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JoelSjogren

complete results

JoelSjogren
Apr 2nd, 2017
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  1. joel@joel-laptop:~/Insync/Desktop/graphs$ time python3 drcubic.py
  2. intersection array
  3. [[3], [1]]
  4. left representation
  5. [Matrix([
  6. [1, 0],
  7. [0, 1]]), Matrix([
  8. [0, 1/3],
  9. [1, 2/3]])]
  10. irreducible characters
  11. Matrix([
  12. [1, -1/3],
  13. [1, 1]])
  14.  
  15. intersection array
  16. [[3, 2], [1, 3]]
  17. left representation
  18. [Matrix([
  19. [1, 0, 0],
  20. [0, 1, 0],
  21. [0, 0, 1]]), Matrix([
  22. [0, 1/3, 0],
  23. [1, 0, 1],
  24. [0, 2/3, 0]]), Matrix([
  25. [0, 0, 1/2],
  26. [0, 1, 0],
  27. [1, 0, 1/2]])]
  28. irreducible characters
  29. Matrix([
  30. [1, -1, 1],
  31. [1, 0, -1/2],
  32. [1, 1, 1]])
  33.  
  34. intersection array
  35. [[3, 2], [1, 1]]
  36. left representation
  37. [Matrix([
  38. [1, 0, 0],
  39. [0, 1, 0],
  40. [0, 0, 1]]), Matrix([
  41. [0, 1/3, 0],
  42. [1, 0, 1/3],
  43. [0, 2/3, 2/3]]), Matrix([
  44. [0, 0, 1/6],
  45. [0, 1/3, 1/3],
  46. [1, 2/3, 1/2]])]
  47. irreducible characters
  48. Matrix([
  49. [1, -2/3, 1/6],
  50. [1, 1/3, -1/3],
  51. [1, 1, 1]])
  52.  
  53. intersection array
  54. [[3, 2, 1], [1, 2, 3]]
  55. left representation
  56. [Matrix([
  57. [1, 0, 0, 0],
  58. [0, 1, 0, 0],
  59. [0, 0, 1, 0],
  60. [0, 0, 0, 1]]), Matrix([
  61. [0, 1/3, 0, 0],
  62. [1, 0, 2/3, 0],
  63. [0, 2/3, 0, 1],
  64. [0, 0, 1/3, 0]]), Matrix([
  65. [0, 0, 1/3, 0],
  66. [0, 2/3, 0, 1],
  67. [1, 0, 2/3, 0],
  68. [0, 1/3, 0, 0]]), Matrix([
  69. [0, 0, 0, 1],
  70. [0, 0, 1, 0],
  71. [0, 1, 0, 0],
  72. [1, 0, 0, 0]])]
  73. irreducible characters
  74. Matrix([
  75. [1, -1, 1, -1],
  76. [1, -1/3, -1/3, 1],
  77. [1, 1/3, -1/3, -1],
  78. [1, 1, 1, 1]])
  79.  
  80. intersection array
  81. [[3, 2, 2], [1, 1, 3]]
  82. left representation
  83. [Matrix([
  84. [1, 0, 0, 0],
  85. [0, 1, 0, 0],
  86. [0, 0, 1, 0],
  87. [0, 0, 0, 1]]), Matrix([
  88. [0, 1/3, 0, 0],
  89. [1, 0, 1/3, 0],
  90. [0, 2/3, 0, 1],
  91. [0, 0, 2/3, 0]]), Matrix([
  92. [0, 0, 1/6, 0],
  93. [0, 1/3, 0, 1/2],
  94. [1, 0, 5/6, 0],
  95. [0, 2/3, 0, 1/2]]), Matrix([
  96. [0, 0, 0, 1/4],
  97. [0, 0, 1/2, 0],
  98. [0, 1, 0, 3/4],
  99. [1, 0, 1/2, 0]])]
  100. irreducible characters
  101. Matrix([
  102. [1, -1, 1, -1],
  103. [1, 1, 1, 1],
  104. [1, -sqrt(2)/3, -1/6, sqrt(2)/4],
  105. [1, sqrt(2)/3, -1/6, -sqrt(2)/4]])
  106.  
