Cohomology of group number 1533 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 4 minimal generators and exponent 4.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 3.
  • It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 4.


Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 3.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t8  +  t7  −  2·t6  +  2·t5  −  3·t4  −  3·t3  −  t2  −  2·t  −  1)

    (t  +  1)2 · (t  −  1)4 · (t2  +  1)3
  • The a-invariants are -∞,-∞,-∞,-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 18 minimal generators of maximal degree 8:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_3, a nilpotent element of degree 1
  3. b_1_1, an element of degree 1
  4. b_1_2, an element of degree 1
  5. a_3_5, a nilpotent element of degree 3
  6. b_3_6, an element of degree 3
  7. b_3_7, an element of degree 3
  8. b_3_8, an element of degree 3
  9. b_3_9, an element of degree 3
  10. b_3_10, an element of degree 3
  11. b_4_16, an element of degree 4
  12. c_4_17, a Duflot regular element of degree 4
  13. c_4_18, a Duflot regular element of degree 4
  14. c_4_19, a Duflot regular element of degree 4
  15. b_5_29, an element of degree 5
  16. b_6_36, an element of degree 6
  17. b_6_38, an element of degree 6
  18. b_8_67, an element of degree 8

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

Ring relations

There are 95 minimal relations of maximal degree 16:

  1. a_1_3·b_1_1 + a_1_0·b_1_2 + a_1_0·b_1_1 + a_1_32
  2. a_1_3·b_1_2 + a_1_0·b_1_1 + a_1_0·a_1_3
  3. b_1_1·b_1_2 + b_1_12 + a_1_02
  4. a_1_33 + a_1_0·a_1_32 + a_1_03
  5. a_1_02·b_1_1 + a_1_0·a_1_32 + a_1_03
  6. a_1_02·b_1_2
  7. b_1_1·b_3_7 + b_1_1·b_3_6 + b_1_14 + b_1_1·a_3_5 + a_1_3·b_3_6 + a_1_0·a_3_5
  8. b_1_2·a_3_5 + a_1_0·b_3_8 + a_1_0·b_3_6 + a_1_0·a_3_5
  9. b_1_1·a_3_5 + a_1_3·b_3_8 + a_1_3·b_3_6
  10. b_1_2·b_3_8 + b_1_2·b_3_7 + b_1_24 + b_1_1·b_3_8 + b_1_1·b_3_6 + b_1_2·a_3_5 + a_1_0·b_3_7
       + a_1_0·a_3_5
  11. b_1_2·b_3_6 + b_1_1·b_3_6 + a_1_0·b_3_9 + a_1_0·b_3_6 + a_1_0·a_3_5
  12. b_1_2·a_3_5 + b_1_1·a_3_5 + a_1_3·b_3_9 + a_1_3·b_3_6 + a_1_0·b_3_7 + a_1_0·b_3_6
       + a_1_3·a_3_5 + a_1_0·a_3_5
  13. b_1_1·b_3_9 + b_1_1·b_3_6 + b_1_14 + b_1_1·a_3_5 + a_1_0·b_3_6
  14. b_1_1·a_3_5 + a_1_0·b_3_10 + a_1_0·b_3_7 + a_1_0·b_3_6 + a_1_3·a_3_5 + a_1_0·a_3_5
  15. b_1_2·a_3_5 + b_1_1·a_3_5 + a_1_3·b_3_10 + a_1_3·b_3_7 + a_1_3·b_3_6 + a_1_3·a_3_5
  16. b_1_2·b_3_10 + b_1_2·b_3_9 + b_1_2·b_3_7 + b_1_1·b_3_10 + a_1_3·b_3_7 + a_1_3·b_3_6
       + a_1_0·b_3_6 + a_1_3·a_3_5
  17. a_1_32·b_3_7 + a_1_32·b_3_6 + a_1_02·b_3_6 + a_1_0·a_1_3·a_3_5
  18. a_1_0·a_1_3·b_3_6 + a_1_02·b_3_9 + a_1_02·b_3_8
  19. a_1_32·b_3_6 + a_1_0·a_1_3·b_3_6 + a_1_02·b_3_10 + a_1_02·b_3_8 + a_1_02·b_3_6
       + a_1_0·a_1_3·a_3_5 + a_1_02·a_3_5
  20. b_4_16·a_1_0 + a_1_02·b_3_8 + a_1_02·b_3_7 + a_1_0·a_1_3·a_3_5 + a_1_02·a_3_5
  21. b_4_16·a_1_3 + a_1_0·a_1_3·b_3_7 + a_1_32·a_3_5
  22. b_1_12·b_3_6 + b_4_16·b_1_1 + a_1_0·a_1_3·b_3_7 + a_1_02·b_3_8 + a_1_02·b_3_6
  23. b_3_9·b_3_10 + b_3_92 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_3_62 + b_1_23·b_3_7 + b_1_13·b_3_10 + b_1_13·b_3_8 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_8 + c_4_17·b_1_12 + c_4_18·a_1_02 + c_4_17·a_1_32
  24. b_3_9·b_3_10 + b_3_92 + b_3_7·b_3_9 + b_3_6·b_3_10 + b_1_13·b_3_10 + a_3_5·b_3_8
       + a_3_5·b_3_7 + a_3_5·b_3_6 + c_4_17·a_1_0·b_1_2 + c_4_18·a_1_0·a_1_3 + c_4_17·a_1_32
       + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_02
  25. b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_9 + b_3_72 + b_3_6·b_3_8
       + b_3_6·b_3_7 + b_3_62 + b_1_23·b_3_9 + b_1_13·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_8
       + a_3_5·b_3_7 + a_3_52 + a_1_03·b_3_6 + c_4_17·b_1_12 + c_4_18·a_1_32
       + c_4_17·a_1_32 + c_4_17·a_1_02
  26. b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_6·b_3_8 + b_3_6·b_3_7 + b_3_62
       + b_1_23·b_3_9 + b_1_13·b_3_10 + b_1_13·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_7
       + a_1_03·b_3_6 + c_4_17·b_1_12 + c_4_18·a_1_0·b_1_2 + c_4_18·a_1_0·b_1_1
       + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_32 + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_02
  27. b_3_9·b_3_10 + b_3_92 + b_3_82 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_1_23·b_3_7 + b_1_26 + b_1_13·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_5·b_3_8 + a_3_52 + a_1_03·b_3_6 + c_4_18·b_1_12 + c_4_17·b_1_12
       + c_4_17·a_1_02
  28. b_3_102 + b_3_9·b_3_10 + b_3_7·b_3_10 + b_3_72 + b_3_6·b_3_9 + b_1_23·b_3_7
       + b_1_13·b_3_10 + b_1_13·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_52
       + a_1_03·b_3_6 + c_4_19·b_1_22 + c_4_17·b_1_22 + c_4_18·a_1_0·b_1_2
       + c_4_17·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_32 + c_4_17·a_1_0·a_1_3
  29. b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_9 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_7 + b_3_62 + b_1_23·b_3_9 + b_1_23·b_3_7 + b_1_13·b_3_10 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_7 + a_3_5·b_3_6 + a_3_52 + a_1_03·b_3_6 + c_4_17·b_1_12
       + c_4_19·a_1_0·b_1_2 + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_32 + c_4_17·a_1_0·a_1_3
       + c_4_17·a_1_02
  30. b_3_9·b_3_10 + b_3_92 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_1_23·b_3_7 + b_1_13·b_3_10 + b_1_13·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_5·b_3_8 + c_4_19·a_1_02 + c_4_17·a_1_32
  31. b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_8 + b_3_6·b_3_7 + b_1_23·b_3_7 + b_1_13·b_3_8
       + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_7 + a_3_5·b_3_6 + a_3_52 + a_1_03·b_3_6
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_2 + c_4_19·a_1_0·a_1_3 + c_4_17·a_1_32
       + c_4_17·a_1_0·a_1_3
  32. b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7
       + b_3_62 + b_1_23·b_3_9 + b_1_23·b_3_7 + b_1_13·b_3_10 + a_3_5·b_3_9 + a_3_5·b_3_7
       + c_4_17·b_1_12 + c_4_19·a_1_32
  33. b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_6·b_3_8 + b_3_6·b_3_7 + b_3_62
       + b_1_23·b_3_9 + b_1_13·b_3_10 + b_1_13·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_7 + a_3_5·b_3_6
       + a_3_52 + a_1_03·b_3_6 + c_4_17·b_1_12 + c_4_19·a_1_0·b_1_1 + c_4_17·a_1_0·b_1_2
       + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_32 + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_02
  34. b_3_102 + b_3_92 + b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_62 + b_1_23·b_3_9 + b_1_23·b_3_7 + b_1_13·b_3_8
       + a_3_5·b_3_9 + a_3_5·b_3_7 + a_1_03·b_3_6 + c_4_19·b_1_12 + c_4_17·a_1_32
       + c_4_17·a_1_02
  35. b_3_9·b_3_10 + b_3_82 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_1_26 + b_1_13·b_3_8 + b_1_16 + b_4_16·b_1_22 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_52 + a_1_03·b_3_6 + c_4_18·b_1_22 + c_4_17·b_1_22
       + c_4_17·a_1_32
