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JoelSjogren

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JoelSjogren
Apr 2nd, 2017
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  1. joel@joel-laptop:~/Insync/Desktop/graphs$ time python3 cyclic.py
  2. n = 2
  3. intersection array
  4. ([1], [1])
  5. left representation
  6. [Matrix([
  7. [1, 0],
  8. [0, 1]]), Matrix([
  9. [0, 1],
  10. [1, 0]])]
  11. irreducible characters
  12. Matrix([
  13. [1, -1],
  14. [1, 1]])
  15.  
  16. n = 3
  17. intersection array
  18. ([2], [1])
  19. left representation
  20. [Matrix([
  21. [1, 0],
  22. [0, 1]]), Matrix([
  23. [0, 1/2],
  24. [1, 1/2]])]
  25. irreducible characters
  26. Matrix([
  27. [1, -1/2],
  28. [1, 1]])
  29.  
  30. n = 4
  31. intersection array
  32. ([2, 1], [1, 2])
  33. left representation
  34. [Matrix([
  35. [1, 0, 0],
  36. [0, 1, 0],
  37. [0, 0, 1]]), Matrix([
  38. [0, 1/2, 0],
  39. [1, 0, 1],
  40. [0, 1/2, 0]]), Matrix([
  41. [0, 0, 1],
  42. [0, 1, 0],
  43. [1, 0, 0]])]
  44. irreducible characters
  45. Matrix([
  46. [1, -1, 1],
  47. [1, 0, -1],
  48. [1, 1, 1]])
  49.  
  50. n = 5
  51. intersection array
  52. ([2, 1], [1, 1])
  53. left representation
  54. [Matrix([
  55. [1, 0, 0],
  56. [0, 1, 0],
  57. [0, 0, 1]]), Matrix([
  58. [0, 1/2, 0],
  59. [1, 0, 1/2],
  60. [0, 1/2, 1/2]]), Matrix([
  61. [0, 0, 1/2],
  62. [0, 1/2, 1/2],
  63. [1, 1/2, 0]])]
  64. irreducible characters
  65. Matrix([
  66. [1, 1, 1],
  67. [1, -1/4 + sqrt(5)/4, -sqrt(5)/4 - 1/4],
  68. [1, -sqrt(5)/4 - 1/4, -1/4 + sqrt(5)/4]])
  69.  
  70. n = 6
  71. intersection array
  72. ([2, 1, 1], [1, 1, 2])
  73. left representation
  74. [Matrix([
  75. [1, 0, 0, 0],
  76. [0, 1, 0, 0],
  77. [0, 0, 1, 0],
  78. [0, 0, 0, 1]]), Matrix([
  79. [0, 1/2, 0, 0],
  80. [1, 0, 1/2, 0],
  81. [0, 1/2, 0, 1],
  82. [0, 0, 1/2, 0]]), Matrix([
  83. [0, 0, 1/2, 0],
  84. [0, 1/2, 0, 1],
  85. [1, 0, 1/2, 0],
  86. [0, 1/2, 0, 0]]), Matrix([
  87. [0, 0, 0, 1],
  88. [0, 0, 1, 0],
  89. [0, 1, 0, 0],
  90. [1, 0, 0, 0]])]
  91. irreducible characters
  92. Matrix([
  93. [1, -1, 1, -1],
  94. [1, -1/2, -1/2, 1],
  95. [1, 1/2, -1/2, -1],
  96. [1, 1, 1, 1]])
  97.  