  107. intersection array
  108. [[3, 2, 2, 1], [1, 1, 2, 3]]
  109. left representation
  110. [Matrix([
  111. [1, 0, 0, 0, 0],
  112. [0, 1, 0, 0, 0],
  113. [0, 0, 1, 0, 0],
  114. [0, 0, 0, 1, 0],
  115. [0, 0, 0, 0, 1]]), Matrix([
  116. [0, 1/3, 0, 0, 0],
  117. [1, 0, 1/3, 0, 0],
  118. [0, 2/3, 0, 2/3, 0],
  119. [0, 0, 2/3, 0, 1],
  120. [0, 0, 0, 1/3, 0]]), Matrix([
  121. [0, 0, 1/6, 0, 0],
  122. [0, 1/3, 0, 1/3, 0],
  123. [1, 0, 1/2, 0, 1],
  124. [0, 2/3, 0, 2/3, 0],
  125. [0, 0, 1/3, 0, 0]]), Matrix([
  126. [0, 0, 0, 1/6, 0],
  127. [0, 0, 1/3, 0, 1/2],
  128. [0, 2/3, 0, 2/3, 0],
  129. [1, 0, 2/3, 0, 1/2],
  130. [0, 1/3, 0, 1/6, 0]]), Matrix([
  131. [0, 0, 0, 0, 1/2],
  132. [0, 0, 0, 1/2, 0],
  133. [0, 0, 1, 0, 0],
  134. [0, 1, 0, 1/2, 0],
  135. [1, 0, 0, 0, 1/2]])]
  136. irreducible characters
  137. Matrix([
  138. [1, -1, 1, -1, 1],
  139. [1, 0, -1/2, 0, 1],
  140. [1, 1, 1, 1, 1],
  141. [1, -sqrt(3)/3, 0, sqrt(3)/6, -1/2],
  142. [1, sqrt(3)/3, 0, -sqrt(3)/6, -1/2]])
  143.  
  144. intersection array
  145. [[3, 2, 2, 1], [1, 1, 1, 2]]
  146. left representation
  147. [Matrix([
  148. [1, 0, 0, 0, 0],
  149. [0, 1, 0, 0, 0],
  150. [0, 0, 1, 0, 0],
  151. [0, 0, 0, 1, 0],
  152. [0, 0, 0, 0, 1]]), Matrix([
  153. [0, 1/3, 0, 0, 0],
  154. [1, 0, 1/3, 0, 0],
  155. [0, 2/3, 0, 1/3, 0],
  156. [0, 0, 2/3, 1/3, 2/3],
  157. [0, 0, 0, 1/3, 1/3]]), Matrix([
  158. [0, 0, 1/6, 0, 0],
  159. [0, 1/3, 0, 1/6, 0],
  160. [1, 0, 1/6, 1/6, 1/3],
  161. [0, 2/3, 1/3, 1/3, 2/3],
  162. [0, 0, 1/3, 1/3, 0]]), Matrix([
  163. [0, 0, 0, 1/12, 0],
  164. [0, 0, 1/6, 1/12, 1/6],
  165. [0, 1/3, 1/6, 1/6, 1/3],
  166. [1, 1/3, 1/3, 1/2, 1/3],
  167. [0, 1/3, 1/3, 1/6, 1/6]]), Matrix([
  168. [0, 0, 0, 0, 1/6],
  169. [0, 0, 0, 1/6, 1/6],
  170. [0, 0, 1/3, 1/3, 0],
  171. [0, 2/3, 2/3, 1/3, 1/3],
  172. [1, 1/3, 0, 1/6, 1/3]])]
  173. irreducible characters
  174. Matrix([
  175. [1, -1/3, -1/3, 1/3, -1/3],
  176. [1, 2/3, 1/6, -1/6, -1/3],
  177. [1, 1, 1, 1, 1],
  178. [1, -1/3 + sqrt(2)/3, -sqrt(2)/3, -1/6, sqrt(2)/6 + 1/3],
  179. [1, -sqrt(2)/3 - 1/3, sqrt(2)/3, -1/6, -sqrt(2)/6 + 1/3]])
  180.  
  181. intersection array
  182. [[3, 2, 2, 2], [1, 1, 1, 3]]
  183. left representation
  184. [Matrix([
  185. [1, 0, 0, 0, 0],
  186. [0, 1, 0, 0, 0],
  187. [0, 0, 1, 0, 0],
  188. [0, 0, 0, 1, 0],
  189. [0, 0, 0, 0, 1]]), Matrix([
  190. [0, 1/3, 0, 0, 0],
  191. [1, 0, 1/3, 0, 0],
  192. [0, 2/3, 0, 1/3, 0],
  193. [0, 0, 2/3, 0, 1],
  194. [0, 0, 0, 2/3, 0]]), Matrix([
  195. [0, 0, 1/6, 0, 0],
  196. [0, 1/3, 0, 1/6, 0],
  197. [1, 0, 1/6, 0, 1/2],
  198. [0, 2/3, 0, 5/6, 0],
  199. [0, 0, 2/3, 0, 1/2]]), Matrix([
  200. [0, 0, 0, 1/12, 0],
  201. [0, 0, 1/6, 0, 1/4],
  202. [0, 1/3, 0, 5/12, 0],
  203. [1, 0, 5/6, 0, 3/4],
  204. [0, 2/3, 0, 1/2, 0]]), Matrix([
  205. [0, 0, 0, 0, 1/8],
  206. [0, 0, 0, 1/4, 0],
  207. [0, 0, 1/2, 0, 3/8],
  208. [0, 1, 0, 3/4, 0],
  209. [1, 0, 1/2, 0, 1/2]])]
  210. irreducible characters
  211. Matrix([
  212. [1, -1, 1, -1, 1],
  213. [1, -2/3, 1/6, 1/6, -1/4],
  214. [1, 0, -1/2, 0, 1/4],
  215. [1, 2/3, 1/6, -1/6, -1/4],
  216. [1, 1, 1, 1, 1]])
  217.  