  36. b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_9 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_7
       + b_1_23·b_3_9 + b_1_23·b_3_7 + b_1_13·b_3_10 + b_4_16·b_1_12 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_5·b_3_7 + a_3_5·b_3_6 + c_4_17·b_1_12
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_32
       + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_02
  37. b_3_9·b_3_10 + b_3_82 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_8 + b_1_2·b_5_29
       + b_1_23·b_3_7 + b_1_16 + a_3_5·b_3_9 + a_3_5·b_3_6 + a_3_52 + c_4_18·b_1_22
       + c_4_17·b_1_12 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_02
  38. b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_8
       + b_1_23·b_3_9 + b_1_13·b_3_10 + b_1_13·b_3_8 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_1_0·b_5_29
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_0·a_1_3
  39. b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7
       + b_3_62 + b_1_23·b_3_9 + b_1_23·b_3_7 + b_1_13·b_3_10 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_5·b_3_7 + a_1_3·b_5_29 + a_1_03·b_3_6 + c_4_17·b_1_12 + c_4_18·a_1_0·b_1_2
  40. b_3_9·b_3_10 + b_3_92 + b_3_7·b_3_10 + b_3_72 + b_3_6·b_3_7 + b_3_62 + b_1_1·b_5_29
       + b_1_13·b_3_8 + b_1_16 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_1_03·b_3_6
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_32 + c_4_17·a_1_0·a_1_3
  41. a_1_0·b_3_6·b_3_8 + a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0·a_1_32 + c_4_19·a_1_02·a_1_3
       + c_4_18·a_1_0·a_1_32 + c_4_18·a_1_02·a_1_3 + c_4_17·a_1_03
  42. b_1_1·b_3_6·b_3_8 + b_4_16·b_3_8 + b_4_16·b_3_7 + b_4_16·b_1_23 + a_1_0·b_3_6·b_3_8
       + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_17·b_1_13 + c_4_19·a_1_02·a_1_3
       + c_4_18·a_1_0·a_1_32 + c_4_18·a_1_02·a_1_3 + c_4_18·a_1_03 + c_4_17·a_1_03
  43. b_4_16·b_3_6 + a_1_0·b_3_6·b_3_8 + a_1_3·a_3_5·b_3_6 + a_1_02·b_5_29 + c_4_17·b_1_13
       + c_4_19·a_1_03 + c_4_18·a_1_02·a_1_3 + c_4_17·a_1_02·a_1_3 + c_4_17·a_1_03
  44. b_4_16·b_3_6 + a_1_0·b_3_6·b_3_8 + b_4_16·a_3_5 + a_1_0·a_1_3·b_5_29 + c_4_17·b_1_13
  45. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_4_16·b_3_6
       + a_1_0·b_3_6·b_3_8 + a_1_32·b_5_29 + a_1_0·a_3_5·b_3_6 + c_4_17·b_1_13
       + c_4_19·a_1_02·a_1_3 + c_4_19·a_1_03 + c_4_18·a_1_0·a_1_32 + c_4_18·a_1_02·a_1_3
       + c_4_18·a_1_03 + c_4_17·a_1_02·a_1_3
  46. b_1_22·b_5_29 + b_1_24·b_3_9 + b_1_24·b_3_7 + b_1_27 + b_1_1·b_3_6·b_3_10
       + b_1_14·b_3_10 + b_1_17 + b_6_36·b_1_2 + b_4_16·b_3_9 + b_4_16·b_1_23
       + a_1_0·b_3_6·b_3_8 + a_1_3·a_3_5·b_3_6 + c_4_18·b_1_13 + c_4_17·b_1_23
       + c_4_19·a_1_02·a_1_3 + c_4_18·a_1_02·a_1_3 + c_4_18·a_1_03 + c_4_17·a_1_0·a_1_32
       + c_4_17·a_1_02·a_1_3 + c_4_17·a_1_03
  47. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_6_36·a_1_0
       + b_4_16·a_3_5 + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_19·a_1_02·a_1_3
       + c_4_18·a_1_03 + c_4_17·a_1_0·a_1_32 + c_4_17·a_1_03
  48. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_4_16·b_3_6
       + b_6_36·a_1_3 + b_4_16·a_3_5 + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_17·b_1_13
       + c_4_19·a_1_03 + c_4_18·a_1_02·a_1_3 + c_4_18·a_1_03 + c_4_17·a_1_03
  49. b_1_1·b_3_6·b_3_10 + b_1_14·b_3_10 + b_1_14·b_3_8 + b_1_17 + b_6_36·b_1_1
       + b_4_16·b_3_6 + b_4_16·b_1_13 + b_4_16·a_3_5 + a_1_0·a_3_5·b_3_6 + c_4_18·b_1_13
       + c_4_17·b_1_13 + c_4_19·a_1_03 + c_4_18·a_1_0·a_1_32 + c_4_18·a_1_03
       + c_4_17·a_1_0·a_1_32
  50. b_1_24·b_3_9 + b_1_27 + b_1_1·b_3_6·b_3_10 + b_1_14·b_3_8 + b_1_17 + b_6_38·b_1_2
       + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_6 + b_4_16·b_1_13 + b_4_16·a_3_5
       + a_1_3·a_3_5·b_3_6 + c_4_19·b_1_13 + c_4_18·b_1_23 + c_4_17·b_1_23
       + c_4_17·b_1_13 + c_4_17·a_1_02·a_1_3
  51. a_1_0·b_3_6·b_3_8 + b_6_38·a_1_0 + b_4_16·a_3_5 + a_1_0·a_3_5·b_3_6 + c_4_19·a_1_03
       + c_4_18·a_1_0·a_1_32 + c_4_18·a_1_03 + c_4_17·a_1_0·a_1_32
       + c_4_17·a_1_02·a_1_3
  52. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_6_38·a_1_3
       + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0·a_1_32 + c_4_18·a_1_02·a_1_3
       + c_4_18·a_1_03
  53. b_1_1·b_3_6·b_3_10 + b_1_14·b_3_8 + b_1_17 + b_6_38·b_1_1 + b_4_16·b_3_10
       + b_4_16·b_3_9 + b_4_16·b_3_7 + b_4_16·b_1_13 + a_1_3·a_3_5·b_3_6 + c_4_19·b_1_13
       + c_4_18·b_1_13 + c_4_19·a_1_02·a_1_3 + c_4_19·a_1_03 + c_4_18·a_1_0·a_1_32
       + c_4_18·a_1_02·a_1_3 + c_4_17·a_1_0·a_1_32 + c_4_17·a_1_02·a_1_3
  54. b_1_25·b_3_7 + b_1_28 + b_4_16·b_1_24 + b_4_162 + c_4_17·b_1_24
  55. a_3_5·b_5_29 + a_1_03·b_5_29 + c_4_19·a_1_3·b_3_7 + c_4_19·a_1_3·b_3_6
       + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_6 + c_4_18·a_1_3·b_3_7 + c_4_18·a_1_3·b_3_6
       + c_4_17·a_1_0·b_3_10 + c_4_17·a_1_0·b_3_9 + c_4_17·a_1_0·b_3_8 + c_4_17·a_1_0·b_3_7
       + c_4_17·a_1_0·b_3_6 + c_4_19·a_1_3·a_3_5 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_0·a_3_5
       + c_4_17·a_1_0·a_3_5
  56. b_3_6·b_5_29 + b_4_16·b_1_1·b_3_8 + b_4_16·b_1_14 + a_1_02·a_1_3·b_5_29
       + c_4_17·b_1_14 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6 + c_4_18·a_1_3·b_3_6
       + c_4_18·a_1_0·b_3_7 + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_10 + c_4_17·a_1_0·b_3_9
       + c_4_17·a_1_0·b_3_7 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_0·a_3_5 + c_4_17·a_1_3·a_3_5
  57. b_3_10·b_5_29 + b_3_7·b_5_29 + b_1_12·b_3_8·b_3_10 + b_6_36·b_1_22
       + b_4_16·b_1_2·b_3_7 + b_4_16·b_1_1·b_3_8 + a_1_02·a_1_3·b_5_29 + a_1_03·b_5_29
       + c_4_19·b_1_2·b_3_7 + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_14 + c_4_18·b_1_2·b_3_7
       + c_4_18·b_1_1·b_3_6 + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_1·b_3_6 + c_4_17·b_1_14
       + c_4_19·a_1_3·b_3_7 + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_7 + c_4_18·a_1_3·b_3_7
       + c_4_18·a_1_3·b_3_6 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_7 + c_4_18·a_1_0·b_3_6
       + c_4_17·a_1_3·b_3_7 + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_9 + c_4_17·a_1_0·b_3_7
       + c_4_18·a_1_3·a_3_5 + c_4_17·a_1_0·a_3_5
  58. b_3_8·b_5_29 + b_1_25·b_3_7 + b_1_28 + b_1_18 + b_6_36·b_1_12 + b_4_16·b_1_2·b_3_7
       + b_4_16·b_1_24 + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_1·b_3_8 + a_1_02·a_1_3·b_5_29
       + a_1_03·b_5_29 + c_4_19·b_1_2·b_3_9 + c_4_19·b_1_24 + c_4_19·b_1_1·b_3_6
       + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_2·b_3_7 + c_4_17·b_1_14 + c_4_19·a_1_3·b_3_6
       + c_4_19·a_1_0·b_3_8 + c_4_19·a_1_0·b_3_7 + c_4_18·a_1_0·b_3_10 + c_4_18·a_1_0·b_3_8
       + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_7 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_3·a_3_5
       + c_4_18·a_1_0·a_3_5 + c_4_17·a_1_0·a_3_5
  59. b_3_10·b_5_29 + b_3_8·b_5_29 + b_1_25·b_3_7 + b_1_12·b_3_8·b_3_10 + b_6_38·b_1_22
