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pari vs gens_two

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Jan 23rd, 2013
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  1. sage: #increasing initial gens, gens_two only
  2. sage: deg=18
  3. sage: R.<x>=ZZ[]
  4. sage: f=x^deg+R.random_element(deg-1)
  5. sage: K.<a>=QQ.extension(f)
  6. sage: for j in range(1,41,5):
  7. ....: for k in range(5):
  8. ....: m=K.random_element()
  9. ....: n=K.random_element()
  10. ....: I=K.ideal([m*K.random_element() for i in range(j)])
  11. ....: J=K.ideal([n*K.random_element() for i in range(j)])
  12. ....: print "=========pari=====",j
  13. ....: time K_pari=K.pari_nf()
  14. ....: time H=K.ideal(K_pari.idealmul(I._pari_(),J._pari_()))
  15. ....: print "===========gens_two======",j
  16. ....: time I1=K.ideal(I.gens_two())
  17. ....: time J1=K.ideal(J.gens_two())
  18. ....: time H1=I1*J1
  19. ....: time H1=K.ideal(H1.gens_two())
  20. ....:
  21. =========pari===== 1
  22. Time: CPU 0.03 s, Wall: 0.03 s
  23. Time: CPU 0.02 s, Wall: 0.02 s
  24. ===========gens_two====== 1
  25. Time: CPU 0.01 s, Wall: 0.01 s
  26. Time: CPU 0.00 s, Wall: 0.00 s
  27. Time: CPU 0.09 s, Wall: 0.09 s
  28. Time: CPU 2.64 s, Wall: 2.74 s
  29. =========pari===== 1
  30. Time: CPU 0.00 s, Wall: 0.00 s
  31. Time: CPU 0.02 s, Wall: 0.02 s
  32. ===========gens_two====== 1
  33. Time: CPU 0.00 s, Wall: 0.00 s
  34. Time: CPU 0.00 s, Wall: 0.00 s
  35. Time: CPU 0.20 s, Wall: 0.20 s
  36. Time: CPU 2.44 s, Wall: 2.51 s
  37. =========pari===== 1
  38. Time: CPU 0.00 s, Wall: 0.00 s
  39. Time: CPU 0.03 s, Wall: 0.03 s
  40. ===========gens_two====== 1
  41. Time: CPU 0.00 s, Wall: 0.00 s
  42. Time: CPU 0.00 s, Wall: 0.00 s
  43. Time: CPU 0.12 s, Wall: 0.12 s
  44. Time: CPU 3.78 s, Wall: 3.97 s
  45. =========pari===== 1
  46. Time: CPU 0.00 s, Wall: 0.00 s
  47. Time: CPU 0.02 s, Wall: 0.02 s
  48. ===========gens_two====== 1
  49. Time: CPU 0.00 s, Wall: 0.00 s
  50. Time: CPU 0.00 s, Wall: 0.00 s
  51. Time: CPU 0.11 s, Wall: 0.13 s
  52. Time: CPU 2.55 s, Wall: 2.68 s
  53. =========pari===== 1
  54. Time: CPU 0.00 s, Wall: 0.00 s
  55. Time: CPU 0.02 s, Wall: 0.02 s
  56. ===========gens_two====== 1
  57. Time: CPU 0.00 s, Wall: 0.00 s
  58. Time: CPU 0.00 s, Wall: 0.00 s
  59. Time: CPU 0.07 s, Wall: 0.07 s
  60. Time: CPU 2.32 s, Wall: 2.35 s
  61. =========pari===== 6
  62. Time: CPU 0.00 s, Wall: 0.00 s
  63. Time: CPU 0.05 s, Wall: 0.05 s
  64. ===========gens_two====== 6