  218. intersection array
  219. [[3, 2, 1, 1, 1], [1, 1, 1, 2, 3]]
  220. left representation
  221. [Matrix([
  222. [1, 0, 0, 0, 0, 0],
  223. [0, 1, 0, 0, 0, 0],
  224. [0, 0, 1, 0, 0, 0],
  225. [0, 0, 0, 1, 0, 0],
  226. [0, 0, 0, 0, 1, 0],
  227. [0, 0, 0, 0, 0, 1]]), Matrix([
  228. [0, 1/3, 0, 0, 0, 0],
  229. [1, 0, 1/3, 0, 0, 0],
  230. [0, 2/3, 1/3, 1/3, 0, 0],
  231. [0, 0, 1/3, 1/3, 2/3, 0],
  232. [0, 0, 0, 1/3, 0, 1],
  233. [0, 0, 0, 0, 1/3, 0]]), Matrix([
  234. [0, 0, 1/6, 0, 0, 0],
  235. [0, 1/3, 1/6, 1/6, 0, 0],
  236. [1, 1/3, 1/6, 1/3, 1/3, 0],
  237. [0, 1/3, 1/3, 1/6, 1/3, 1],
  238. [0, 0, 1/6, 1/6, 1/3, 0],
  239. [0, 0, 0, 1/6, 0, 0]]), Matrix([
  240. [0, 0, 0, 1/6, 0, 0],
  241. [0, 0, 1/6, 1/6, 1/3, 0],
  242. [0, 1/3, 1/3, 1/6, 1/3, 1],
  243. [1, 1/3, 1/6, 1/3, 1/3, 0],
  244. [0, 1/3, 1/6, 1/6, 0, 0],
  245. [0, 0, 1/6, 0, 0, 0]]), Matrix([
  246. [0, 0, 0, 0, 1/3, 0],
  247. [0, 0, 0, 1/3, 0, 1],
  248. [0, 0, 1/3, 1/3, 2/3, 0],
  249. [0, 2/3, 1/3, 1/3, 0, 0],
  250. [1, 0, 1/3, 0, 0, 0],
  251. [0, 1/3, 0, 0, 0, 0]]), Matrix([
  252. [0, 0, 0, 0, 0, 1],
  253. [0, 0, 0, 0, 1, 0],
  254. [0, 0, 0, 1, 0, 0],
  255. [0, 0, 1, 0, 0, 0],
  256. [0, 1, 0, 0, 0, 0],
  257. [1, 0, 0, 0, 0, 0]])]
  258. irreducible characters
  259. Matrix([
  260. [1, -2/3, 1/6, 1/6, -2/3, 1],
  261. [1, 0, -1/2, 1/2, 0, -1],
  262. [1, 1/3, -1/3, -1/3, 1/3, 1],
  263. [1, 1, 1, 1, 1, 1],
  264. [1, -sqrt(5)/3, 1/3, -1/3, sqrt(5)/3, -1],
  265. [1, sqrt(5)/3, 1/3, -1/3, -sqrt(5)/3, -1]])
  266.  