       + b_4_16·b_1_2·b_3_9 + b_4_16·b_1_24 + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_1·b_3_8
       + a_1_03·b_5_29 + c_4_19·b_1_2·b_3_7 + c_4_19·b_1_1·b_3_6 + c_4_18·b_1_2·b_3_7
       + c_4_18·b_1_24 + c_4_18·b_1_1·b_3_6 + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_1·b_3_6
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6 + c_4_18·a_1_3·b_3_7
       + c_4_18·a_1_0·b_3_10 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_8 + c_4_18·a_1_0·b_3_7
       + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_9 + c_4_17·a_1_0·b_3_8 + c_4_19·a_1_3·a_3_5
       + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_3·a_3_5 + c_4_17·a_1_3·a_3_5
  60. b_3_10·b_5_29 + b_3_9·b_5_29 + b_3_8·b_5_29 + b_3_7·b_5_29 + b_1_25·b_3_7 + b_1_28
       + b_1_12·b_3_8·b_3_10 + b_1_18 + b_6_38·b_1_12 + b_4_16·b_1_2·b_3_7
       + b_4_16·b_1_24 + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_1·b_3_8 + a_1_03·b_5_29
       + c_4_19·b_1_2·b_3_9 + c_4_19·b_1_24 + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_14
       + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_2·b_3_7 + c_4_17·b_1_14 + c_4_19·a_1_3·b_3_6
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_7 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_8
       + c_4_18·a_1_0·b_3_6 + c_4_17·a_1_3·b_3_7 + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_10
       + c_4_17·a_1_0·b_3_8 + c_4_17·a_1_0·b_3_6 + c_4_19·a_1_3·a_3_5 + c_4_18·a_1_3·a_3_5
       + c_4_17·a_1_0·a_3_5
  61. b_6_36·a_3_5 + c_4_19·a_1_02·b_3_10 + c_4_19·a_1_02·b_3_7 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_02·b_3_10 + c_4_18·a_1_02·b_3_8 + c_4_17·a_1_0·a_1_3·b_3_7
       + c_4_17·a_1_02·b_3_7 + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_32·a_3_5
       + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_02·a_3_5 + c_4_18·a_1_32·a_3_5
       + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_32·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
  62. b_6_36·b_3_6 + b_4_16·b_1_12·b_3_10 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15
       + c_4_17·b_1_12·b_3_10 + c_4_17·b_1_15 + b_4_16·c_4_18·b_1_1
       + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_8
       + c_4_18·a_1_02·b_3_10 + c_4_18·a_1_02·b_3_9 + c_4_18·a_1_02·b_3_6
       + c_4_17·a_1_02·b_3_10 + c_4_17·a_1_02·b_3_8 + c_4_19·a_1_32·a_3_5
       + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_32·a_3_5 + c_4_17·a_1_02·a_3_5
  63. b_6_36·b_3_7 + b_6_36·b_1_13 + b_4_16·b_5_29 + b_4_16·b_1_22·b_3_7 + b_4_16·b_1_25
       + b_4_16·b_1_12·b_3_10 + b_4_162·b_1_2 + c_4_19·b_1_22·b_3_9 + c_4_19·b_1_15
       + c_4_17·b_1_22·b_3_9 + c_4_17·b_1_12·b_3_10 + c_4_17·b_1_15 + b_4_16·c_4_19·b_1_1
       + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_0·a_1_3·b_3_7
       + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_6 + c_4_18·a_1_02·b_3_9
       + c_4_18·a_1_02·b_3_7 + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_02·b_3_10
       + c_4_17·a_1_02·b_3_9 + c_4_17·a_1_02·b_3_8 + c_4_17·a_1_02·b_3_6
       + c_4_19·a_1_32·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_02·a_3_5
       + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_02·a_3_5
  64. b_3_6·b_3_8·b_3_10 + b_1_13·b_3_8·b_3_10 + b_1_19 + b_6_36·b_3_8 + b_6_36·b_1_23
       + b_4_16·b_5_29 + b_4_16·b_1_22·b_3_7 + b_4_16·b_1_25 + b_4_16·b_1_12·b_3_10
       + b_4_162·b_1_2 + c_4_19·b_1_22·b_3_9 + c_4_19·b_1_15 + c_4_18·b_1_12·b_3_8
       + c_4_17·b_1_22·b_3_9 + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_17·b_1_2
       + c_4_19·a_1_02·b_3_10 + c_4_19·a_1_02·b_3_9 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_02·b_3_10 + c_4_18·a_1_02·b_3_9 + c_4_18·a_1_02·b_3_7
       + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_02·b_3_10 + c_4_17·a_1_02·b_3_7
       + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_32·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5
       + c_4_19·a_1_02·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
  65. b_6_36·b_3_9 + b_6_36·b_1_13 + b_4_16·b_1_22·b_3_7 + b_4_16·b_1_25
       + b_4_16·b_1_12·b_3_10 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15 + b_4_162·b_1_2
       + c_4_19·b_1_22·b_3_7 + c_4_19·b_1_25 + c_4_18·b_1_22·b_3_7 + c_4_18·b_1_25
       + c_4_17·b_1_12·b_3_10 + c_4_17·b_1_15 + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_18·b_1_2
       + b_4_16·c_4_18·b_1_1 + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_7
       + c_4_19·a_1_02·b_3_6 + c_4_18·a_1_02·b_3_10 + c_4_18·a_1_02·b_3_9
       + c_4_18·a_1_02·b_3_8 + c_4_18·a_1_02·b_3_6 + c_4_17·a_1_0·a_1_3·b_3_7
       + c_4_17·a_1_02·b_3_10 + c_4_17·a_1_02·b_3_9 + c_4_17·a_1_02·b_3_8
       + c_4_19·a_1_32·a_3_5 + c_4_18·a_1_32·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5
       + c_4_17·a_1_32·a_3_5 + c_4_17·a_1_02·a_3_5
  66. b_1_13·b_3_8·b_3_10 + b_1_19 + b_6_38·b_1_13 + b_6_36·b_3_10 + b_4_16·b_5_29
       + c_4_19·b_1_22·b_3_9 + c_4_19·b_1_22·b_3_7 + c_4_19·b_1_25 + c_4_19·b_1_15
       + c_4_18·b_1_22·b_3_7 + c_4_18·b_1_25 + c_4_18·b_1_12·b_3_10 + c_4_18·b_1_15
       + c_4_17·b_1_22·b_3_9 + c_4_17·b_1_15 + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_18·b_1_2
       + b_4_16·c_4_17·b_1_2 + b_4_16·c_4_17·b_1_1 + c_4_19·a_1_02·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_8 + c_4_18·a_1_02·b_3_7
       + c_4_18·a_1_02·b_3_6 + c_4_17·a_1_02·b_3_9 + c_4_17·a_1_02·b_3_8
       + c_4_19·a_1_32·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_02·a_3_5
       + c_4_18·a_1_32·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_32·a_3_5
       + c_4_17·a_1_02·a_3_5
  67. b_1_29 + b_6_38·b_3_10 + b_6_36·b_3_10 + b_6_36·b_1_23 + b_4_16·b_1_22·b_3_9
       + b_4_16·b_1_25 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15 + c_4_19·b_1_22·b_3_9
       + c_4_19·b_1_22·b_3_7 + c_4_19·b_1_12·b_3_10 + c_4_19·b_1_15 + c_4_18·b_1_22·b_3_9
       + c_4_17·b_1_22·b_3_7 + c_4_17·b_1_25 + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_2
       + b_4_16·c_4_17·b_1_2 + b_4_16·c_4_17·b_1_1 + c_4_19·a_1_0·a_1_3·b_3_7
       + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_7 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_02·b_3_8 + c_4_18·a_1_02·b_3_6 + c_4_17·a_1_02·b_3_10
       + c_4_17·a_1_02·b_3_8 + c_4_17·a_1_02·b_3_7 + c_4_19·a_1_0·a_1_3·a_3_5
       + c_4_19·a_1_02·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_02·a_3_5
       + c_4_17·a_1_32·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_02·a_3_5
  68. b_6_38·a_3_5 + c_4_19·a_1_02·b_3_6 + c_4_18·a_1_02·b_3_7 + c_4_17·a_1_02·b_3_10
       + c_4_17·a_1_02·b_3_8 + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_02·a_3_5
       + c_4_18·a_1_32·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_02·a_3_5
       + c_4_17·a_1_0·a_1_3·a_3_5
  69. b_6_38·b_3_6 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15 + c_4_17·b_1_15
       + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_1 + c_4_19·a_1_02·b_3_9
       + c_4_19·a_1_02·b_3_8 + c_4_19·a_1_02·b_3_7 + c_4_19·a_1_02·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_9 + c_4_18·a_1_02·b_3_8
       + c_4_18·a_1_02·b_3_7 + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_02·b_3_9
       + c_4_17·a_1_02·b_3_8 + c_4_17·a_1_02·b_3_7 + c_4_18·a_1_32·a_3_5
  70. b_6_38·b_3_7 + b_6_38·b_1_23 + b_6_36·b_1_23 + b_6_36·b_1_13
       + b_4_16·b_1_22·b_3_9 + b_4_16·b_1_25 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15
       + b_4_162·b_1_2 + c_4_18·b_1_22·b_3_7 + c_4_18·b_1_25 + c_4_17·b_1_22·b_3_7
       + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_02·b_3_10
       + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_7 + c_4_19·a_1_02·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_9 + c_4_18·a_1_02·b_3_8
       + c_4_18·a_1_02·b_3_7 + c_4_17·a_1_02·b_3_10 + c_4_17·a_1_02·b_3_9
       + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_02·a_3_5 + c_4_18·a_1_32·a_3_5
       + c_4_17·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_02·a_3_5
  71. b_1_19 + b_6_38·b_3_8 + b_6_36·b_1_23 + b_4_16·b_1_22·b_3_9 + b_4_16·b_1_25
       + b_4_16·b_1_12·b_3_10 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15 + b_4_162·b_1_2
       + c_4_19·b_1_12·b_3_8 + c_4_18·b_1_22·b_3_7 + c_4_18·b_1_25 + c_4_18·b_1_12·b_3_8
       + c_4_17·b_1_22·b_3_7 + c_4_17·b_1_15 + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_19·b_1_1
       + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_0·a_1_3·b_3_7
       + c_4_19·a_1_02·b_3_10 + c_4_19·a_1_02·b_3_8 + c_4_18·a_1_02·b_3_8
       + c_4_18·a_1_02·b_3_7 + c_4_18·a_1_02·b_3_6 + c_4_17·a_1_0·a_1_3·b_3_7
       + c_4_17·a_1_02·b_3_9 + c_4_17·a_1_02·b_3_8 + c_4_17·a_1_02·b_3_7
       + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5
       + c_4_17·a_1_32·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
  72. b_1_29 + b_1_19 + b_6_38·b_3_9 + b_6_38·b_1_23 + b_4_16·b_5_29 + b_4_162·b_1_2
       + c_4_19·b_1_25 + c_4_19·b_1_15 + c_4_18·b_1_22·b_3_9 + c_4_18·b_1_15
       + c_4_17·b_1_22·b_3_9 + c_4_17·b_1_25 + c_4_17·b_1_15 + b_4_16·c_4_19·b_1_1
       + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_02·b_3_7 + c_4_19·a_1_02·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_9 + c_4_18·a_1_02·b_3_7
       + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_02·b_3_9 + c_4_17·a_1_02·b_3_8
       + c_4_17·a_1_02·b_3_7 + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_02·a_3_5
       + c_4_17·a_1_02·a_3_5
  73. b_3_6·b_3_8·b_3_10 + b_1_19 + b_8_67·b_1_2 + b_6_36·b_3_10 + b_6_36·b_1_23
       + b_4_16·b_1_22·b_3_9 + b_4_16·b_1_25 + c_4_19·b_1_22·b_3_9 + c_4_19·b_1_25
       + c_4_19·b_1_12·b_3_10 + c_4_19·b_1_12·b_3_8 + c_4_18·b_1_25 + c_4_18·b_1_12·b_3_8
       + c_4_18·b_1_15 + c_4_17·b_1_25 + c_4_17·b_1_12·b_3_8 + c_4_17·b_1_15
       + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_1
       + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_02·b_3_10 + c_4_19·a_1_02·b_3_8
       + c_4_19·a_1_02·b_3_6 + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_8
       + c_4_18·a_1_02·b_3_6 + c_4_17·a_1_02·b_3_10 + c_4_17·a_1_02·b_3_9
       + c_4_17·a_1_02·b_3_7 + c_4_17·a_1_02·b_3_6 + c_4_19·a_1_0·a_1_3·a_3_5
       + c_4_18·a_1_32·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
  74. b_8_67·a_1_0 + c_4_19·a_1_02·b_3_10 + c_4_19·a_1_02·b_3_9 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_02·b_3_10 + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_02·b_3_9
       + c_4_17·a_1_02·b_3_6 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_02·a_3_5
       + c_4_17·a_1_02·a_3_5
  75. b_8_67·a_1_3 + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_7
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_10 + c_4_18·a_1_02·b_3_6
       + c_4_17·a_1_02·b_3_9 + c_4_17·a_1_02·b_3_8 + c_4_17·a_1_02·b_3_6
       + c_4_19·a_1_32·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_02·a_3_5
       + c_4_18·a_1_02·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
  76. b_3_6·b_3_8·b_3_10 + b_1_19 + b_8_67·b_1_1 + b_6_36·b_3_10 + b_6_36·b_1_13
       + b_4_16·b_5_29 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_15 + c_4_19·b_1_22·b_3_9
       + c_4_19·b_1_22·b_3_7 + c_4_19·b_1_25 + c_4_19·b_1_12·b_3_10 + c_4_19·b_1_12·b_3_8
       + c_4_19·b_1_15 + c_4_18·b_1_22·b_3_7 + c_4_18·b_1_25 + c_4_18·b_1_12·b_3_8
       + c_4_17·b_1_22·b_3_9 + c_4_17·b_1_12·b_3_8 + c_4_17·b_1_15 + b_4_16·c_4_19·b_1_2
       + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_2 + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_2
       + b_4_16·c_4_17·b_1_1 + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_02·b_3_10
       + c_4_19·a_1_02·b_3_9 + c_4_19·a_1_02·b_3_8 + c_4_19·a_1_02·b_3_7
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_02·b_3_8 + c_4_18·a_1_02·b_3_6
       + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_02·b_3_10 + c_4_17·a_1_02·b_3_9
       + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_32·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5
       + c_4_18·a_1_02·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_02·a_3_5
  77. b_6_36·b_1_24 + b_6_36·b_1_14 + b_4_16·b_1_2·b_5_29 + b_4_16·b_1_23·b_3_9
       + b_4_16·b_1_23·b_3_7 + b_4_16·b_1_26 + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_16
       + b_4_16·b_6_36 + b_4_162·b_1_22 + c_4_17·b_1_23·b_3_9 + c_4_17·b_1_13·b_3_10
       + b_4_16·c_4_18·b_1_12 + b_4_16·c_4_17·b_1_22 + c_4_17·a_1_03·b_3_6
  78. b_4_16·b_1_23·b_3_9 + b_4_16·b_1_23·b_3_7 + b_4_16·b_1_26 + b_4_16·b_1_13·b_3_8
       + b_4_16·b_6_38 + c_4_19·b_1_26 + c_4_19·b_1_16 + c_4_17·b_1_23·b_3_7
       + c_4_17·b_1_26 + c_4_17·b_1_16 + b_4_16·c_4_19·b_1_12 + b_4_16·c_4_18·b_1_22
       + b_4_16·c_4_17·b_1_22 + c_4_19·a_1_03·b_3_6 + c_4_18·a_1_03·b_3_6
  79. b_5_292 + b_6_38·b_1_1·b_3_8 + b_6_36·b_1_1·b_3_10 + b_6_36·b_1_1·b_3_8
       + b_6_36·b_1_14 + b_4_16·b_3_8·b_3_10 + b_4_16·b_1_2·b_5_29 + b_4_16·b_1_23·b_3_9
       + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_16 + b_4_162·b_1_22 + c_4_19·b_1_23·b_3_7
       + c_4_19·b_1_26 + c_4_19·b_1_13·b_3_8 + c_4_19·b_1_16 + c_4_18·b_1_23·b_3_7
       + c_4_18·b_1_13·b_3_10 + c_4_18·b_1_16 + c_4_17·b_1_16 + b_4_16·c_4_18·b_1_12
       + b_4_16·c_4_17·b_1_22 + c_4_18·a_1_03·b_3_6 + c_4_17·a_1_03·b_3_6
       + c_4_192·b_1_22 + c_4_192·b_1_12 + c_4_18·c_4_19·b_1_22
       + c_4_18·c_4_19·b_1_12 + c_4_17·c_4_19·b_1_22 + c_4_17·c_4_19·b_1_12
       + c_4_17·c_4_18·b_1_22 + c_4_17·c_4_18·b_1_12 + c_4_172·b_1_22
       + c_4_172·b_1_12 + c_4_182·a_1_32 + c_4_182·a_1_02 + c_4_17·c_4_19·a_1_32
       + c_4_17·c_4_19·a_1_02 + c_4_17·c_4_18·a_1_32 + c_4_172·a_1_32
       + c_4_172·a_1_02
  80. b_6_36·b_5_29 + b_6_36·b_1_12·b_3_8 + b_6_36·b_1_15 + b_4_16·b_1_27
       + b_4_16·b_1_17 + b_4_16·b_6_38·b_1_2 + b_4_16·b_6_38·b_1_1 + b_4_16·b_6_36·b_1_1