  98. n = 7
  99. intersection array
  100. ([2, 1, 1], [1, 1, 1])
  101. left representation
  102. [Matrix([
  103. [1, 0, 0, 0],
  104. [0, 1, 0, 0],
  105. [0, 0, 1, 0],
  106. [0, 0, 0, 1]]), Matrix([
  107. [0, 1/2, 0, 0],
  108. [1, 0, 1/2, 0],
  109. [0, 1/2, 0, 1/2],
  110. [0, 0, 1/2, 1/2]]), Matrix([
  111. [0, 0, 1/2, 0],
  112. [0, 1/2, 0, 1/2],
  113. [1, 0, 0, 1/2],
  114. [0, 1/2, 1/2, 0]]), Matrix([
  115. [0, 0, 0, 1/2],
  116. [0, 0, 1/2, 1/2],
  117. [0, 1/2, 1/2, 0],
  118. [1, 1/2, 0, 0]])]
  119. irreducible characters
  120. Matrix([
  121. [1, 1, 1, 1],
  122. [1, -1/6 - 2**(2/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(1/3)/24 - 2**(2/3)*(7 + 21*sqrt(3)*I)**(1/3)/24 + 2**(1/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(2/3)/84 + 2**(1/3)*(7 + 21*sqrt(3)*I)**(2/3)/42, -1/6 - 5*2**(1/3)*(7 + 21*sqrt(3)*I)**(2/3)/168 - 2**(2/3)*(7 + 21*sqrt(3)*I)**(1/3)/24 + 2**(1/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(2/3)/168 + 2**(2/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(1/3)/24, -1/6 + 7/(36*(7/432 + 7*sqrt(3)*I/144)**(1/3)) + (7/432 + 7*sqrt(3)*I/144)**(1/3)],
  123. [1, -1/6 - 98**(1/3)*(1 + 3*sqrt(3)*I)**(2/3)/63 - 5*(28 + 84*sqrt(3)*I)**(1/3)/72 - 2**(1/3)*(7 + 21*sqrt(3)*I)**(2/3)/72 - sqrt(3)*98**(1/3)*I*(1 + 3*sqrt(3)*I)**(2/3)/126 + 2**(2/3)*(7 + 21*sqrt(3)*I)**(1/3)/36 + sqrt(3)*I*(28 + 84*sqrt(3)*I)**(1/3)/72 + 2**(1/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(2/3)/72 + 2**(2/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(1/3)/36, -1/6 - 2**(1/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(2/3)/72 - sqrt(3)*I*(28 + 84*sqrt(3)*I)**(1/3)/72 - 98**(1/3)*(1 + 3*sqrt(3)*I)**(2/3)/126 - sqrt(3)*98**(1/3)*I*(1 + 3*sqrt(3)*I)**(2/3)/252 + 2**(2/3)*(7 + 21*sqrt(3)*I)**(1/3)/72 + 2**(2/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(1/3)/72 + 2**(1/3)*(7 + 21*sqrt(3)*I)**(2/3)/72 + 5*(28 + 84*sqrt(3)*I)**(1/3)/72, -1/6 + (-1/2 - sqrt(3)*I/2)*(7/432 + 7*sqrt(3)*I/144)**(1/3) + 7/(36*(-1/2 - sqrt(3)*I/2)*(7/432 + 7*sqrt(3)*I/144)**(1/3))],
  124. [1, -1/6 - 2**(2/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(1/3)/36 - 2**(1/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(2/3)/72 - 2**(1/3)*(7 + 21*sqrt(3)*I)**(2/3)/72 - sqrt(3)*98**(1/3)*I*(1 + 3*sqrt(3)*I)**(2/3)/252 + 2**(2/3)*(7 + 21*sqrt(3)*I)**(1/3)/36 + (28 + 84*sqrt(3)*I)**(1/3)/18 + 5*98**(1/3)*(1 + 3*sqrt(3)*I)**(2/3)/252 + sqrt(3)*I*(28 + 84*sqrt(3)*I)**(1/3)/36, -1/6 - sqrt(3)*I*(28 + 84*sqrt(3)*I)**(1/3)/36 - (28 + 84*sqrt(3)*I)**(1/3)/18 - 2**(2/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(1/3)/72 - sqrt(3)*98**(1/3)*I*(1 + 3*sqrt(3)*I)**(2/3)/504 + 2**(2/3)*(7 + 21*sqrt(3)*I)**(1/3)/72 + 5*98**(1/3)*(1 + 3*sqrt(3)*I)**(2/3)/504 + 2**(1/3)*(7 + 21*sqrt(3)*I)**(2/3)/72 + 2**(1/3)*sqrt(3)*I*(7 + 21*sqrt(3)*I)**(2/3)/72, -1/6 + 7/(36*(-1/2 + sqrt(3)*I/2)*(7/432 + 7*sqrt(3)*I/144)**(1/3)) + (-1/2 + sqrt(3)*I/2)*(7/432 + 7*sqrt(3)*I/144)**(1/3)]])
  125.  
  126. n = 8
  127. intersection array
  128. ([2, 1, 1, 1], [1, 1, 1, 2])
  129. left representation
  130. [Matrix([
  131. [1, 0, 0, 0, 0],
  132. [0, 1, 0, 0, 0],
  133. [0, 0, 1, 0, 0],
  134. [0, 0, 0, 1, 0],
  135. [0, 0, 0, 0, 1]]), Matrix([
  136. [0, 1/2, 0, 0, 0],
  137. [1, 0, 1/2, 0, 0],
  138. [0, 1/2, 0, 1/2, 0],
  139. [0, 0, 1/2, 0, 1],
  140. [0, 0, 0, 1/2, 0]]), Matrix([
  141. [0, 0, 1/2, 0, 0],
  142. [0, 1/2, 0, 1/2, 0],
  143. [1, 0, 0, 0, 1],
  144. [0, 1/2, 0, 1/2, 0],
  145. [0, 0, 1/2, 0, 0]]), Matrix([
  146. [0, 0, 0, 1/2, 0],
  147. [0, 0, 1/2, 0, 1],
  148. [0, 1/2, 0, 1/2, 0],
  149. [1, 0, 1/2, 0, 0],
  150. [0, 1/2, 0, 0, 0]]), Matrix([
  151. [0, 0, 0, 0, 1],
  152. [0, 0, 0, 1, 0],
  153. [0, 0, 1, 0, 0],
  154. [0, 1, 0, 0, 0],
  155. [1, 0, 0, 0, 0]])]
  156. irreducible characters
  157. Matrix([
  158. [1, -1, 1, -1, 1],
  159. [1, 0, -1, 0, 1],
  160. [1, 1, 1, 1, 1],
  161. [1, -sqrt(2)/2, 0, sqrt(2)/2, -1],
  162. [1, sqrt(2)/2, 0, -sqrt(2)/2, -1]])
  163.  
