src/Tests/Face.hs

   1 module Tests.Face
   2 where
   3
   4 -- -- | Given in Sorokina and Zeilfelder, p. 78.
   5 -- prop_cijk1_identity :: Cube -> Bool
   6 -- prop_cijk1_identity cube =
   7 --      and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
   8 --                             (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
   9 --                             (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
  10 --                             (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
  11 --                                                                     j <- [0..2],
  12 --                                                                     k <- [0..2],
  13 --                                                                     i + j + k == 2]
  14 --       where
  15 --         t0 = tetrahedron0 (face0 cube)
  16 --         t1 = tetrahedron1 (face0 cube)
  17 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  18 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  19
  20 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  21 -- prop_c0120_identity1 :: Cube -> Bool
  22 -- prop_c0120_identity1 cube =
  23 --     c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
  24 --       where
  25 --         t0 = tetrahedron0 (face0 cube)
  26 --         t1 = tetrahedron1 (face0 cube)
  27 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  28 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  29
  30
  31 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  32 -- prop_c0210_identity1 :: Cube -> Bool
  33 -- prop_c0210_identity1 cube =
  34 --     c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
  35 --       where
  36 --         t0 = tetrahedron0 (face0 cube)
  37 --         t1 = tetrahedron1 (face0 cube)
  38 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  39 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  40
  41
  42 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  43 -- prop_c0300_identity1 :: Cube -> Bool
  44 -- prop_c0300_identity1 cube =
  45 --     c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
  46 --       where
  47 --         t0 = tetrahedron0 (face0 cube)
  48 --         t1 = tetrahedron1 (face0 cube)
  49 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  50 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  51
  52 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  53 -- prop_c1110_identity :: Cube -> Bool
  54 -- prop_c1110_identity cube =
  55 --     c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
  56 --       where
  57 --         t0 = tetrahedron0 (face0 cube)
  58 --         t1 = tetrahedron1 (face0 cube)
  59 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  60 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  61
  62
  63 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  64 -- prop_c1200_identity1 :: Cube -> Bool
  65 -- prop_c1200_identity1 cube =
  66 --     c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
  67 --       where
  68 --         t0 = tetrahedron0 (face0 cube)
  69 --         t1 = tetrahedron1 (face0 cube)
  70 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  71 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  72
  73
  74 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  75 -- prop_c2100_identity1 :: Cube -> Bool
  76 -- prop_c2100_identity1 cube =
  77 --     c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
  78 --       where
  79 --         t0 = tetrahedron0 (face0 cube)
  80 --         t1 = tetrahedron1 (face0 cube)
  81 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  82 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
  83
  84
  85 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  86 -- prop_c0102_identity1 :: Cube -> Bool
  87 -- prop_c0102_identity1 cube =
  88 --     c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
  89 --       where
  90 --         t0 = tetrahedron0 (face0 cube)
  91 --         t3 = tetrahedron3 (face0 cube)
  92 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
  93 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
  94
  95
  96 -- -- | Given in Sorokina and Zeilfelder, p. 79.
  97 -- prop_c0201_identity1 :: Cube -> Bool
  98 -- prop_c0201_identity1 cube =
  99 --     c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
 100 --       where
 101 --         t0 = tetrahedron0 (face0 cube)
 102 --         t3 = tetrahedron3 (face0 cube)
 103 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 104 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 105
 106
 107 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 108 -- prop_c0300_identity2 :: Cube -> Bool
 109 -- prop_c0300_identity2 cube =
 110 --     c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
 111 --       where
 112 --         t0 = tetrahedron0 (face0 cube)
 113 --         t3 = tetrahedron3 (face0 cube)
 114 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 115 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 116
 117 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 118 -- prop_c1101_identity :: Cube -> Bool
 119 -- prop_c1101_identity cube =
 120 --     c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
 121 --       where
 122 --         t0 = tetrahedron0 (face0 cube)
 123 --         t3 = tetrahedron3 (face0 cube)
 124 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 125 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 126
 127
 128 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 129 -- prop_c1200_identity2 :: Cube -> Bool
 130 -- prop_c1200_identity2 cube =
 131 --     c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
 132 --       where
 133 --         t0 = tetrahedron0 (face0 cube)
 134 --         t3 = tetrahedron3 (face0 cube)
 135 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 136 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 137
 138