       + c_4_19·b_1_27 + c_4_19·b_1_17 + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1
       + c_4_17·b_6_36·b_1_2 + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_1_23
       + b_4_16·c_4_19·b_1_13 + b_4_16·c_4_18·b_3_7 + b_4_16·c_4_18·b_1_23
       + c_4_19·a_1_3·a_3_5·b_3_6 + c_4_19·a_1_32·b_5_29 + c_4_19·a_1_02·b_5_29
       + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_32·b_5_29 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_18·a_1_02·b_5_29 + c_4_17·a_1_32·b_5_29 + c_4_192·b_1_23 + c_4_192·b_1_13
       + c_4_17·c_4_18·b_1_23 + c_4_18·c_4_19·a_1_0·a_1_32 + c_4_18·c_4_19·a_1_03
       + c_4_182·a_1_03 + c_4_17·c_4_18·a_1_02·a_1_3 + c_4_17·c_4_18·a_1_03
       + c_4_172·a_1_02·a_1_3 + c_4_172·a_1_03
  81. b_6_38·b_5_29 + b_6_38·b_1_22·b_3_9 + b_6_38·b_1_12·b_3_8 + b_6_36·b_5_29
       + b_6_36·b_1_12·b_3_8 + b_6_36·b_1_15 + b_4_16·b_1_27 + b_4_16·b_1_17
       + b_4_16·b_6_36·b_1_1 + b_4_162·b_3_7 + b_4_162·b_1_23 + c_4_19·b_1_24·b_3_7
       + c_4_19·b_1_27 + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1 + c_4_18·b_6_36·b_1_2
       + c_4_18·b_6_36·b_1_1 + c_4_17·b_1_27 + c_4_17·b_1_17 + c_4_17·b_6_38·b_1_2
       + c_4_17·b_6_38·b_1_1 + b_4_16·c_4_19·b_3_9 + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_7
       + b_4_16·c_4_18·b_1_23 + b_4_16·c_4_18·b_1_13 + b_4_16·c_4_17·b_1_23
       + c_4_19·a_1_32·b_5_29 + c_4_19·a_1_0·a_1_3·b_5_29 + c_4_19·a_1_02·b_5_29
       + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_32·b_5_29 + c_4_18·a_1_0·a_3_5·b_3_6
       + c_4_18·a_1_0·a_1_3·b_5_29 + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_32·b_5_29
       + c_4_17·a_1_0·a_3_5·b_3_6 + c_4_17·a_1_0·a_1_3·b_5_29 + c_4_192·b_1_23
       + c_4_192·b_1_13 + c_4_17·c_4_19·b_1_13 + c_4_17·c_4_18·b_1_23
       + c_4_17·c_4_18·b_1_13 + c_4_18·c_4_19·a_1_02·a_1_3 + c_4_182·a_1_0·a_1_32
       + c_4_17·c_4_19·a_1_02·a_1_3 + c_4_17·c_4_19·a_1_03 + c_4_17·c_4_18·a_1_02·a_1_3
       + c_4_172·a_1_0·a_1_32
  82. b_8_67·b_3_10 + b_6_36·b_5_29 + b_6_36·b_1_12·b_3_10 + b_6_36·b_1_12·b_3_8
       + b_6_36·b_1_15 + b_4_16·b_6_38·b_1_2 + b_4_162·b_3_9 + c_4_19·b_1_1·b_3_8·b_3_10
       + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1 + c_4_19·b_6_36·b_1_2 + c_4_19·b_6_36·b_1_1
       + c_4_18·b_1_1·b_3_8·b_3_10 + c_4_18·b_6_38·b_1_2 + c_4_18·b_6_38·b_1_1
       + c_4_18·b_6_36·b_1_2 + c_4_17·b_1_24·b_3_7 + c_4_17·b_1_27
       + c_4_17·b_1_1·b_3_8·b_3_10 + c_4_17·b_6_38·b_1_2 + c_4_17·b_6_38·b_1_1
       + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_3_10 + b_4_16·c_4_19·b_3_8
       + b_4_16·c_4_19·b_1_23 + b_4_16·c_4_18·b_1_23 + b_4_16·c_4_18·b_1_13
       + b_4_16·c_4_17·b_3_10 + b_4_16·c_4_17·b_3_9 + b_4_16·c_4_17·b_3_8
       + b_4_16·c_4_17·b_3_7 + b_4_16·c_4_17·b_1_23 + c_4_19·a_1_0·a_3_5·b_3_6
       + c_4_19·a_1_0·a_1_3·b_5_29 + c_4_19·a_1_02·b_5_29 + c_4_18·a_1_3·a_3_5·b_3_6
       + c_4_18·a_1_32·b_5_29 + c_4_18·a_1_0·a_3_5·b_3_6 + c_4_18·a_1_02·b_5_29
       + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_0·a_1_3·b_5_29 + c_4_17·a_1_02·b_5_29
       + c_4_192·b_1_13 + c_4_18·c_4_19·b_1_23 + c_4_182·b_1_23
       + c_4_17·c_4_19·b_1_13 + c_4_17·c_4_18·b_1_23 + c_4_17·c_4_18·b_1_13
       + c_4_172·b_1_23 + c_4_172·b_1_13 + c_4_192·a_1_02·a_1_3
       + c_4_182·a_1_02·a_1_3 + c_4_182·a_1_03 + c_4_17·c_4_19·a_1_02·a_1_3
       + c_4_17·c_4_19·a_1_03 + c_4_17·c_4_18·a_1_0·a_1_32 + c_4_172·a_1_02·a_1_3
  83. b_8_67·a_3_5 + c_4_19·a_1_3·a_3_5·b_3_6 + c_4_19·a_1_0·a_3_5·b_3_6
       + c_4_19·a_1_0·a_1_3·b_5_29 + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_32·b_5_29
       + c_4_18·a_1_0·a_1_3·b_5_29 + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_32·b_5_29
       + c_4_17·a_1_02·b_5_29 + c_4_192·a_1_0·a_1_32 + c_4_192·a_1_03
       + c_4_18·c_4_19·a_1_03 + c_4_182·a_1_02·a_1_3 + c_4_182·a_1_03
       + c_4_17·c_4_19·a_1_0·a_1_32 + c_4_17·c_4_19·a_1_02·a_1_3
       + c_4_17·c_4_18·a_1_0·a_1_32 + c_4_17·c_4_18·a_1_03
  84. b_8_67·b_3_6 + b_6_36·b_5_29 + b_6_36·b_1_12·b_3_8 + b_6_36·b_1_15 + b_4_16·b_1_27
       + b_4_16·b_1_1·b_3_8·b_3_10 + b_4_16·b_1_17 + b_4_16·b_6_38·b_1_2 + c_4_19·b_1_27
       + c_4_19·b_1_17 + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1
       + c_4_17·b_1_1·b_3_8·b_3_10 + c_4_17·b_6_38·b_1_1 + c_4_17·b_6_36·b_1_2
       + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_3_10 + b_4_16·c_4_19·b_3_9
       + b_4_16·c_4_19·b_3_8 + b_4_16·c_4_19·b_1_13 + b_4_16·c_4_18·b_3_10
       + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_8 + b_4_16·c_4_18·b_3_7
       + b_4_16·c_4_18·b_1_13 + b_4_16·c_4_17·b_3_8 + b_4_16·c_4_17·b_3_7
       + b_4_16·c_4_17·b_1_23 + b_4_16·c_4_17·b_1_13 + c_4_19·a_1_3·a_3_5·b_3_6
       + c_4_19·a_1_32·b_5_29 + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_32·b_5_29
       + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_0·a_3_5·b_3_6 + c_4_192·b_1_23
       + c_4_192·b_1_13 + c_4_17·c_4_19·b_1_13 + c_4_17·c_4_18·b_1_23
       + c_4_17·c_4_18·b_1_13 + c_4_172·b_1_13 + c_4_192·a_1_02·a_1_3
       + c_4_17·c_4_19·a_1_02·a_1_3 + c_4_17·c_4_19·a_1_03 + c_4_17·c_4_18·a_1_0·a_1_32
       + c_4_17·c_4_18·a_1_03 + c_4_172·a_1_03
  85. b_8_67·b_3_7 + b_6_38·b_1_12·b_3_8 + b_6_36·b_1_12·b_3_10 + b_4_16·b_1_27
       + b_4_16·b_1_17 + b_4_16·b_6_38·b_1_2 + b_4_16·b_6_36·b_1_2 + b_4_16·b_6_36·b_1_1
       + b_4_162·b_3_9 + b_4_162·b_3_7 + c_4_19·b_1_24·b_3_7 + c_4_19·b_1_17
       + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_36·b_1_1 + c_4_18·b_1_24·b_3_7 + c_4_18·b_1_17
       + c_4_17·b_1_27 + c_4_17·b_1_1·b_3_8·b_3_10 + c_4_17·b_6_38·b_1_1
       + c_4_17·b_6_36·b_1_2 + b_4_16·c_4_19·b_3_9 + b_4_16·c_4_19·b_3_8 + b_4_16·c_4_19·b_3_7
       + b_4_16·c_4_19·b_1_13 + b_4_16·c_4_18·b_3_10 + b_4_16·c_4_18·b_3_9
       + b_4_16·c_4_18·b_3_8 + b_4_16·c_4_18·b_3_7 + b_4_16·c_4_17·b_3_10
       + b_4_16·c_4_17·b_3_9 + b_4_16·c_4_17·b_3_8 + b_4_16·c_4_17·b_1_23
       + b_4_16·c_4_17·b_1_13 + c_4_19·a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0·a_1_3·b_5_29
       + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_32·b_5_29 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_17·a_1_32·b_5_29 + c_4_17·a_1_0·a_1_3·b_5_29 + c_4_192·b_1_23
       + c_4_17·c_4_18·b_1_23 + c_4_172·b_1_13 + c_4_192·a_1_0·a_1_32
       + c_4_18·c_4_19·a_1_0·a_1_32 + c_4_182·a_1_0·a_1_32 + c_4_182·a_1_03
       + c_4_17·c_4_19·a_1_0·a_1_32 + c_4_17·c_4_19·a_1_02·a_1_3
       + c_4_17·c_4_18·a_1_0·a_1_32 + c_4_17·c_4_18·a_1_02·a_1_3 + c_4_172·a_1_02·a_1_3
       + c_4_172·a_1_03
  86. b_8_67·b_3_8 + b_6_36·b_1_12·b_3_8 + b_4_16·b_1_27 + b_4_16·b_6_38·b_1_2
       + b_4_162·b_3_9 + b_4_162·b_1_23 + c_4_19·b_1_27 + c_4_19·b_1_1·b_3_8·b_3_10
       + c_4_19·b_1_17 + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1 + c_4_19·b_6_36·b_1_1
       + c_4_18·b_1_1·b_3_8·b_3_10 + c_4_18·b_1_17 + c_4_17·b_1_24·b_3_7 + c_4_17·b_1_27