  164. n = 9
  165. intersection array
  166. ([2, 1, 1, 1], [1, 1, 1, 1])
  167. left representation
  168. [Matrix([
  169. [1, 0, 0, 0, 0],
  170. [0, 1, 0, 0, 0],
  171. [0, 0, 1, 0, 0],
  172. [0, 0, 0, 1, 0],
  173. [0, 0, 0, 0, 1]]), Matrix([
  174. [0, 1/2, 0, 0, 0],
  175. [1, 0, 1/2, 0, 0],
  176. [0, 1/2, 0, 1/2, 0],
  177. [0, 0, 1/2, 0, 1/2],
  178. [0, 0, 0, 1/2, 1/2]]), Matrix([
  179. [0, 0, 1/2, 0, 0],
  180. [0, 1/2, 0, 1/2, 0],
  181. [1, 0, 0, 0, 1/2],
  182. [0, 1/2, 0, 0, 1/2],
  183. [0, 0, 1/2, 1/2, 0]]), Matrix([
  184. [0, 0, 0, 1/2, 0],
  185. [0, 0, 1/2, 0, 1/2],
  186. [0, 1/2, 0, 0, 1/2],
  187. [1, 0, 0, 1/2, 0],
  188. [0, 1/2, 1/2, 0, 0]]), Matrix([
  189. [0, 0, 0, 0, 1/2],
  190. [0, 0, 0, 1/2, 1/2],
  191. [0, 0, 1/2, 1/2, 0],
  192. [0, 1/2, 1/2, 0, 0],
  193. [1, 1/2, 0, 0, 0]])]
  194. irreducible characters
  195. Matrix([
  196. [1, -1/2, -1/2, 1, -1/2],
  197. [1, 1, 1, 1, 1],
  198. [1, 2**(1/3)*(-2 - 2**(1/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) - 2**(1/3)*(1 + sqrt(3)*I)**(2/3) + 2*sqrt(3)*I)/(1 + sqrt(3)*I)**(10/3), -2**(2/3)*(1 + 2**(2/3)*(1 + sqrt(3)*I)**(1/3) + sqrt(3)*I)/(4*(1 + sqrt(3)*I)**(2/3)), -1/2, -(-1/2 + sqrt(3)*I/2)*(27/16 + 27*sqrt(3)*I/16)**(1/3)/3 - 3/(4*(-1/2 + sqrt(3)*I/2)*(27/16 + 27*sqrt(3)*I/16)**(1/3))],
  199. [1, 2**(1/3)*(-1 + 2**(1/3)*(1 + sqrt(3)*I)**(2/3) + sqrt(3)*I)/(2*(1 + sqrt(3)*I)**(4/3)), 2**(1/3)*(-2 - 2**(1/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) - 2**(1/3)*(1 + sqrt(3)*I)**(2/3) + 2*sqrt(3)*I)/(1 + sqrt(3)*I)**(10/3), -1/2, -(27/16 + 27*sqrt(3)*I/16)**(1/3)/3 - 3/(4*(27/16 + 27*sqrt(3)*I/16)**(1/3))],
  200. [1, -2**(1/3)*(2 + 2**(1/3)*(1 + sqrt(3)*I)**(2/3))/(4*(1 + sqrt(3)*I)**(1/3)), 2**(1/3)*(2**(1/3) - (1 + sqrt(3)*I)**(1/3) + sqrt(3)*I*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I)/(2*(1 + sqrt(3)*I)**(5/3)), -1/2, -3/(4*(-1/2 - sqrt(3)*I/2)*(27/16 + 27*sqrt(3)*I/16)**(1/3)) - (-1/2 - sqrt(3)*I/2)*(27/16 + 27*sqrt(3)*I/16)**(1/3)/3]])
  201.  
  202.  
  203. real 1m2.185s
  204. user 0m57.135s
  205. sys 0m0.353s
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