12·c_1_22·c_1_35 + c_1_12·c_1_24·c_1_33 + c_1_12·c_1_25·c_1_32
       + c_1_12·c_1_26·c_1_3 + c_1_12·c_1_27 + c_1_14·c_1_35
       + c_1_14·c_1_23·c_1_32 + c_1_14·c_1_25 + c_1_16·c_1_2·c_1_32
       + c_1_16·c_1_22·c_1_3 + c_1_0·c_1_1·c_1_2·c_1_36 + c_1_0·c_1_1·c_1_22·c_1_35
       + c_1_0·c_1_1·c_1_23·c_1_34 + c_1_0·c_1_1·c_1_24·c_1_33
       + c_1_0·c_1_1·c_1_25·c_1_32 + c_1_0·c_1_1·c_1_26·c_1_3 + c_1_0·c_1_12·c_1_36
       + c_1_0·c_1_12·c_1_2·c_1_35 + c_1_0·c_1_12·c_1_23·c_1_33
       + c_1_0·c_1_12·c_1_25·c_1_3 + c_1_0·c_1_12·c_1_26 + c_1_0·c_1_14·c_1_34
       + c_1_0·c_1_14·c_1_22·c_1_32 + c_1_0·c_1_14·c_1_24 + c_1_02·c_1_2·c_1_36
       + c_1_02·c_1_22·c_1_35 + c_1_02·c_1_1·c_1_36 + c_1_02·c_1_1·c_1_2·c_1_35
       + c_1_02·c_1_1·c_1_23·c_1_33 + c_1_02·c_1_1·c_1_25·c_1_3
       + c_1_02·c_1_1·c_1_26 + c_1_02·c_1_14·c_1_33 + c_1_02·c_1_14·c_1_22·c_1_3
       + c_1_02·c_1_14·c_1_23 + c_1_04·c_1_22·c_1_33 + c_1_04·c_1_24·c_1_3
       + c_1_04·c_1_1·c_1_34 + c_1_04·c_1_1·c_1_22·c_1_32 + c_1_04·c_1_1·c_1_24
       + c_1_04·c_1_12·c_1_33 + c_1_04·c_1_12·c_1_2·c_1_32
       + c_1_04·c_1_12·c_1_23 + c_1_06·c_1_2·c_1_32 + c_1_06·c_1_22·c_1_3, an element of degree 9
  20. b_9_0 → c_1_1·c_1_24·c_1_34 + c_1_1·c_1_26·c_1_32 + c_1_12·c_1_23·c_1_34
       + c_1_12·c_1_26·c_1_3 + c_1_13·c_1_22·c_1_34 + c_1_13·c_1_24·c_1_32
       + c_1_14·c_1_2·c_1_34 + c_1_14·c_1_23·c_1_32 + c_1_16·c_1_2·c_1_32
       + c_1_16·c_1_22·c_1_3 + c_1_0·c_1_24·c_1_34 + c_1_0·c_1_26·c_1_32
       + c_1_0·c_1_1·c_1_2·c_1_36 + c_1_0·c_1_1·c_1_22·c_1_35
       + c_1_0·c_1_1·c_1_23·c_1_34 + c_1_0·c_1_1·c_1_24·c_1_33
       + c_1_0·c_1_1·c_1_25·c_1_32 + c_1_0·c_1_1·c_1_26·c_1_3 + c_1_0·c_1_12·c_1_36
       + c_1_0·c_1_12·c_1_2·c_1_35 + c_1_0·c_1_12·c_1_22·c_1_34
       + c_1_0·c_1_12·c_1_23·c_1_33 + c_1_0·c_1_12·c_1_24·c_1_32
       + c_1_0·c_1_12·c_1_25·c_1_3 + c_1_0·c_1_12·c_1_26 + c_1_0·c_1_14·c_1_34
       + c_1_0·c_1_14·c_1_22·c_1_32 + c_1_0·c_1_14·c_1_24 + c_1_02·c_1_2·c_1_36
       + c_1_02·c_1_22·c_1_35 + c_1_02·c_1_24·c_1_33 + c_1_02·c_1_25·c_1_32