  267. intersection array
  268. [[3, 2, 2, 1, 1], [1, 1, 2, 2, 3]]
  269. left representation
  270. [Matrix([
  271. [1, 0, 0, 0, 0, 0],
  272. [0, 1, 0, 0, 0, 0],
  273. [0, 0, 1, 0, 0, 0],
  274. [0, 0, 0, 1, 0, 0],
  275. [0, 0, 0, 0, 1, 0],
  276. [0, 0, 0, 0, 0, 1]]), Matrix([
  277. [0, 1/3, 0, 0, 0, 0],
  278. [1, 0, 1/3, 0, 0, 0],
  279. [0, 2/3, 0, 2/3, 0, 0],
  280. [0, 0, 2/3, 0, 2/3, 0],
  281. [0, 0, 0, 1/3, 0, 1],
  282. [0, 0, 0, 0, 1/3, 0]]), Matrix([
  283. [0, 0, 1/6, 0, 0, 0],
  284. [0, 1/3, 0, 1/3, 0, 0],
  285. [1, 0, 1/2, 0, 2/3, 0],
  286. [0, 2/3, 0, 1/2, 0, 1],
  287. [0, 0, 1/3, 0, 1/3, 0],
  288. [0, 0, 0, 1/6, 0, 0]]), Matrix([
  289. [0, 0, 0, 1/6, 0, 0],
  290. [0, 0, 1/3, 0, 1/3, 0],
  291. [0, 2/3, 0, 1/2, 0, 1],
  292. [1, 0, 1/2, 0, 2/3, 0],
  293. [0, 1/3, 0, 1/3, 0, 0],
  294. [0, 0, 1/6, 0, 0, 0]]), Matrix([
  295. [0, 0, 0, 0, 1/3, 0],
  296. [0, 0, 0, 1/3, 0, 1],
  297. [0, 0, 2/3, 0, 2/3, 0],
  298. [0, 2/3, 0, 2/3, 0, 0],
  299. [1, 0, 1/3, 0, 0, 0],
  300. [0, 1/3, 0, 0, 0, 0]]), Matrix([
  301. [0, 0, 0, 0, 0, 1],
  302. [0, 0, 0, 0, 1, 0],
  303. [0, 0, 0, 1, 0, 0],
  304. [0, 0, 1, 0, 0, 0],
  305. [0, 1, 0, 0, 0, 0],
  306. [1, 0, 0, 0, 0, 0]])]
  307. irreducible characters
  308. Matrix([
  309. [1, -1, 1, -1, 1, -1],
  310. [1, -2/3, 1/6, 1/6, -2/3, 1],
  311. [1, -1/3, -1/3, 1/3, 1/3, -1],
  312. [1, 1/3, -1/3, -1/3, 1/3, 1],
  313. [1, 2/3, 1/6, -1/6, -2/3, -1],
  314. [1, 1, 1, 1, 1, 1]])
  315.  
  316. intersection array
  317. [[3, 2, 2, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 3]]
  318. left representation
  319. [Matrix([
  320. [1, 0, 0, 0, 0, 0, 0, 0],
  321. [0, 1, 0, 0, 0, 0, 0, 0],
  322. [0, 0, 1, 0, 0, 0, 0, 0],
  323. [0, 0, 0, 1, 0, 0, 0, 0],
  324. [0, 0, 0, 0, 1, 0, 0, 0],
  325. [0, 0, 0, 0, 0, 1, 0, 0],
  326. [0, 0, 0, 0, 0, 0, 1, 0],
  327. [0, 0, 0, 0, 0, 0, 0, 1]]), Matrix([
  328. [0, 1/3, 0, 0, 0, 0, 0, 0],
  329. [1, 0, 1/3, 0, 0, 0, 0, 0],
  330. [0, 2/3, 0, 1/3, 0, 0, 0, 0],
  331. [0, 0, 2/3, 0, 1/3, 0, 0, 0],
  332. [0, 0, 0, 2/3, 1/3, 1/3, 0, 0],
  333. [0, 0, 0, 0, 1/3, 1/3, 1/3, 0],
  334. [0, 0, 0, 0, 0, 1/3, 1/3, 1],
  335. [0, 0, 0, 0, 0, 0, 1/3, 0]]), Matrix([
  336. [0, 0, 1/6, 0, 0, 0, 0, 0],
  337. [0, 1/3, 0, 1/6, 0, 0, 0, 0],
  338. [1, 0, 1/6, 0, 1/6, 0, 0, 0],
  339. [0, 2/3, 0, 1/6, 1/6, 1/6, 0, 0],
  340. [0, 0, 2/3, 1/3, 1/6, 1/3, 1/6, 0],
  341. [0, 0, 0, 1/3, 1/3, 0, 1/3, 1/2],
  342. [0, 0, 0, 0, 1/6, 1/3, 1/3, 1/2],
  343. [0, 0, 0, 0, 0, 1/6, 1/6, 0]]), Matrix([
  344. [0, 0, 0, 1/12, 0, 0, 0, 0],
  345. [0, 0, 1/6, 0, 1/12, 0, 0, 0],
  346. [0, 1/3, 0, 1/12, 1/12, 1/12, 0, 0],
  347. [1, 0, 1/6, 1/6, 1/12, 1/6, 1/12, 0],
  348. [0, 2/3, 1/3, 1/6, 1/4, 1/6, 1/4, 1/4],
  349. [0, 0, 1/3, 1/3, 1/6, 1/6, 1/4, 1/2],
  350. [0, 0, 0, 1/6, 1/4, 1/4, 5/12, 0],
  351. [0, 0, 0, 0, 1/12, 1/6, 0, 1/4]]), Matrix([
  352. [0, 0, 0, 0, 1/24, 0, 0, 0],
  353. [0, 0, 0, 1/12, 1/24, 1/24, 0, 0],
  354. [0, 0, 1/6, 1/12, 1/24, 1/12, 1/24, 0],
  355. [0, 1/3, 1/6, 1/12, 1/8, 1/12, 1/8, 1/8],
  356. [1, 1/3, 1/6, 1/4, 5/24, 1/6, 1/4, 3/8],
  357. [0, 1/3, 1/3, 1/6, 1/6, 7/24, 7/24, 1/8],
  358. [0, 0, 1/6, 1/4, 1/4, 7/24, 1/6, 3/8],
  359. [0, 0, 0, 1/12, 1/8, 1/24, 1/8, 0]]), Matrix([
  360. [0, 0, 0, 0, 0, 1/24, 0, 0],
  361. [0, 0, 0, 0, 1/24, 1/24, 1/24, 0],
  362. [0, 0, 0, 1/12, 1/12, 0, 1/12, 1/8],
  363. [0, 0, 1/6, 1/6, 1/12, 1/12, 1/8, 1/4],
  364. [0, 1/3, 1/3, 1/6, 1/6, 7/24, 7/24, 1/8],
  365. [1, 1/3, 0, 1/6, 7/24, 7/24, 1/6, 1/4],
  366. [0, 1/3, 1/3, 1/4, 7/24, 1/6, 1/4, 1/8],
  367. [0, 0, 1/6, 1/6, 1/24, 1/12, 1/24, 1/8]]), Matrix([
  368. [0, 0, 0, 0, 0, 0, 1/24, 0],
  369. [0, 0, 0, 0, 0, 1/24, 1/24, 1/8],
