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  1.  
  2. #!/usr/bin/python2
  5. def expand(l):
  7. return expand_help(l, [], 1)
  10. def expand_help(l, r, s):
  12. """
  13. Basically what we want to do is walk through a list like
  14. l = [(0, 2), (0, 1), (1, 2)] and turn it into something like
  15. r = [(-1, [(0, 2)]), (-1, [(0, 1), (1, 2)])], so there are a
  16. few different cases.
  18. if l[0] is a list then we should expand that, if not then it must be
  19. (1, [(0, 2)]) by definition of phi_b_ext.
  21. if l[1] is a list, expand that, then if l[2] is a list as well expand
  22. it and foil, otherwise multiply each element of l[1] by l[2],
  24. similarly, if l[2] is a list, multiply each element of l[2] by l[1],
  25. otherwise just multiply l[1] and l[2]
  26. """
  28. if type(l[0]) == list:
  29. r.extend(expand_help(l[0], [], -1*s))
  30. else:
  31. r.append((-1*s, [l[0]]))
  33. t = []
  34. if type(l[1]) == list:
  35. a = expand_help(l[1], [], -1*s)
  36. if type(l[2]) == list:
  37. b = expand_help(l[2], [], s)
  38. for i in a:
  39. s_a, els_a = i
  40. for j in b:
  41. n_a = list(els_a)
  42. s_b, els_b = j
  43. n_a.extend(els_b)
  44. t.append((s_a*s_b, n_a))
  45. else:
  46. for i in a:
  47. x, y = i
  48. y.append(l[2])
  49. t.append((x, y))
  50. else:
  51. if type(l[2]) == list:
  52. a = expand_help(l[2], [], s)
  53. for i in a:
  54. x, y = i
  55. if type(y) == list:
  56. new_l1 = [l[1]]
  57. new_l1.extend(y)
  58. t.append((-1*s*x, new_l1))
  59. else:
  60. t.append((-1*s*x, [l[1], y]))
  61. else:
  62. t.append((-1*s, [l[1]]))
  63. t[-1][1].append(l[2])
  65. r.extend(t)
  66. return r
  68. def test_expand():
  70. a = [(0, 2), (0, 1), (1, 2)]
  71. r = [(-1, [(0, 2)]), (-1, [(0, 1), (1, 2)])]
  72. t = expand(a)
  74. print "test 1:"
  75. print "-as2 - as1a12"
  76. print "a = " + str(a)
  77. print "r = " + str(r)
  78. print "t = " + str(t)
  80. try:
  81. assert t == r
  82. print "PASS"
  83. except AssertionError:
  84. print "FAILED"
  85. exit()
  87. print
  89. a = [[(0, 2), (0, 1), (1, 2)], (2, 1), (1, 0)]
  90. r = [(1, [(0, 2)]), (1, [(0, 1), (1, 2)]), (-1, [(2, 1), (1, 0)])]
  91. t = expand(a)
  93. print "test 2:"
  94. print "-(-as2 - as1*a12) - a21*a1s"
  95. print "a = " + str(a)
  96. print "r = " + str(r)
  97. print "t = " + str(t)
  99. try:
  100. assert t == r
  101. print "PASS"
  102. except AssertionError:
  103. print "FAILED"
  104. exit()
  106. print
  108. a = [(1, 0), (2, 1), [(0, 1), (1, 2), (2, 0)]]
  109. r = [(-1, [(1, 0)]), (1, [(2, 1), (0, 1)]), (1, [(2, 1), (1, 2), (2, 0)])]
  110. t = expand(a)
  112. print "test 3:"
  113. print "-a1s - a21*(-as1 - a12*a2s)"
  114. print "a = " + str(a)
  115. print "r = " + str(r)
  116. print "t = " + str(t)
  118. try:
  119. assert t == r
  120. print "PASS"
  121. except AssertionError:
  122. print "FAILED"
  123. exit()
  125. print [57/418]
  127. a = [[(2, 0), (2, 1), (1, 0)], (2, 1), [(1, 0), (1, 2), [(2, 0), (2, 1), (1, 0)]]]
  128. r = [(1, [(2, 0)]), (1, [(2, 1), (1, 0)]), (1, [(2, 1), (1, 0)]), (-1, [(2, 1), (1
  129. , 2), (2, 0)]), (-1, [(2, 1), (1, 2), (2, 1), (1, 0)])]
  130. t = expand(a)
  132. print "test 4:"
  133. print "-(-a2s - a21*a1s) - a21*(-a1s - a12*(-a2s - a21*a1s))"
  134. print "a = " + str(a)
  135. print "r = " + str(r)
  136. print "t = " + str(t)
  138. try:
  139. assert t == r
  140. print "PASS"
  141. except AssertionError:
  142. print "FAILED"
  143. exit()
  145. print
  147. a = [(0, 1), [(0, 2), (0, 1), (1, 2)], (2, 1)]
  148. r = [(-1, [(0, 1)]), (1, [(0, 2), (2, 1)]), (1, [(0, 1), (1, 2), (2, 1)])]
  149. t = expand(a)
  151. print "test 5:"
  152. print "-as1 - (-as2 - as1*a12)*a21"
  153. print "a = " + str(a)
  154. print "r = " + str(r)
  155. print "t = " + str(t)
  157. try:
  158. assert t == r
  159. print "PASS"
  160. except AssertionError:
  161. print "FAILED"
  162. exit()
  164. print
  166. a = [(1, 0), [(1, 2), (2, 0), (1, 0)], [(2, 1), (1, 0), (2, 0)]]
  167. r = [(-1, [(1, 0)]), (-1, [(1, 2), (2, 1)]),
  168. (-1, [(1, 2), (1, 0), (2, 0)]), (-1, [(2, 0), (1, 0), (2, 1)]),
  169. (-1, [(2, 0), (1, 0), (1, 0), (2, 0)])]
  170. t = expand(a)
  172. print "test 6:"
  173. print "-as1 - (-a12 + a2s*a1s)(-a21 - a1s*a2s)"
  174. print "a = " + str(a)
  175. print "r = " + str(r)
  176. print "t = " + str(t)
  178. try:
  179. assert t == r
  180. print "PASS"
  181. except AssertionError:
  182. print "FAILED"
  183. exit()
  185. print
  187. a = [(1, 0), [(1, 2), [(0, 2), (0, 1), (1, 2)], (1, 0)],
  188. [(2, 1), (1, 0), (2, 0)]]
  189. r = [(-1, [(1, 0)]), (-1, [(1, 2), (2, 1)]),
  190. (-1, [(1, 2), (1, 0), (2, 0)]),
  191. (1, [(0, 2), (1, 0), (2, 1)]), (1, [(0, 2), (1, 0), (1, 0), (2, 0)]),
  192. (1, [(0, 1), (1, 2), (1, 0), (2, 1)]),
  193. (1, [(0, 1), (1, 2), (1, 0), (1, 0), (2, 0)])]
  194. t = expand(a)
  196. print "test 7:"
  197. print "-a1s - (-a12 - (-as2 - as1*a12)*a1s)*(-a12 - a1s*a2s)"
  198. print "a = " + str(a)
  199. print "r = " + str(r)
  200. print "t = " + str(t)
  202. try:
  203. assert t == r
  204. print "PASS"
  205. except AssertionError:
  206. print "FAILED"
  207. exit()
  209. print
  211. print "test 9:"
  213. a = [(1, 0), [(1, 2), (2, 0), (1, 0)], [(2, 1), [(0, 2), (0, 1), (1, 2)],
  214. (2, 0)]]
  215. r = [(-1, [(1, 0)]),
  216. (-1, [(1, 2), (2, 1)]),
  217. (1, [(1, 2), (0, 2), (2, 0)]),
  218. (1, [(1, 2), (0, 1), (1, 2), (2, 0)]),
  219. (-1, [(2, 0), (1, 0), (2, 1)]),
  220. (1, [(2, 0), (1, 0), (0, 2), (2, 0)]),
  221. (1, [(2, 0), (1, 0), (0, 1), (1, 2), (2, 0)])]
  222. t = expand(a)
  224. print "-a1s - (-a12 - a2s*a1s)(-a21 - (-as2 - as1*a12)*a2s)"
  225. print "a = " + str(a)
  226. print "r = " + str(r)
  227. print "t = " + str(t)
  229. try:
  230. assert t == r
  231. print "PASS"
  232. except AssertionError:
  233. print "FAILED"
  234. exit()
  236. print
  238. test_expand()
  240. a = [[[[(3, 0), (3, 1), (1, 0)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [(2, 0), (2, 1), (1, 0)]], [[(3, 1), [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], (2, 1)], [[[[(3, 4), (3, 1), (1, 4)], (3, 1), (1, 4)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [(4, 1), [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], (2, 1)]], [[(1, 0), [(1, 4), (1, 2), [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(4, 0), (4, 1), (1, 0)], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [(2, 0), (2, 1), (1, 0)]]], [[(1, 3), (1, 2), [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [(1, 4), (1, 2), [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[[[(4, 3), (4, 1), (1, 3)], (4, 1), (1, 3)], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]]], [[(3, 0), (3, 1), (1, 0)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [(2, 0), (2, 1), (1, 0)]]]], [[[[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[[[(3, 4), (3, 1), (1, 4)], (3, 1), (1, 4)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)]], [[(3, 1), [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], (2, 1)], [[[[(3, 4), (3, 1), (1, 4)], (3, 1), (1, 4)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [(4, 1), [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], (2, 1)]], [[[[(1, 2), [(1, 4), (1, 2), [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)]], [(1, 4), (1, 2), [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)]], [[(1, 3), (1, 2), [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [(1, 4), (1, 2), [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[[[(4, 3), (4, 1), (1, 3)], (4, 1), (1, 3)], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]]], [[[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[[[(3, 4), (3, 1), (1, 4)], (3, 1), (1, 4)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)]]], [[(1, 3), (1, 2), [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [(1, 4), (1, 2), [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[[[(4, 3), (4, 1), (1, 3)], (4, 1), (1, 3)], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]]], [[[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[[[(3, 4), (3, 1), (1, 4)], (3, 1), (1, 4)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)]]]], [[[(2, 0), (2, 1), (1, 0)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)], [[(4, 0), (4, 1), (1, 0)], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [(2, 0), (2, 1), (1, 0)]]], [[[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)], [[(2, 4), (2, 1), (1, 4)], (2, 1), (1, 4)], [[[[(4, 3), (4, 1), (1, 3)], (4, 1), (1, 3)], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]], [[(4, 2), (4, 1), (1, 2)], (4, 1), (1, 2)], [[(2, 3), (2, 1), (1, 3)], (2, 1), (1, 3)]]], [[(3, 0), (3, 1), (1, 0)], [[(3, 2), (3, 1), (1, 2)], (3, 1), (1, 2)], [(2, 0), (2, 1), (1, 0)]]]]
  242. print "calling expand on a"
  243. print expand(a)
  244.  
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