       + c_4_17·b_6_38·b_1_1 + c_4_17·b_6_36·b_1_2 + b_4_16·c_4_19·b_3_10
       + b_4_16·c_4_19·b_3_8 + b_4_16·c_4_19·b_1_23 + b_4_16·c_4_18·b_3_10
       + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_8 + b_4_16·c_4_18·b_3_7
       + b_4_16·c_4_18·b_1_23 + b_4_16·c_4_18·b_1_13 + b_4_16·c_4_17·b_3_10
       + b_4_16·c_4_17·b_3_9 + b_4_16·c_4_17·b_3_7 + b_4_16·c_4_17·b_1_13
       + c_4_19·a_1_32·b_5_29 + c_4_19·a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0·a_1_3·b_5_29
       + c_4_18·a_1_32·b_5_29 + c_4_18·a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_17·a_1_32·b_5_29 + c_4_17·a_1_0·a_3_5·b_3_6 + c_4_17·a_1_0·a_1_3·b_5_29
       + c_4_192·b_1_23 + c_4_192·b_1_13 + c_4_182·b_1_13 + c_4_17·c_4_19·b_1_13
       + c_4_17·c_4_18·b_1_23 + c_4_192·a_1_0·a_1_32 + c_4_192·a_1_02·a_1_3
       + c_4_18·c_4_19·a_1_03 + c_4_182·a_1_0·a_1_32 + c_4_17·c_4_19·a_1_03
       + c_4_17·c_4_18·a_1_02·a_1_3 + c_4_172·a_1_02·a_1_3
  87. b_8_67·b_3_9 + b_6_38·b_1_12·b_3_8 + b_6_36·b_1_12·b_3_10 + b_4_16·b_6_38·b_1_2
       + b_4_16·b_6_36·b_1_2 + b_4_16·b_6_36·b_1_1 + b_4_162·b_3_7 + c_4_19·b_1_24·b_3_7
       + c_4_19·b_1_27 + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_36·b_1_2 + c_4_18·b_1_24·b_3_7
       + c_4_18·b_1_17 + c_4_18·b_6_38·b_1_2 + c_4_18·b_6_38·b_1_1 + c_4_18·b_6_36·b_1_2
       + c_4_18·b_6_36·b_1_1 + c_4_17·b_1_24·b_3_7 + c_4_17·b_1_1·b_3_8·b_3_10
       + c_4_17·b_1_17 + c_4_17·b_6_38·b_1_2 + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_3_8
       + b_4_16·c_4_19·b_3_7 + b_4_16·c_4_19·b_1_23 + b_4_16·c_4_19·b_1_13
       + b_4_16·c_4_18·b_3_10 + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_8
       + b_4_16·c_4_18·b_1_13 + b_4_16·c_4_17·b_3_10 + b_4_16·c_4_17·b_3_9
       + b_4_16·c_4_17·b_3_8 + b_4_16·c_4_17·b_3_7 + b_4_16·c_4_17·b_1_23
       + c_4_19·a_1_3·a_3_5·b_3_6 + c_4_19·a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_17·a_1_32·b_5_29 + c_4_192·b_1_13 + c_4_18·c_4_19·b_1_23
       + c_4_18·c_4_19·b_1_13 + c_4_182·b_1_23 + c_4_182·b_1_13
       + c_4_17·c_4_19·b_1_13 + c_4_17·c_4_18·b_1_23 + c_4_17·c_4_18·b_1_13
       + c_4_172·b_1_23 + c_4_172·b_1_13 + c_4_192·a_1_03 + c_4_182·a_1_0·a_1_32
       + c_4_182·a_1_02·a_1_3 + c_4_17·c_4_19·a_1_0·a_1_32 + c_4_17·c_4_19·a_1_02·a_1_3
       + c_4_17·c_4_19·a_1_03 + c_4_17·c_4_18·a_1_0·a_1_32 + c_4_172·a_1_0·a_1_32
       + c_4_172·a_1_02·a_1_3 + c_4_172·a_1_03
  88. b_6_36·b_1_13·b_3_10 + b_6_36·b_6_38 + b_6_362 + b_4_16·b_1_12·b_3_8·b_3_10
       + b_4_16·b_1_18 + b_4_16·b_6_38·b_1_22 + b_4_16·b_6_36·b_1_22
       + b_4_16·b_6_36·b_1_12 + c_4_19·b_6_38·b_1_22 + c_4_19·b_6_38·b_1_12
       + c_4_19·b_6_36·b_1_12 + c_4_18·b_6_36·b_1_22 + c_4_18·b_6_36·b_1_12
       + c_4_17·b_1_28 + c_4_17·b_1_18 + c_4_17·b_6_38·b_1_22
       + b_4_16·c_4_19·b_1_2·b_3_9 + b_4_16·c_4_19·b_1_2·b_3_7 + b_4_16·c_4_18·b_1_1·b_3_10
       + b_4_16·c_4_18·b_1_14 + b_4_16·c_4_17·b_1_2·b_3_7 + b_4_16·c_4_17·b_1_14
       + b_4_162·c_4_19 + b_4_162·c_4_18 + b_4_162·c_4_17 + c_4_19·a_1_02·a_1_3·b_5_29
       + c_4_19·a_1_03·b_5_29 + c_4_18·a_1_02·a_1_3·b_5_29 + c_4_17·a_1_02·a_1_3·b_5_29
       + c_4_192·b_1_24 + c_4_192·b_1_14 + c_4_17·c_4_19·b_1_14 + c_4_172·b_1_14
  89. b_6_36·b_1_13·b_3_10 + b_6_36·b_1_13·b_3_8 + b_6_36·b_1_16 + b_6_362
       + b_4_16·b_1_12·b_3_8·b_3_10 + b_4_16·b_1_18 + b_4_16·b_6_38·b_1_12
       + b_4_16·b_6_36·b_1_12 + b_4_162·b_1_24 + c_4_18·b_6_36·b_1_12 + c_4_17·b_1_18
       + c_4_17·b_6_38·b_1_12 + b_4_16·c_4_18·b_1_24 + b_4_16·c_4_18·b_1_1·b_3_10
       + c_4_18·a_1_02·a_1_3·b_5_29 + c_4_18·a_1_03·b_5_29 + c_4_17·a_1_03·b_5_29
       + c_4_192·b_1_24 + c_4_192·b_1_14 + c_4_18·c_4_19·b_1_24
       + c_4_18·c_4_19·b_1_14 + c_4_17·c_4_18·b_1_14 + c_4_172·b_1_14
  90. b_6_38·b_1_23·b_3_9 + b_6_38·b_1_26 + b_6_382 + b_6_36·b_3_8·b_3_10
       + b_6_36·b_1_13·b_3_10 + b_6_36·b_1_16 + b_6_36·b_6_38 + b_6_362
       + b_4_16·b_1_12·b_3_8·b_3_10 + b_4_162·b_1_2·b_3_9 + b_4_162·b_1_2·b_3_7
       + b_4_162·b_1_24 + c_4_19·b_6_38·b_1_22 + c_4_19·b_6_36·b_1_22
       + c_4_18·b_1_12·b_3_8·b_3_10 + c_4_18·b_1_18 + c_4_18·b_6_38·b_1_22
       + c_4_18·b_6_36·b_1_22 + c_4_17·b_1_28 + c_4_17·b_1_18 + c_4_17·b_6_36·b_1_22
       + c_4_17·b_6_36·b_1_12 + b_4_16·c_4_19·b_1_2·b_3_9 + b_4_16·c_4_19·b_1_24
       + b_4_16·c_4_19·b_1_1·b_3_8 + b_4_16·c_4_19·b_1_14 + b_4_16·c_4_18·b_1_24
       + b_4_16·c_4_18·b_1_14 + b_4_16·c_4_17·b_1_1·b_3_8 + b_4_16·c_4_17·b_1_14
       + b_4_162·c_4_19 + c_4_19·a_1_03·b_5_29 + c_4_17·a_1_02·a_1_3·b_5_29
       + c_4_17·a_1_03·b_5_29 + c_4_18·c_4_19·b_1_24 + c_4_18·c_4_19·b_1_14
       + c_4_182·b_1_14 + c_4_17·c_4_19·b_1_14 + c_4_172·b_1_14
  91. b_6_36·b_1_13·b_3_10 + b_6_36·b_6_38 + b_6_362 + b_4_16·b_1_18 + b_4_16·b_8_67
       + b_4_16·b_6_36·b_1_22 + b_4_162·b_1_2·b_3_7 + b_4_162·b_1_24
       + c_4_19·b_6_36·b_1_12 + c_4_18·b_6_36·b_1_22 + c_4_18·b_6_36·b_1_12
       + c_4_17·b_1_28 + c_4_17·b_1_12·b_3_8·b_3_10 + c_4_17·b_1_18
       + c_4_17·b_6_38·b_1_22 + c_4_17·b_6_38·b_1_12 + c_4_17·b_6_36·b_1_22
       + c_4_17·b_6_36·b_1_12 + b_4_16·c_4_19·b_1_2·b_3_9 + b_4_16·c_4_19·b_1_2·b_3_7
       + b_4_16·c_4_19·b_1_1·b_3_10 + b_4_16·c_4_19·b_1_1·b_3_8 + b_4_16·c_4_18·b_1_2·b_3_7
       + b_4_16·c_4_18·b_1_24 + b_4_16·c_4_18·b_1_1·b_3_8 + b_4_16·c_4_17·b_1_2·b_3_7
       + b_4_16·c_4_17·b_1_1·b_3_8 + b_4_16·c_4_17·b_1_14 + c_4_19·a_1_02·a_1_3·b_5_29
       + c_4_19·a_1_03·b_5_29 + c_4_17·a_1_02·a_1_3·b_5_29 + c_4_17·a_1_03·b_5_29
       + c_4_192·b_1_24 + c_4_192·b_1_14 + c_4_18·c_4_19·b_1_24
       + c_4_18·c_4_19·b_1_14 + c_4_17·c_4_19·b_1_24 + c_4_17·c_4_19·b_1_14
       + c_4_172·b_1_24 + c_4_172·b_1_14
  92. b_8_67·b_5_29 + b_6_36·b_1_1·b_3_8·b_3_10 + b_4_16·b_6_38·b_3_8 + b_4_16·b_6_36·b_3_8
       + b_4_16·b_6_36·b_1_13 + b_4_162·b_5_29 + b_4_162·b_1_25 + b_4_163·b_1_2
       + c_4_19·b_6_38·b_3_8 + c_4_19·b_6_36·b_3_10 + c_4_19·b_6_36·b_1_13
       + c_4_18·b_6_38·b_3_9 + c_4_18·b_6_38·b_1_13 + c_4_18·b_6_36·b_1_23
       + c_4_18·b_6_36·b_1_13 + c_4_17·b_6_38·b_3_9 + c_4_17·b_6_36·b_1_23
       + b_4_16·c_4_19·b_1_22·b_3_9 + b_4_16·c_4_19·b_1_25 + b_4_16·c_4_18·b_1_22·b_3_9
       + b_4_16·c_4_18·b_1_25 + b_4_16·c_4_18·b_1_12·b_3_8 + b_4_16·c_4_17·b_1_22·b_3_9
       + b_4_16·c_4_17·b_1_22·b_3_7 + b_4_16·c_4_17·b_1_25 + b_4_16·c_4_17·b_1_12·b_3_10
       + b_4_16·c_4_17·b_1_12·b_3_8 + b_4_16·c_4_17·b_1_15 + b_4_162·c_4_19·b_1_2
       + b_4_162·c_4_18·b_1_2 + b_4_162·c_4_17·b_1_2 + c_4_192·b_1_22·b_3_7
       + c_4_192·b_1_25 + c_4_192·b_1_12·b_3_8 + c_4_192·b_1_15
       + c_4_18·c_4_19·b_1_22·b_3_9 + c_4_18·c_4_19·b_1_25 + c_4_18·c_4_19·b_1_12·b_3_10
       + c_4_18·c_4_19·b_1_12·b_3_8 + c_4_18·c_4_19·b_1_15 + c_4_182·b_1_22·b_3_9
       + c_4_182·b_1_25 + c_4_182·b_1_15 + c_4_17·c_4_19·b_1_22·b_3_7
       + c_4_17·c_4_19·b_1_25 + c_4_17·c_4_19·b_1_15 + c_4_17·c_4_18·b_1_22·b_3_9