  65. Time: CPU 0.00 s, Wall: 0.00 s
  66. Time: CPU 0.00 s, Wall: 0.00 s
  67. Time: CPU 0.02 s, Wall: 0.02 s
  68. Time: CPU 0.95 s, Wall: 0.95 s
  69. =========pari===== 6
  70. Time: CPU 0.00 s, Wall: 0.00 s
  71. Time: CPU 0.05 s, Wall: 0.05 s
  72. ===========gens_two====== 6
  73. Time: CPU 0.00 s, Wall: 0.00 s
  74. Time: CPU 0.00 s, Wall: 0.00 s
  75. Time: CPU 0.04 s, Wall: 0.05 s
  76. Time: CPU 1.25 s, Wall: 1.54 s
  77. =========pari===== 6
  78. Time: CPU 0.00 s, Wall: 0.00 s
  79. Time: CPU 0.06 s, Wall: 0.06 s
  80. ===========gens_two====== 6
  81. Time: CPU 0.01 s, Wall: 0.01 s
  82. Time: CPU 0.00 s, Wall: 0.00 s
  83. Time: CPU 0.06 s, Wall: 0.06 s
  84. Time: CPU 0.95 s, Wall: 1.08 s
  85. =========pari===== 6
  86. Time: CPU 0.00 s, Wall: 0.00 s
  87. Time: CPU 0.06 s, Wall: 0.06 s
  88. ===========gens_two====== 6
  89. Time: CPU 0.00 s, Wall: 0.00 s
  90. Time: CPU 0.00 s, Wall: 0.00 s
  91. Time: CPU 0.05 s, Wall: 0.05 s
  92. Time: CPU 1.06 s, Wall: 1.07 s
  93. =========pari===== 6
  94. Time: CPU 0.00 s, Wall: 0.00 s
  95. Time: CPU 0.05 s, Wall: 0.05 s
  96. ===========gens_two====== 6
  97. Time: CPU 0.00 s, Wall: 0.00 s
  98. Time: CPU 0.00 s, Wall: 0.00 s
  99. Time: CPU 0.06 s, Wall: 0.07 s
  100. Time: CPU 0.94 s, Wall: 0.97 s
  101. =========pari===== 11
  102. Time: CPU 0.00 s, Wall: 0.00 s
  103. Time: CPU 0.10 s, Wall: 0.10 s
  104. ===========gens_two====== 11
  105. Time: CPU 0.00 s, Wall: 0.00 s
  106. Time: CPU 0.00 s, Wall: 0.00 s
  107. Time: CPU 0.08 s, Wall: 0.08 s
  108. Time: CPU 0.93 s, Wall: 0.93 s
  109. =========pari===== 11
  110. Time: CPU 0.00 s, Wall: 0.00 s
  111. Time: CPU 0.10 s, Wall: 0.12 s
  112. ===========gens_two====== 11
  113. Time: CPU 0.00 s, Wall: 0.00 s
  114. Time: CPU 0.00 s, Wall: 0.00 s
  115. Time: CPU 0.03 s, Wall: 0.03 s
  116. Time: CPU 0.94 s, Wall: 0.95 s
  117. =========pari===== 11
  118. Time: CPU 0.00 s, Wall: 0.00 s
  119. Time: CPU 0.09 s, Wall: 0.09 s
  120. ===========gens_two====== 11
  121. Time: CPU 0.00 s, Wall: 0.00 s
  122. Time: CPU 0.00 s, Wall: 0.00 s
  123. Time: CPU 0.03 s, Wall: 0.03 s
  124. Time: CPU 1.21 s, Wall: 1.23 s
  125. =========pari===== 11
  126. Time: CPU 0.00 s, Wall: 0.00 s
  127. Time: CPU 0.10 s, Wall: 0.10 s
  128. ===========gens_two====== 11
  129. Time: CPU 0.00 s, Wall: 0.00 s
  130. Time: CPU 0.00 s, Wall: 0.00 s
  131. Time: CPU 0.02 s, Wall: 0.02 s
  132. Time: CPU 1.16 s, Wall: 1.17 s
  133. =========pari===== 11
  134. Time: CPU 0.00 s, Wall: 0.00 s