  370. [0, 0, 0, 0, 1/24, 1/12, 1/12, 1/8],
  371. [0, 0, 0, 1/12, 1/8, 1/8, 5/24, 0],
  372. [0, 0, 1/6, 1/4, 1/4, 7/24, 1/6, 3/8],
  373. [0, 1/3, 1/3, 1/4, 7/24, 1/6, 1/4, 1/8],
  374. [1, 1/3, 1/3, 5/12, 1/6, 1/4, 1/8, 1/4],
  375. [0, 1/3, 1/6, 0, 1/8, 1/24, 1/12, 0]]), Matrix([
  376. [0, 0, 0, 0, 0, 0, 0, 1/8],
  377. [0, 0, 0, 0, 0, 0, 1/8, 0],
  378. [0, 0, 0, 0, 0, 1/8, 1/8, 0],
  379. [0, 0, 0, 0, 1/8, 1/4, 0, 3/8],
  380. [0, 0, 0, 1/4, 3/8, 1/8, 3/8, 0],
  381. [0, 0, 1/2, 1/2, 1/8, 1/4, 1/8, 3/8],
  382. [0, 1, 1/2, 0, 3/8, 1/8, 1/4, 0],
  383. [1, 0, 0, 1/4, 0, 1/8, 0, 1/8]])]
  384. irreducible characters
  385. Matrix([
  386. [1, 0, -1/2, 0, 1/4, -1/4, 0, 1/4],
  387. [1, 2/3, 1/6, -1/6, -1/4, -1/12, 1/6, 1/4],
  388. [1, 1, 1, 1, 1, 1, 1, 1],
  389. [1, -(2*2**(1/3) + (1 + sqrt(3)*I)**(1/3) + 2*2**(1/3)*sqrt(3)*I/3 + sqrt(3)*I*(1 + sqrt(3)*I)**(1/3) + 2*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/3)/(-2**(1/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 4*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I + 4*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), (3*2**(1/3)/2 - 3*(2 + 2*sqrt(3)*I)**(2/3)/4 - 2**(1/3)*sqrt(3)*I/2 - sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/2 - (1 + sqrt(3)*I)**(1/3)/2 + sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/4)/(-2**(1/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 4*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I + 4*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), 2**(1/3)*(18 + 15*2**(1/3)*(1 + sqrt(3)*I)**(2/3) + 11*2**(1/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 26*sqrt(3)*I)/(24*(-2**(1/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 4*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I + 4*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3))), -(2**(1/3)/8 + (1 + sqrt(3)*I)**(1/3)/8 + sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/8 + (2 + 2*sqrt(3)*I)**(2/3)/4 + sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/8 + 3*2**(1/3)*sqrt(3)*I/8)/(-2**(1/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 4*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I + 4*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), (-7*2**(1/3)/8 - 13*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/48 - 5*2**(1/3)*sqrt(3)*I/24 + (2 + 2*sqrt(3)*I)**(2/3)/16 + 3*(1 + sqrt(3)*I)**(1/3)/8 + 3*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/8)/(-2**(1/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 4*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I + 4*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), (7*2**(1/3)/4 - sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/24 + 2**(1/3)*sqrt(3)*I/12 + (1 + sqrt(3)*I)**(1/3) + 7*(2 + 2*sqrt(3)*I)**(2/3)/8)/(2*2**(1/3) - 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2*2**(1/3)*sqrt(3)*I + 16*(1 + sqrt(3)*I)**(1/3)), -1/4 + 1/(64*(-1/2 + sqrt(3)*I/2)*(1/1024 + sqrt(3)*I/1024)**(1/3)) + (-1/2 + sqrt(3)*I/2)*(1/1024 + sqrt(3)*I/1024)**(1/3)],
  390. [1, (4*2**(1/3) - 2*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/3 - 4*(1 + sqrt(3)*I)**(1/3) + 4*2**(1/3)*sqrt(3)*I/3 + 2*(2 + 2*sqrt(3)*I)**(2/3))/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 16*(1 + sqrt(3)*I)**(1/3)), (-3*2**(1/3) - 3*(2 + 2*sqrt(3)*I)**(2/3)/2 - sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/2 - 2*(1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I)/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 16*(1 + sqrt(3)*I)**(1/3)), 2**(1/3)*(-18 - 26*sqrt(3)*I - 9*2**(1/3)*(1 + sqrt(3)*I)**(2/3) + 13*2**(1/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3))/(12*(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 