       + c_1_02·c_1_1·c_1_2·c_1_35 + c_1_02·c_1_1·c_1_22·c_1_34
       + c_1_02·c_1_1·c_1_23·c_1_33 + c_1_02·c_1_1·c_1_25·c_1_3
       + c_1_02·c_1_12·c_1_35 + c_1_02·c_1_12·c_1_24·c_1_3 + c_1_02·c_1_12·c_1_25
       + c_1_02·c_1_14·c_1_33 + c_1_02·c_1_14·c_1_22·c_1_3 + c_1_02·c_1_14·c_1_23
       + c_1_03·c_1_36 + c_1_03·c_1_22·c_1_34 + c_1_03·c_1_26 + c_1_04·c_1_35
       + c_1_04·c_1_2·c_1_34 + c_1_04·c_1_23·c_1_32 + c_1_04·c_1_24·c_1_3
       + c_1_04·c_1_25 + c_1_04·c_1_12·c_1_2·c_1_32 + c_1_04·c_1_12·c_1_22·c_1_3
       + c_1_05·c_1_34 + c_1_05·c_1_22·c_1_32 + c_1_05·c_1_24 + c_1_06·c_1_33
       + c_1_06·c_1_22·c_1_3 + c_1_06·c_1_23, an element of degree 9
  21. b_10_15 → c_1_24·c_1_36 + c_1_25·c_1_35 + c_1_26·c_1_34 + c_1_27·c_1_33
       + c_1_1·c_1_22·c_1_37 + c_1_1·c_1_23·c_1_36 + c_1_1·c_1_24·c_1_35
       + c_1_1·c_1_27·c_1_32 + c_1_12·c_1_2·c_1_37 + c_1_12·c_1_23·c_1_35
       + c_1_12·c_1_24·c_1_34 + c_1_12·c_1_27·c_1_3 + c_1_13·c_1_2·c_1_36
       + c_1_13·c_1_22·c_1_35 + c_1_13·c_1_23·c_1_34 + c_1_13·c_1_24·c_1_33
       + c_1_14·c_1_36 + c_1_14·c_1_22·c_1_34 + c_1_14·c_1_24·c_1_32
       + c_1_14·c_1_25·c_1_3 + c_1_14·c_1_26 + c_1_15·c_1_23·c_1_32
       + c_1_15·c_1_24·c_1_3 + c_1_16·c_1_22·c_1_32 + c_1_16·c_1_23·c_1_3
       + c_1_17·c_1_2·c_1_32 + c_1_17·c_1_22·c_1_3 + c_1_18·c_1_32
       + c_1_18·c_1_2·c_1_3 + c_1_18·c_1_22 + c_1_0·c_1_2·c_1_38
       + c_1_0·c_1_23·c_1_36 + c_1_0·c_1_24·c_1_35 + c_1_0·c_1_26·c_1_33
       + c_1_0·c_1_27·c_1_32 + c_1_0·c_1_28·c_1_3 + c_1_0·c_1_1·c_1_22·c_1_36
       + c_1_0·c_1_1·c_1_26·c_1_32 + c_1_0·c_1_12·c_1_22·c_1_35
       + c_1_0·c_1_12·c_1_26·c_1_3 + c_1_0·c_1_13·c_1_36
       + c_1_0·c_1_13·c_1_22·c_1_34 + c_1_0·c_1_13·c_1_26 + c_1_0·c_1_14·c_1_35
       + c_1_0·c_1_14·c_1_2·c_1_34 + c_1_0·c_1_14·c_1_22·c_1_33
       + c_1_0·c_1_14·c_1_24·c_1_3 + c_1_0·c_1_14·c_1_25 + c_1_0·c_1_15·c_1_34
       + c_1_0·c_1_15·c_1_22·c_1_32 + c_1_0·c_1_15·c_1_24 + c_1_0·c_1_16·c_1_33
       + c_1_0·c_1_16·c_1_2·c_1_32 + c_1_0·c_1_16·c_1_23 + c_1_02·c_1_38