  135. Time: CPU 0.10 s, Wall: 0.10 s
  136. ===========gens_two====== 11
  137. Time: CPU 0.00 s, Wall: 0.00 s
  138. Time: CPU 0.00 s, Wall: 0.00 s
  139. Time: CPU 0.04 s, Wall: 0.06 s
  140. Time: CPU 1.08 s, Wall: 1.11 s
  141. =========pari===== 16
  142. Time: CPU 0.00 s, Wall: 0.00 s
  143. Time: CPU 0.14 s, Wall: 0.14 s
  144. ===========gens_two====== 16
  145. Time: CPU 0.00 s, Wall: 0.00 s
  146. Time: CPU 0.00 s, Wall: 0.00 s
  147. Time: CPU 0.02 s, Wall: 0.02 s
  148. Time: CPU 1.27 s, Wall: 1.33 s
  149. =========pari===== 16
  150. Time: CPU 0.00 s, Wall: 0.00 s
  151. Time: CPU 0.13 s, Wall: 0.13 s
  152. ===========gens_two====== 16
  153. Time: CPU 0.00 s, Wall: 0.00 s
  154. Time: CPU 0.00 s, Wall: 0.00 s
  155. Time: CPU 0.02 s, Wall: 0.02 s
  156. Time: CPU 1.08 s, Wall: 1.09 s
  157. =========pari===== 16
  158. Time: CPU 0.00 s, Wall: 0.00 s
  159. Time: CPU 0.12 s, Wall: 0.13 s
  160. ===========gens_two====== 16
  161. Time: CPU 0.00 s, Wall: 0.00 s
  162. Time: CPU 0.00 s, Wall: 0.00 s
  163. Time: CPU 0.01 s, Wall: 0.02 s
  164. Time: CPU 0.53 s, Wall: 0.56 s
  165. =========pari===== 16
  166. Time: CPU 0.00 s, Wall: 0.00 s
  167. Time: CPU 0.12 s, Wall: 0.12 s
  168. ===========gens_two====== 16
  169. Time: CPU 0.00 s, Wall: 0.00 s
  170. Time: CPU 0.00 s, Wall: 0.00 s
  171. Time: CPU 0.02 s, Wall: 0.02 s
  172. Time: CPU 0.72 s, Wall: 0.73 s
  173. =========pari===== 16
  174. Time: CPU 0.00 s, Wall: 0.00 s
  175. Time: CPU 0.13 s, Wall: 0.14 s
  176. ===========gens_two====== 16
  177. Time: CPU 0.00 s, Wall: 0.00 s
  178. Time: CPU 0.00 s, Wall: 0.00 s
  179. Time: CPU 0.04 s, Wall: 0.04 s
  180. Time: CPU 0.95 s, Wall: 0.97 s
  181. =========pari===== 21
  182. Time: CPU 0.00 s, Wall: 0.00 s
  183. Time: CPU 0.16 s, Wall: 0.16 s
  184. ===========gens_two====== 21
  185. Time: CPU 0.00 s, Wall: 0.00 s
  186. Time: CPU 0.00 s, Wall: 0.00 s
  187. Time: CPU 0.04 s, Wall: 0.04 s
  188. Time: CPU 0.90 s, Wall: 0.91 s
  189. =========pari===== 21
  190. Time: CPU 0.00 s, Wall: 0.00 s
  191. Time: CPU 0.15 s, Wall: 0.16 s
  192. ===========gens_two====== 21
  193. Time: CPU 0.00 s, Wall: 0.00 s
  194. Time: CPU 0.00 s, Wall: 0.00 s
  195. Time: CPU 0.01 s, Wall: 0.02 s
  196. Time: CPU 0.64 s, Wall: 0.65 s
  197. =========pari===== 21
  198. Time: CPU 0.00 s, Wall: 0.00 s
  199. Time: CPU 0.20 s, Wall: 0.20 s
  200. ===========gens_two====== 21
  201. Time: CPU 0.00 s, Wall: 0.00 s
  202. Time: CPU 0.00 s, Wall: 0.00 s
  203. Time: CPU 0.03 s, Wall: 0.03 s