       + c_4_17·c_4_18·b_1_25 + c_4_17·c_4_18·b_1_15 + b_4_16·c_4_192·b_1_2
       + b_4_16·c_4_192·b_1_1 + b_4_16·c_4_17·c_4_19·b_1_2 + c_4_192·a_1_0·a_1_3·b_3_7
       + c_4_192·a_1_02·b_3_10 + c_4_192·a_1_02·b_3_7 + c_4_192·a_1_02·b_3_6
       + c_4_18·c_4_19·a_1_02·b_3_7 + c_4_182·a_1_02·b_3_7
       + c_4_17·c_4_19·a_1_0·a_1_3·b_3_7 + c_4_17·c_4_19·a_1_02·b_3_10
       + c_4_17·c_4_19·a_1_02·b_3_8 + c_4_17·c_4_19·a_1_02·b_3_7
       + c_4_17·c_4_18·a_1_02·b_3_8 + c_4_17·c_4_18·a_1_02·b_3_6 + c_4_172·a_1_02·b_3_10
       + c_4_172·a_1_02·b_3_9 + c_4_172·a_1_02·b_3_7 + c_4_192·a_1_32·a_3_5
       + c_4_18·c_4_19·a_1_0·a_1_3·a_3_5 + c_4_182·a_1_32·a_3_5 + c_4_182·a_1_02·a_3_5
       + c_4_17·c_4_19·a_1_0·a_1_3·a_3_5 + c_4_17·c_4_18·a_1_32·a_3_5
       + c_4_17·c_4_18·a_1_0·a_1_3·a_3_5 + c_4_172·a_1_02·a_3_5
  93. b_6_36·b_1_12·b_3_8·b_3_10 + b_6_36·b_8_67 + b_6_36·b_6_38·b_1_12
       + b_6_362·b_1_12 + b_4_16·b_6_38·b_1_1·b_3_8 + b_4_16·b_6_36·b_1_1·b_3_10
       + b_4_16·b_6_36·b_1_14 + b_4_162·b_1_2·b_5_29 + b_4_162·b_1_23·b_3_7
       + b_4_162·b_1_26 + b_4_162·b_6_36 + c_4_19·b_6_36·b_1_1·b_3_10
       + c_4_19·b_6_36·b_1_1·b_3_8 + c_4_18·b_6_36·b_1_1·b_3_10 + c_4_18·b_6_36·b_1_1·b_3_8
       + c_4_18·b_6_36·b_1_14 + c_4_17·b_6_36·b_1_1·b_3_10 + c_4_17·b_6_36·b_1_1·b_3_8
       + b_4_16·c_4_19·b_1_2·b_5_29 + b_4_16·c_4_19·b_6_38 + b_4_16·c_4_19·b_6_36
       + b_4_16·c_4_18·b_3_8·b_3_10 + b_4_16·c_4_18·b_1_23·b_3_7 + b_4_16·c_4_18·b_1_26
       + b_4_16·c_4_18·b_1_13·b_3_8 + b_4_16·c_4_18·b_6_38 + b_4_16·c_4_18·b_6_36
       + b_4_16·c_4_17·b_1_2·b_5_29 + b_4_16·c_4_17·b_1_23·b_3_7 + b_4_16·c_4_17·b_1_26
       + b_4_16·c_4_17·b_1_16 + b_4_16·c_4_17·b_6_36 + b_4_162·c_4_19·b_1_22
       + b_4_162·c_4_18·b_1_22 + c_4_192·b_1_23·b_3_9 + c_4_192·b_1_26
       + c_4_18·c_4_19·b_1_23·b_3_9 + c_4_18·c_4_19·b_1_26 + c_4_17·c_4_19·b_1_23·b_3_9
       + c_4_17·c_4_19·b_1_23·b_3_7 + c_4_17·c_4_19·b_1_26 + c_4_17·c_4_19·b_1_13·b_3_8
       + c_4_17·c_4_18·b_1_23·b_3_9 + c_4_17·c_4_18·b_1_23·b_3_7 + c_4_17·c_4_18·b_1_26
       + c_4_17·c_4_18·b_1_13·b_3_10 + c_4_172·b_1_23·b_3_9 + c_4_172·b_1_13·b_3_10
       + c_4_172·b_1_13·b_3_8 + b_4_16·c_4_192·b_1_22 + b_4_16·c_4_192·b_1_12
       + b_4_16·c_4_18·c_4_19·b_1_22 + b_4_16·c_4_182·b_1_22
       + b_4_16·c_4_17·c_4_19·b_1_12 + b_4_16·c_4_17·c_4_18·b_1_12
       + b_4_16·c_4_172·b_1_22 + b_4_16·c_4_172·b_1_12 + c_4_17·c_4_19·a_1_03·b_3_6
  94. b_6_38·b_8_67 + b_6_36·b_1_12·b_3_8·b_3_10 + b_4_16·b_6_38·b_1_1·b_3_8
       + b_4_16·b_6_36·b_1_1·b_3_8 + b_4_16·b_6_36·b_1_14 + b_4_162·b_1_2·b_5_29
       + b_4_162·b_1_23·b_3_7 + b_4_162·b_1_26 + b_4_162·b_6_36 + c_4_19·b_6_36·b_1_14
       + c_4_18·b_6_38·b_1_24 + c_4_18·b_6_38·b_1_1·b_3_8 + c_4_18·b_6_36·b_1_1·b_3_8
       + c_4_18·b_6_36·b_1_14 + c_4_17·b_6_38·b_1_24 + c_4_17·b_6_38·b_1_1·b_3_8
       + c_4_17·b_6_36·b_1_14 + b_4_16·c_4_19·b_3_8·b_3_10 + b_4_16·c_4_19·b_1_2·b_5_29
       + b_4_16·c_4_19·b_1_26 + b_4_16·c_4_19·b_1_13·b_3_10 + b_4_16·c_4_19·b_1_16
       + b_4_16·c_4_18·b_1_2·b_5_29 + b_4_16·c_4_18·b_1_23·b_3_7 + b_4_16·c_4_18·b_1_26
       + b_4_16·c_4_18·b_1_13·b_3_8 + b_4_16·c_4_18·b_6_38 + b_4_16·c_4_17·b_1_2·b_5_29
       + b_4_16·c_4_17·b_1_13·b_3_10 + b_4_16·c_4_17·b_1_16 + b_4_16·c_4_17·b_6_38
       + b_4_16·c_4_17·b_6_36 + b_4_162·c_4_17·b_1_22 + c_4_192·b_1_26
       + c_4_192·b_1_13·b_3_10 + c_4_192·b_1_13·b_3_8 + c_4_18·c_4_19·b_1_23·b_3_7
       + c_4_18·c_4_19·b_1_13·b_3_8 + c_4_182·b_1_23·b_3_7 + c_4_182·b_1_26
       + c_4_182·b_1_13·b_3_10 + c_4_182·b_1_13·b_3_8 + c_4_17·c_4_19·b_1_23·b_3_9
       + c_4_17·c_4_19·b_1_26 + c_4_17·c_4_19·b_1_16 + c_4_17·c_4_18·b_1_23·b_3_9
       + c_4_17·c_4_18·b_1_23·b_3_7 + c_4_17·c_4_18·b_1_16 + c_4_172·b_1_23·b_3_9
       + c_4_172·b_1_23·b_3_7 + c_4_172·b_1_13·b_3_10 + b_4_16·c_4_192·b_1_12
       + b_4_16·c_4_182·b_1_12 + b_4_16·c_4_17·c_4_18·b_1_22
       + b_4_16·c_4_17·c_4_18·b_1_12 + c_4_192·a_1_03·b_3_6
       + c_4_18·c_4_19·a_1_03·b_3_6 + c_4_182·a_1_03·b_3_6 + c_4_17·c_4_19·a_1_03·b_3_6
       + c_4_172·a_1_03·b_3_6
  95. b_8_672 + b_6_36·b_6_38·b_1_1·b_3_8 + b_6_362·b_1_1·b_3_10
       + b_4_16·b_6_36·b_3_8·b_3_10 + b_4_16·b_6_36·b_1_16 + b_4_16·b_6_362
       + b_4_163·b_1_24 + b_4_164 + c_4_19·b_6_36·b_3_8·b_3_10 + c_4_19·b_6_36·b_1_16
       + c_4_19·b_6_36·b_6_38 + c_4_19·b_6_362 + c_4_18·b_6_36·b_3_8·b_3_10
       + c_4_18·b_6_36·b_1_16 + c_4_18·b_6_36·b_6_38 + c_4_17·b_6_36·b_1_16
       + c_4_17·b_6_36·b_6_38 + c_4_17·b_6_362 + b_4_16·c_4_19·b_6_38·b_1_22
       + b_4_16·c_4_19·b_6_38·b_1_12 + b_4_16·c_4_18·b_8_67
       + b_4_16·c_4_18·b_6_38·b_1_12 + b_4_16·c_4_18·b_6_36·b_1_22
       + b_4_16·c_4_17·b_8_67 + b_4_16·c_4_17·b_6_38·b_1_12
       + b_4_16·c_4_17·b_6_36·b_1_12 + b_4_162·c_4_19·b_1_2·b_3_7
       + b_4_162·c_4_19·b_1_24 + b_4_162·c_4_18·b_1_2·b_3_7 + b_4_162·c_4_18·b_1_24
       + b_4_162·c_4_17·b_1_2·b_3_7 + b_4_162·c_4_17·b_1_24 + b_4_163·c_4_19
       + b_4_163·c_4_18 + b_4_163·c_4_17 + c_4_192·b_1_18 + c_4_192·b_6_38·b_1_22
       + c_4_192·b_6_38·b_1_12 + c_4_192·b_6_36·b_1_22
       + c_4_18·c_4_19·b_1_12·b_3_8·b_3_10 + c_4_18·c_4_19·b_1_18
       + c_4_18·c_4_19·b_6_36·b_1_12 + c_4_182·b_1_28 + c_4_182·b_1_12·b_3_8·b_3_10
       + c_4_182·b_1_18 + c_4_182·b_6_38·b_1_12 + c_4_182·b_6_36·b_1_22
       + c_4_17·c_4_19·b_1_28 + c_4_17·c_4_19·b_6_38·b_1_22
       + c_4_17·c_4_19·b_6_36·b_1_22 + c_4_17·c_4_18·b_1_28
       + c_4_17·c_4_18·b_1_12·b_3_8·b_3_10 + c_4_17·c_4_18·b_1_18
       + c_4_17·c_4_18·b_6_38·b_1_22 + c_4_17·c_4_18·b_6_38·b_1_12
       + c_4_17·c_4_18·b_6_36·b_1_22 + c_4_172·b_1_12·b_3_8·b_3_10 + c_4_172·b_1_18
       + c_4_172·b_6_38·b_1_22 + c_4_172·b_6_38·b_1_12 + c_4_172·b_6_36·b_1_22
       + b_4_16·c_4_192·b_1_2·b_3_9 + b_4_16·c_4_192·b_1_1·b_3_8
       + b_4_16·c_4_192·b_1_14 + b_4_16·c_4_18·c_4_19·b_1_2·b_3_9
       + b_4_16·c_4_18·c_4_19·b_1_2·b_3_7 + b_4_16·c_4_18·c_4_19·b_1_24
       + b_4_16·c_4_182·b_1_24 + b_4_16·c_4_182·b_1_1·b_3_10
       + b_4_16·c_4_182·b_1_1·b_3_8 + b_4_16·c_4_17·c_4_19·b_1_2·b_3_9
       + b_4_16·c_4_17·c_4_19·b_1_1·b_3_10 + b_4_16·c_4_17·c_4_19·b_1_14
       + b_4_16·c_4_17·c_4_18·b_1_24 + b_4_16·c_4_17·c_4_18·b_1_1·b_3_10
       + b_4_16·c_4_17·c_4_18·b_1_1·b_3_8 + b_4_16·c_4_17·c_4_18·b_1_14
       + b_4_16·c_4_172·b_1_2·b_3_7 + b_4_16·c_4_172·b_1_24
       + b_4_16·c_4_172·b_1_1·b_3_10 + b_4_16·c_4_172·b_1_1·b_3_8 + b_4_162·c_4_192
       + b_4_162·c_4_182 + c_4_18·c_4_19·a_1_03·b_5_29 + c_4_182·a_1_03·b_5_29
       + c_4_17·c_4_19·a_1_02·a_1_3·b_5_29 + c_4_17·c_4_18·a_1_02·a_1_3·b_5_29
       + c_4_17·c_4_18·a_1_03·b_5_29 + c_4_193·b_1_24 + c_4_18·c_4_192·b_1_14
       + c_4_17·c_4_192·b_1_24 + c_4_17·c_4_192·b_1_14 + c_4_17·c_4_18·c_4_19·b_1_14
       + c_4_17·c_4_182·b_1_14 + c_4_172·c_4_18·b_1_24 + c_4_172·c_4_18·b_1_14
       + c_4_173·b_1_24 + c_4_173·b_1_14


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 16.