16*(1 + sqrt(3)*I)**(1/3))), (2**(1/3)/4 - 3*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/8 - (1 + sqrt(3)*I)**(1/3)/2 + (2 + 2*sqrt(3)*I)**(2/3)/8 + 3*2**(1/3)*sqrt(3)*I/4)/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 16*(1 + sqrt(3)*I)**(1/3)), (7*2**(1/3)/4 - 5*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/24 + 3*(1 + sqrt(3)*I)**(1/3)/2 + 5*2**(1/3)*sqrt(3)*I/12 + 7*(2 + 2*sqrt(3)*I)**(2/3)/8)/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 16*(1 + sqrt(3)*I)**(1/3)), (7*2**(1/3)/8 - 5*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/24 - (2 + 2*sqrt(3)*I)**(2/3)/4 - (1 + sqrt(3)*I)**(1/3)/4 + 2**(1/3)*sqrt(3)*I/24 + sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/4)/(2**(1/3) - 4*(1 + sqrt(3)*I)**(1/3) - 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(1/3)*sqrt(3)*I + 4*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), -1/4 + (-1/2 - sqrt(3)*I/2)*(1/1024 + sqrt(3)*I/1024)**(1/3) + 1/(64*(-1/2 - sqrt(3)*I/2)*(1/1024 + sqrt(3)*I/1024)**(1/3))],
  391. [1, (4*2**(1/3) - 2*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3) - 2*(2 + 2*sqrt(3)*I)**(2/3) - 2*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/3 + 2*(1 + sqrt(3)*I)**(1/3) + 4*2**(1/3)*sqrt(3)*I/3)/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I - 8*(1 + sqrt(3)*I)**(1/3) - 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 8*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), (-3*2**(1/3) - sqrt(3)*I*(1 + sqrt(3)*I)**(1/3) + (1 + sqrt(3)*I)**(1/3) + 2**(1/3)*sqrt(3)*I + sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3))/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I - 8*(1 + sqrt(3)*I)**(1/3) - 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 8*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), 2**(1/3)*(-9 - 13*sqrt(3)*I - 2**(1/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 12*2**(1/3)*(1 + sqrt(3)*I)**(2/3))/(6*(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I - 8*(1 + sqrt(3)*I)**(1/3) - 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 8*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3))), (2**(1/3)/4 - 5*(2 + 2*sqrt(3)*I)**(2/3)/8 - sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/4 + (1 + sqrt(3)*I)**(1/3)/4 + sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/8 + 3*2**(1/3)*sqrt(3)*I/4)/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I - 8*(1 + sqrt(3)*I)**(1/3) - 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 8*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), (7*2**(1/3)/4 - 3*(2 + 2*sqrt(3)*I)**(2/3)/4 - sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/3 - 3*(1 + sqrt(3)*I)**(1/3)/4 + 5*2**(1/3)*sqrt(3)*I/12 + 3*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/4)/(2*2**(1/3) - 2*2**(1/3)*sqrt(3)*I - 8*(1 + sqrt(3)*I)**(1/3) - 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 8*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)), (7*2**(1/3)/4 - sqrt(3)*I*(1 + sqrt(3)*I)**(1/3)/2 - 3*(2 + 2*sqrt(3)*I)**(2/3)/8 - (1 + sqrt(3)*I)**(1/3)/2 + 2**(1/3)*sqrt(3)*I/12 + 11*sqrt(3)*I*(2 + 2*sqrt(3)*I)**(2/3)/24)/(2*2**(1/3) - 8*sqrt(3)*I*(1 + sqrt(3)*I)**(1/3) - 8*(1 + sqrt(3)*I)**(1/3) + 2**(2/3)*(1 + sqrt(3)*I)**(2/3) + 2**(2/3)*sqrt(3)*I*(1 + sqrt(3)*I)**(2/3) + 2*2**(1/3)*sqrt(3)*I), -1/4 + 1/(64*(1/1024 + sqrt(3)*I/1024)**(1/3)) + (1/1024 + sqrt(3)*I/1024)**(1/3)],
  392. [1, 1/6 + sqrt(17)/6, 1/4 + sqrt(17)/12, 1/3, -1/24 + sqrt(17)/24, -sqrt(17)/24 + 1/24, -1/3, -sqrt(17)/8 + 1/8],
  393. [1, -sqrt(17)/6 + 1/6, -sqrt(17)/12 + 1/4, 1/3, -sqrt(17)/24 - 1/24, 1/24 + sqrt(17)/24, -1/3, 1/8 + sqrt(17)/8]])
  394.  