  204. Time: CPU 1.80 s, Wall: 1.81 s
  205. =========pari===== 21
  206. Time: CPU 0.00 s, Wall: 0.00 s
  207. Time: CPU 0.15 s, Wall: 0.15 s
  208. ===========gens_two====== 21
  209. Time: CPU 0.00 s, Wall: 0.00 s
  210. Time: CPU 0.00 s, Wall: 0.00 s
  211. Time: CPU 0.04 s, Wall: 0.04 s
  212. Time: CPU 0.62 s, Wall: 0.62 s
  213. =========pari===== 21
  214. Time: CPU 0.00 s, Wall: 0.00 s
  215. Time: CPU 0.17 s, Wall: 0.21 s
  216. ===========gens_two====== 21
  217. Time: CPU 0.00 s, Wall: 0.00 s
  218. Time: CPU 0.00 s, Wall: 0.00 s
  219. Time: CPU 0.03 s, Wall: 0.04 s
  220. Time: CPU 1.01 s, Wall: 1.04 s
  221. =========pari===== 26
  222. Time: CPU 0.00 s, Wall: 0.00 s
  223. Time: CPU 0.16 s, Wall: 0.17 s
  224. ===========gens_two====== 26
  225. Time: CPU 0.00 s, Wall: 0.00 s
  226. Time: CPU 0.00 s, Wall: 0.00 s
  227. Time: CPU 0.05 s, Wall: 0.05 s
  228. Time: CPU 0.48 s, Wall: 0.49 s
  229. =========pari===== 26
  230. Time: CPU 0.00 s, Wall: 0.00 s
  231. Time: CPU 0.20 s, Wall: 0.20 s
  232. ===========gens_two====== 26
  233. Time: CPU 0.00 s, Wall: 0.00 s
  234. Time: CPU 0.00 s, Wall: 0.00 s
  235. Time: CPU 0.02 s, Wall: 0.02 s
  236. Time: CPU 1.10 s, Wall: 1.12 s
  237. =========pari===== 26
  238. Time: CPU 0.00 s, Wall: 0.00 s
  239. Time: CPU 0.22 s, Wall: 0.22 s
  240. ===========gens_two====== 26
  241. Time: CPU 0.00 s, Wall: 0.00 s
  242. Time: CPU 0.00 s, Wall: 0.00 s
  243. Time: CPU 0.05 s, Wall: 0.05 s
  244. Time: CPU 1.29 s, Wall: 1.31 s
  245. =========pari===== 26
  246. Time: CPU 0.00 s, Wall: 0.00 s
  247. Time: CPU 0.18 s, Wall: 0.18 s
  248. ===========gens_two====== 26
  249. Time: CPU 0.00 s, Wall: 0.00 s
  250. Time: CPU 0.00 s, Wall: 0.00 s
  251. Time: CPU 0.03 s, Wall: 0.03 s
  252. Time: CPU 0.64 s, Wall: 0.65 s
  253. =========pari===== 26
  254. Time: CPU 0.00 s, Wall: 0.00 s
  255. Time: CPU 0.21 s, Wall: 0.21 s
  256. ===========gens_two====== 26
  257. Time: CPU 0.00 s, Wall: 0.00 s
  258. Time: CPU 0.00 s, Wall: 0.00 s
  259. Time: CPU 0.03 s, Wall: 0.03 s
  260. Time: CPU 1.06 s, Wall: 1.08 s
  261. =========pari===== 31
  262. Time: CPU 0.00 s, Wall: 0.00 s
  263. Time: CPU 0.23 s, Wall: 0.23 s
  264. ===========gens_two====== 31
  265. Time: CPU 0.00 s, Wall: 0.00 s
  266. Time: CPU 0.00 s, Wall: 0.00 s
  267. Time: CPU 0.06 s, Wall: 0.06 s
  268. Time: CPU 0.92 s, Wall: 0.94 s
  269. =========pari===== 31
  270. Time: CPU 0.00 s, Wall: 0.00 s
  271. Time: CPU 0.24 s, Wall: 0.25 s
  272. ===========gens_two====== 31
  273. Time: CPU 0.00 s, Wall: 0.00 s