  • 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_4_17, a Duflot regular element of degree 4
    2. c_4_18, a Duflot regular element of degree 4
    3. c_4_19, a Duflot regular element of degree 4
    4. b_1_22, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 8, 10].
  • 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 3

  1. a_1_00, an element of degree 1
  2. a_1_30, an element of degree 1
  3. b_1_10, an element of degree 1
  4. b_1_20, an element of degree 1
  5. a_3_50, an element of degree 3
  6. b_3_60, an element of degree 3
  7. b_3_70, an element of degree 3
  8. b_3_80, an element of degree 3
  9. b_3_90, an element of degree 3
  10. b_3_100, an element of degree 3
  11. b_4_160, an element of degree 4
  12. c_4_17c_1_24, an element of degree 4
  13. c_4_18c_1_04, an element of degree 4
  14. c_4_19c_1_24 + c_1_14 + c_1_04, an element of degree 4
  15. b_5_290, an element of degree 5
  16. b_6_360, an element of degree 6
  17. b_6_380, an element of degree 6
  18. b_8_670, an element of degree 8

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

  1. a_1_00, an element of degree 1
  2. a_1_30, an element of degree 1
  3. b_1_10, an element of degree 1
  4. b_1_2c_1_3, an element of degree 1
  5. a_3_50, an element of degree 3
  6. b_3_60, an element of degree 3
  7. b_3_7c_1_33 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  8. b_3_8c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  9. b_3_9c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  10. b_3_10c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  11. b_4_16c_1_2·c_1_33 + c_1_22·c_1_32, an element of degree 4
  12. c_4_17c_1_2·c_1_33 + c_1_24 + c_1_1·c_1_33 + c_1_12·c_1_32 + c_1_0·c_1_33
       + c_1_02·c_1_32, an element of degree 4
  13. c_4_18c_1_34 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  14. c_4_19c_1_2·c_1_33 + c_1_24 + c_1_12·c_1_32 + c_1_14 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  15. b_5_29c_1_35 + c_1_2·c_1_34 + c_1_24·c_1_3 + c_1_1·c_1_2·c_1_33
       + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_33 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_14·c_1_3 + c_1_0·c_1_34 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_33 + c_1_0·c_1_12·c_1_32
       + c_1_02·c_1_33 + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3
       + c_1_02·c_1_1·c_1_32 + c_1_02·c_1_12·c_1_3, an element of degree 5
  16. b_6_36c_1_2·c_1_35 + c_1_24·c_1_32 + c_1_1·c_1_35 + c_1_14·c_1_32 + c_1_0·c_1_35
       + c_1_0·c_1_2·c_1_34 + c_1_0·c_1_22·c_1_33 + c_1_0·c_1_1·c_1_34
       + c_1_0·c_1_12·c_1_33 + c_1_02·c_1_34 + 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_12·c_1_32, an element of degree 6
  17. b_6_38c_1_36 + c_1_2·c_1_35 + c_1_24·c_1_32 + c_1_1·c_1_2·c_1_34
       + c_1_1·c_1_22·c_1_33 + c_1_12·c_1_2·c_1_33 + c_1_12·c_1_22·c_1_32
       + c_1_0·c_1_35 + c_1_0·c_1_2·c_1_34 + c_1_0·c_1_22·c_1_33
       + c_1_02·c_1_2·c_1_33 + c_1_02·c_1_22·c_1_32 + c_1_04·c_1_32, an element of degree 6
  18. b_8_67c_1_38 + c_1_22·c_1_36 + c_1_24·c_1_34 + c_1_1·c_1_2·c_1_36
       + c_1_1·c_1_24·c_1_33 + c_1_12·c_1_36 + c_1_12·c_1_2·c_1_35
       + c_1_12·c_1_24·c_1_32 + c_1_13·c_1_35 + c_1_15·c_1_33 + c_1_16·c_1_32
       + c_1_0·c_1_2·c_1_36 + c_1_0·c_1_22·c_1_35 + 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_12·c_1_35
       + c_1_0·c_1_12·c_1_2·c_1_34 + c_1_0·c_1_12·c_1_22·c_1_33
       + c_1_0·c_1_14·c_1_33 + c_1_02·c_1_2·c_1_35 + c_1_02·c_1_22·c_1_34
       + c_1_02·c_1_1·c_1_2·c_1_34 + c_1_02·c_1_1·c_1_22·c_1_33
       + c_1_02·c_1_12·c_1_34 + c_1_02·c_1_12·c_1_2·c_1_33
       + c_1_02·c_1_12·c_1_22·c_1_32 + c_1_02·c_1_14·c_1_32, an element of degree 8

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

  1. a_1_00, an element of degree 1
  2. a_1_30, an element of degree 1
  3. b_1_1c_1_3, an element of degree 1
  4. b_1_2c_1_3, an element of degree 1
  5. a_3_50, an element of degree 3
  6. b_3_6c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  7. b_3_7c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  8. b_3_8c_1_33 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  9. b_3_9c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  10. b_3_10c_1_33 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  11. b_4_16c_1_2·c_1_33 + c_1_22·c_1_32, an element of degree 4
  12. c_4_17c_1_22·c_1_32 + c_1_24, an element of degree 4
  13. c_4_18c_1_1·c_1_33 + c_1_12·c_1_32 + c_1_0·c_1_33 + c_1_04, an element of degree 4
  14. c_4_19c_1_34 + c_1_22·c_1_32 + c_1_24 + c_1_1·c_1_33 + c_1_14 + c_1_02·c_1_32
       + c_1_04, an element of degree 4
  15. b_5_29c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_0·c_1_34 + c_1_02·c_1_33, an element of degree 5
  16. b_6_36c_1_36 + c_1_1·c_1_2·c_1_34 + c_1_1·c_1_22·c_1_33 + c_1_12·c_1_2·c_1_33
       + c_1_12·c_1_22·c_1_32 + c_1_0·c_1_35 + c_1_0·c_1_2·c_1_34
       + c_1_0·c_1_22·c_1_33 + c_1_02·c_1_2·c_1_33 + c_1_02·c_1_22·c_1_32
       + c_1_04·c_1_32, an element of degree 6
  17. b_6_38c_1_36 + c_1_2·c_1_35 + c_1_24·c_1_32 + c_1_12·c_1_34 + c_1_14·c_1_32, an element of degree 6
  18. b_8_67c_1_38 + c_1_2·c_1_37 + c_1_22·c_1_36 + c_1_23·c_1_35 + c_1_24·c_1_34
       + c_1_25·c_1_33 + c_1_26·c_1_32 + c_1_1·c_1_37 + c_1_1·c_1_22·c_1_35
       + c_1_1·c_1_24·c_1_33 + c_1_12·c_1_2·c_1_35 + c_1_12·c_1_24·c_1_32
       + c_1_13·c_1_35 + c_1_14·c_1_2·c_1_33 + c_1_14·c_1_22·c_1_32
       + c_1_15·c_1_33 + c_1_16·c_1_32 + c_1_0·c_1_2·c_1_36 + c_1_0·c_1_24·c_1_33
       + 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_12·c_1_2·c_1_34 + c_1_0·c_1_12·c_1_22·c_1_33 + c_1_02·c_1_36
       + 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_22·c_1_33 + c_1_02·c_1_12·c_1_2·c_1_33
       + c_1_02·c_1_12·c_1_22·c_1_32 + c_1_04·c_1_34 + c_1_04·c_1_2·c_1_33
       + c_1_04·c_1_22·c_1_32, an element of degree 8


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