       + c_1_02·c_1_22·c_1_36 + c_1_02·c_1_24·c_1_34 + c_1_02·c_1_27·c_1_3
       + c_1_02·c_1_28 + c_1_02·c_1_1·c_1_22·c_1_35 + c_1_02·c_1_1·c_1_23·c_1_34
       + c_1_02·c_1_1·c_1_24·c_1_33 + c_1_02·c_1_1·c_1_26·c_1_3
       + c_1_02·c_1_12·c_1_36 + c_1_02·c_1_12·c_1_23·c_1_33
       + c_1_02·c_1_12·c_1_26 + c_1_02·c_1_13·c_1_35
       + c_1_02·c_1_13·c_1_2·c_1_34 + c_1_02·c_1_13·c_1_25
       + c_1_02·c_1_14·c_1_2·c_1_33 + c_1_02·c_1_14·c_1_22·c_1_32
       + c_1_02·c_1_15·c_1_33 + c_1_02·c_1_15·c_1_22·c_1_3 + c_1_02·c_1_15·c_1_23
       + c_1_02·c_1_16·c_1_32 + c_1_02·c_1_16·c_1_2·c_1_3 + c_1_02·c_1_16·c_1_22
       + c_1_03·c_1_37 + c_1_03·c_1_24·c_1_33 + c_1_03·c_1_27
       + c_1_03·c_1_1·c_1_36 + c_1_03·c_1_1·c_1_24·c_1_32 + c_1_03·c_1_1·c_1_26
       + c_1_03·c_1_12·c_1_35 + c_1_03·c_1_12·c_1_24·c_1_3 + c_1_03·c_1_12·c_1_25
       + c_1_03·c_1_14·c_1_2·c_1_32 + c_1_03·c_1_14·c_1_22·c_1_3
       + c_1_04·c_1_22·c_1_34 + c_1_04·c_1_23·c_1_33 + c_1_04·c_1_1·c_1_35
       + c_1_04·c_1_1·c_1_23·c_1_32 + c_1_04·c_1_1·c_1_25
       + c_1_04·c_1_12·c_1_22·c_1_32 + c_1_04·c_1_12·c_1_23·c_1_3
       + c_1_04·c_1_13·c_1_2·c_1_32 + c_1_04·c_1_13·c_1_22·c_1_3
       + c_1_04·c_1_14·c_1_32 + c_1_04·c_1_14·c_1_2·c_1_3 + c_1_04·c_1_14·c_1_22
       + c_1_05·c_1_35 + c_1_05·c_1_2·c_1_34 + c_1_05·c_1_22·c_1_33
       + c_1_05·c_1_24·c_1_3 + c_1_05·c_1_25 + c_1_05·c_1_1·c_1_34
       + c_1_05·c_1_1·c_1_22·c_1_32 + c_1_05·c_1_1·c_1_24 + c_1_05·c_1_12·c_1_33
       + c_1_05·c_1_12·c_1_2·c_1_32 + c_1_05·c_1_12·c_1_23 + c_1_06·c_1_34
       + c_1_06·c_1_2·c_1_33 + c_1_06·c_1_24 + c_1_06·c_1_1·c_1_33
       + c_1_06·c_1_1·c_1_22·c_1_3 + c_1_06·c_1_1·c_1_23 + c_1_06·c_1_12·c_1_32
       + c_1_06·c_1_12·c_1_2·c_1_3 + c_1_06·c_1_12·c_1_22 + c_1_07·c_1_2·c_1_32
       + c_1_07·c_1_22·c_1_3, an element of degree 10

About the group Ring generators Ring relations Completion information Restriction maps


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
Office: Zi. 3529, Ernst-Abbe-Platz 2

Last change: 14.12.2010