  395. intersection array
  396. [[3, 2, 2, 2, 2, 1, 1, 1], [1, 1, 1, 1, 2, 2, 2, 3]]
  397. left representation
  398. [Matrix([
  399. [1, 0, 0, 0, 0, 0, 0, 0, 0],
  400. [0, 1, 0, 0, 0, 0, 0, 0, 0],
  401. [0, 0, 1, 0, 0, 0, 0, 0, 0],
  402. [0, 0, 0, 1, 0, 0, 0, 0, 0],
  403. [0, 0, 0, 0, 1, 0, 0, 0, 0],
  404. [0, 0, 0, 0, 0, 1, 0, 0, 0],
  405. [0, 0, 0, 0, 0, 0, 1, 0, 0],
  406. [0, 0, 0, 0, 0, 0, 0, 1, 0],
  407. [0, 0, 0, 0, 0, 0, 0, 0, 1]]), Matrix([
  408. [0, 1/3, 0, 0, 0, 0, 0, 0, 0],
  409. [1, 0, 1/3, 0, 0, 0, 0, 0, 0],
  410. [0, 2/3, 0, 1/3, 0, 0, 0, 0, 0],
  411. [0, 0, 2/3, 0, 1/3, 0, 0, 0, 0],
  412. [0, 0, 0, 2/3, 0, 2/3, 0, 0, 0],
  413. [0, 0, 0, 0, 2/3, 0, 2/3, 0, 0],
  414. [0, 0, 0, 0, 0, 1/3, 0, 2/3, 0],
  415. [0, 0, 0, 0, 0, 0, 1/3, 0, 1],
  416. [0, 0, 0, 0, 0, 0, 0, 1/3, 0]]), Matrix([
  417. [0, 0, 1/6, 0, 0, 0, 0, 0, 0],
  418. [0, 1/3, 0, 1/6, 0, 0, 0, 0, 0],
  419. [1, 0, 1/6, 0, 1/6, 0, 0, 0, 0],
  420. [0, 2/3, 0, 1/6, 0, 1/3, 0, 0, 0],
  421. [0, 0, 2/3, 0, 1/2, 0, 2/3, 0, 0],
  422. [0, 0, 0, 2/3, 0, 1/2, 0, 2/3, 0],
  423. [0, 0, 0, 0, 1/3, 0, 1/6, 0, 1],
  424. [0, 0, 0, 0, 0, 1/6, 0, 1/3, 0],
  425. [0, 0, 0, 0, 0, 0, 1/6, 0, 0]]), Matrix([
  426. [0, 0, 0, 1/12, 0, 0, 0, 0, 0],
  427. [0, 0, 1/6, 0, 1/12, 0, 0, 0, 0],
  428. [0, 1/3, 0, 1/12, 0, 1/6, 0, 0, 0],
  429. [1, 0, 1/6, 0, 1/4, 0, 1/3, 0, 0],
  430. [0, 2/3, 0, 1/2, 0, 1/2, 0, 2/3, 0],
  431. [0, 0, 2/3, 0, 1/2, 0, 1/2, 0, 1],
  432. [0, 0, 0, 1/3, 0, 1/4, 0, 1/3, 0],
  433. [0, 0, 0, 0, 1/6, 0, 1/6, 0, 0],
  434. [0, 0, 0, 0, 0, 1/12, 0, 0, 0]]), Matrix([
  435. [0, 0, 0, 0, 1/24, 0, 0, 0, 0],
  436. [0, 0, 0, 1/12, 0, 1/12, 0, 0, 0],
  437. [0, 0, 1/6, 0, 1/8, 0, 1/6, 0, 0],
  438. [0, 1/3, 0, 1/4, 0, 1/4, 0, 1/3, 0],
  439. [1, 0, 1/2, 0, 1/2, 0, 1/2, 0, 1],
  440. [0, 2/3, 0, 1/2, 0, 1/2, 0, 2/3, 0],
  441. [0, 0, 1/3, 0, 1/4, 0, 1/3, 0, 0],
  442. [0, 0, 0, 1/6, 0, 1/6, 0, 0, 0],
  443. [0, 0, 0, 0, 1/12, 0, 0, 0, 0]]), Matrix([
  444. [0, 0, 0, 0, 0, 1/24, 0, 0, 0],
  445. [0, 0, 0, 0, 1/12, 0, 1/12, 0, 0],
  446. [0, 0, 0, 1/6, 0, 1/8, 0, 1/6, 0],