  274. Time: CPU 0.00 s, Wall: 0.00 s
  275. Time: CPU 0.02 s, Wall: 0.02 s
  276. Time: CPU 1.02 s, Wall: 1.02 s
  277. =========pari===== 31
  278. Time: CPU 0.00 s, Wall: 0.00 s
  279. Time: CPU 0.23 s, Wall: 0.25 s
  280. ===========gens_two====== 31
  281. Time: CPU 0.00 s, Wall: 0.00 s
  282. Time: CPU 0.00 s, Wall: 0.00 s
  283. Time: CPU 0.02 s, Wall: 0.02 s
  284. Time: CPU 0.93 s, Wall: 1.06 s
  285. =========pari===== 31
  286. Time: CPU 0.00 s, Wall: 0.00 s
  287. Time: CPU 0.23 s, Wall: 0.24 s
  288. ===========gens_two====== 31
  289. Time: CPU 0.00 s, Wall: 0.00 s
  290. Time: CPU 0.00 s, Wall: 0.00 s
  291. Time: CPU 0.04 s, Wall: 0.04 s
  292. Time: CPU 1.00 s, Wall: 1.02 s
  293. =========pari===== 31
  294. Time: CPU 0.00 s, Wall: 0.00 s
  295. Time: CPU 0.22 s, Wall: 0.24 s
  296. ===========gens_two====== 31
  297. Time: CPU 0.00 s, Wall: 0.00 s
  298. Time: CPU 0.00 s, Wall: 0.00 s
  299. Time: CPU 0.03 s, Wall: 0.03 s
  300. Time: CPU 0.79 s, Wall: 0.80 s
  301. =========pari===== 36
  302. Time: CPU 0.00 s, Wall: 0.00 s
  303. Time: CPU 0.24 s, Wall: 0.27 s
  304. ===========gens_two====== 36
  305. Time: CPU 0.00 s, Wall: 0.00 s
  306. Time: CPU 0.00 s, Wall: 0.00 s
  307. Time: CPU 0.04 s, Wall: 0.04 s
  308. Time: CPU 0.73 s, Wall: 0.76 s
  309. =========pari===== 36
  310. Time: CPU 0.00 s, Wall: 0.00 s
  311. Time: CPU 0.31 s, Wall: 0.32 s
  312. ===========gens_two====== 36
  313. Time: CPU 0.00 s, Wall: 0.00 s
  314. Time: CPU 0.00 s, Wall: 0.00 s
  315. Time: CPU 0.04 s, Wall: 0.05 s
  316. Time: CPU 1.33 s, Wall: 1.34 s
  317. =========pari===== 36
  318. Time: CPU 0.00 s, Wall: 0.00 s
  319. Time: CPU 0.30 s, Wall: 0.34 s
  320. ===========gens_two====== 36
  321. Time: CPU 0.00 s, Wall: 0.00 s
  322. Time: CPU 0.00 s, Wall: 0.00 s
  323. Time: CPU 0.02 s, Wall: 0.02 s
  324. Time: CPU 1.22 s, Wall: 1.23 s
  325. =========pari===== 36
  326. Time: CPU 0.00 s, Wall: 0.00 s
  327. Time: CPU 0.24 s, Wall: 0.24 s
  328. ===========gens_two====== 36
  329. Time: CPU 0.00 s, Wall: 0.00 s
  330. Time: CPU 0.00 s, Wall: 0.00 s
  331. Time: CPU 0.02 s, Wall: 0.02 s
  332. Time: CPU 0.57 s, Wall: 0.59 s
  333. =========pari===== 36
  334. Time: CPU 0.00 s, Wall: 0.00 s
  335. Time: CPU 0.31 s, Wall: 0.31 s
  336. ===========gens_two====== 36
  337. Time: CPU 0.00 s, Wall: 0.00 s
  338. Time: CPU 0.00 s, Wall: 0.00 s
  339. Time: CPU 0.05 s, Wall: 0.05 s
  340. Time: CPU 1.48 s, Wall: 1.56 s
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