 139 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 140 -- prop_c2100_identity2 :: Cube -> Bool
 141 -- prop_c2100_identity2 cube =
 142 --     c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
 143 --       where
 144 --         t0 = tetrahedron0 (face0 cube)
 145 --         t3 = tetrahedron3 (face0 cube)
 146 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 147 --         t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
 148
 149
 150 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 151 -- prop_c3000_identity :: Cube -> Bool
 152 -- prop_c3000_identity cube =
 153 --     c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
 154 --       where
 155 --         t0 = tetrahedron0 (face0 cube)
 156 --         t2 = tetrahedron2 (face5 cube)
 157 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 158 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 159
 160
 161 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 162 -- prop_c2010_identity :: Cube -> Bool
 163 -- prop_c2010_identity cube =
 164 --     c t0' 2 0 1 0 ~= c t0' 1 1 1 0 + c t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
 165 --       where
 166 --         t0 = tetrahedron0 (face0 cube)
 167 --         t2 = tetrahedron2 (face5 cube)
 168 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 169 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 170
 171
 172 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 173 -- prop_c2001_identity :: Cube -> Bool
 174 -- prop_c2001_identity cube =
 175 --     c t0' 2 0 0 1 ~= c t0' 1 1 0 1 + c t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
 176 --       where
 177 --         t0 = tetrahedron0 (face0 cube)
 178 --         t2 = tetrahedron2 (face5 cube)
 179 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 180 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 181
 182 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 183 -- prop_c1020_identity :: Cube -> Bool
 184 -- prop_c1020_identity cube =
 185 --     c t0' 1 0 2 0 ~= c t0' 0 1 2 0 + c t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
 186 --       where
 187 --         t0 = tetrahedron0 (face0 cube)
 188 --         t2 = tetrahedron2 (face5 cube)
 189 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 190 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 191
 192
 193 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 194 -- prop_c1002_identity :: Cube -> Bool
 195 -- prop_c1002_identity cube =
 196 --     c t0' 1 0 0 2 ~= c t0' 0 1 0 2 + c t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
 197 --       where
 198 --         t0 = tetrahedron0 (face0 cube)
 199 --         t2 = tetrahedron2 (face5 cube)
 200 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 201 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 202
 203
 204 -- -- | Given in Sorokina and Zeilfelder, p. 79.
 205 -- prop_c1011_identity :: Cube -> Bool
 206 -- prop_c1011_identity cube =
 207 --     c t0' 1 0 1 1 ~= c t0' 0 1 1 1 + c t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
 208 --       where
 209 --         t0 = tetrahedron0 (face0 cube)
 210 --         t2 = tetrahedron2 (face5 cube)
 211 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 212 --         t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
 213
 214
 215 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 216 -- prop_c0120_identity2 :: Cube -> Bool
 217 -- prop_c0120_identity2 cube =
 218 --         c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
 219 --       where
 220 --         t0 = tetrahedron0 (face0 cube)
 221 --         t1 = tetrahedron0 (face2 (top cube))
 222 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 223 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 224
 225
 226 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 227 -- prop_c0102_identity2 :: Cube -> Bool
 228 -- prop_c0102_identity2 cube =
 229 --     c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
 230 --       where
 231 --         t0 = tetrahedron0 (face0 cube)
 232 --         t1 = tetrahedron0 (face2 (top cube))
 233 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 234 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 235
 236
 237 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 238 -- prop_c0111_identity :: Cube -> Bool
 239 -- prop_c0111_identity cube =
 240 --     c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
 241 --       where
 242 --         t0 = tetrahedron0 (face0 cube)
 243 --         t1 = tetrahedron0 (face2 (top cube))
 244 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 245 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 246
 247
 248 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 249 -- prop_c0210_identity2 :: Cube -> Bool
 250 -- prop_c0210_identity2 cube =
 251 --     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
 252 --       where
 253 --         t0 = tetrahedron0 (face0 cube)
 254 --         t1 = tetrahedron0 (face2 (top cube))
 255 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 256 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 257
 258
 259 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 260 -- prop_c0201_identity2 :: Cube -> Bool
 261 -- prop_c0201_identity2 cube =
 262 --     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
 263 --       where
 264 --         t0 = tetrahedron0 (face0 cube)
 265 --         t1 = tetrahedron0 (face2 (top cube))
 266 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 267 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
 268
 269
 270 -- -- | Given in Sorokina and Zeilfelder, p. 80.
 271 -- prop_c0300_identity3 :: Cube -> Bool
 272 -- prop_c0300_identity3 cube =
 273 --     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
 274 --       where
 275 --         t0 = tetrahedron0 (face0 cube)
 276 --         t1 = tetrahedron0 (face2 (top cube))
 277 --         t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
 278 --         t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)