  447. [0, 0, 1/3, 0, 1/4, 0, 1/4, 0, 1/2],
  448. [0, 2/3, 0, 1/2, 0, 1/2, 0, 2/3, 0],
  449. [1, 0, 1/2, 0, 1/2, 0, 7/12, 0, 1/2],
  450. [0, 1/3, 0, 1/4, 0, 7/24, 0, 1/6, 0],
  451. [0, 0, 1/6, 0, 1/6, 0, 1/12, 0, 0],
  452. [0, 0, 0, 1/12, 0, 1/24, 0, 0, 0]]), Matrix([
  453. [0, 0, 0, 0, 0, 0, 1/12, 0, 0],
  454. [0, 0, 0, 0, 0, 1/12, 0, 1/6, 0],
  455. [0, 0, 0, 0, 1/6, 0, 1/12, 0, 1/2],
  456. [0, 0, 0, 1/3, 0, 1/4, 0, 1/3, 0],
  457. [0, 0, 2/3, 0, 1/2, 0, 2/3, 0, 0],
  458. [0, 2/3, 0, 1/2, 0, 7/12, 0, 1/3, 0],
  459. [1, 0, 1/6, 0, 1/3, 0, 1/12, 0, 1/2],
  460. [0, 1/3, 0, 1/6, 0, 1/12, 0, 1/6, 0],
  461. [0, 0, 1/6, 0, 0, 0, 1/12, 0, 0]]), Matrix([
  462. [0, 0, 0, 0, 0, 0, 0, 1/6, 0],
  463. [0, 0, 0, 0, 0, 0, 1/6, 0, 1/2],
  464. [0, 0, 0, 0, 0, 1/6, 0, 1/3, 0],
  465. [0, 0, 0, 0, 1/3, 0, 1/3, 0, 0],
  466. [0, 0, 0, 2/3, 0, 2/3, 0, 0, 0],
  467. [0, 0, 2/3, 0, 2/3, 0, 1/3, 0, 0],
  468. [0, 2/3, 0, 1/3, 0, 1/6, 0, 1/3, 0],
  469. [1, 0, 1/3, 0, 0, 0, 1/6, 0, 1/2],
  470. [0, 1/3, 0, 0, 0, 0, 0, 1/6, 0]]), Matrix([
  471. [0, 0, 0, 0, 0, 0, 0, 0, 1/2],
  472. [0, 0, 0, 0, 0, 0, 0, 1/2, 0],
  473. [0, 0, 0, 0, 0, 0, 1/2, 0, 0],
  474. [0, 0, 0, 0, 0, 1/2, 0, 0, 0],
  475. [0, 0, 0, 0, 1, 0, 0, 0, 0],
  476. [0, 0, 0, 1, 0, 1/2, 0, 0, 0],
  477. [0, 0, 1, 0, 0, 0, 1/2, 0, 0],
  478. [0, 1, 0, 0, 0, 0, 0, 1/2, 0],
  479. [1, 0, 0, 0, 0, 0, 0, 0, 1/2]])]
  480. irreducible characters
  481. Matrix([
  482. [1, -1, 1, -1, 1, -1, 1, -1, 1],
  483. [1, -2/3, 1/6, 1/6, -1/4, 1/6, 1/6, -2/3, 1],
  484. [1, -1/3, -1/3, 1/3, 0, -1/6, 1/6, 1/6, -1/2],
  485. [1, 0, -1/2, 0, 1/4, 0, -1/2, 0, 1],
  486. [1, 1/3, -1/3, -1/3, 0, 1/6, 1/6, -1/6, -1/2],
  487. [1, 2/3, 1/6, -1/6, -1/4, -1/6, 1/6, 2/3, 1],
  488. [1, 1, 1, 1, 1, 1, 1, 1, 1],
  489. [1, -sqrt(6)/3, 1/2, -sqrt(6)/12, 0, sqrt(6)/24, -1/4, sqrt(6)/6, -1/2],
  490. [1, sqrt(6)/3, 1/2, sqrt(6)/12, 0, -sqrt(6)/24, -1/4, -sqrt(6)/6, -1/2]])
  491.  
  492.  
  493. real 6m55.140s
  494. user 5m59.206s
  495. sys 0m1.217s
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