import Test.QuickCheck
-import Cube (Cube(grid))
-import Face (tetrahedrons)
+import Comparisons
+import Cube (Cube(grid), top)
+import Face (face0,
+ face2,
+ face5,
+ tetrahedron0,
+ tetrahedron1,
+ tetrahedron2,
+ tetrahedron3,
+ tetrahedrons)
import Grid (Grid(h))
-import Tetrahedron (volume)
+import Tetrahedron
-- QuickCheck Tests.
-prop_all_volumes_nonnegative :: Cube -> Property
-prop_all_volumes_nonnegative c =
- (delta > 0) ==> (null negative_volumes)
+
+-- | Since the grid size is necessarily positive, all tetrahedrons
+-- (which comprise cubes of positive volume) must have positive volume
+-- as well.
+prop_all_volumes_positive :: Cube -> Property
+prop_all_volumes_positive c =
+ (delta > 0) ==> (null nonpositive_volumes)
where
delta = h (grid c)
ts = tetrahedrons c
volumes = map volume ts
- negative_volumes = filter (< 0) volumes
+ nonpositive_volumes = filter (<= 0) volumes
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c0120_identity1 :: Cube -> Bool
+prop_c0120_identity1 cube =
+ c t0' 0 1 2 0 ~= (c t0' 0 0 2 1 + c t1' 0 0 2 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c0210_identity1 :: Cube -> Bool
+prop_c0210_identity1 cube =
+ c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c0300_identity1 :: Cube -> Bool
+prop_c0300_identity1 cube =
+ c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1110_identity :: Cube -> Bool
+prop_c1110_identity cube =
+ c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1200_identity1 :: Cube -> Bool
+prop_c1200_identity1 cube =
+ c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2100_identity1 :: Cube -> Bool
+prop_c2100_identity1 cube =
+ c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c0102_identity1 :: Cube -> Bool
+prop_c0102_identity1 cube =
+ c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t3 = tetrahedron3 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c0201_identity1 :: Cube -> Bool
+prop_c0201_identity1 cube =
+ c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t3 = tetrahedron3 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c0300_identity2 :: Cube -> Bool
+prop_c0300_identity2 cube =
+ c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t3 = tetrahedron3 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1101_identity :: Cube -> Bool
+prop_c1101_identity cube =
+ c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t3 = tetrahedron3 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1200_identity2 :: Cube -> Bool
+prop_c1200_identity2 cube =
+ c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t3 = tetrahedron3 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2100_identity2 :: Cube -> Bool
+prop_c2100_identity2 cube =
+ c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t3 = tetrahedron3 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c3000_identity :: Cube -> Bool
+prop_c3000_identity cube =
+ 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)
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t2 = tetrahedron2 (face5 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2010_identity :: Cube -> Bool
+prop_c2010_identity cube =
+ 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)
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t2 = tetrahedron2 (face5 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c2001_identity :: Cube -> Bool
+prop_c2001_identity cube =
+ 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)
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t2 = tetrahedron2 (face5 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1020_identity :: Cube -> Bool
+prop_c1020_identity cube =
+ 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)
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t2 = tetrahedron2 (face5 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1002_identity :: Cube -> Bool
+prop_c1002_identity cube =
+ 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)
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t2 = tetrahedron2 (face5 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79.
+prop_c1011_identity :: Cube -> Bool
+prop_c1011_identity cube =
+ 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)
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t2 = tetrahedron2 (face5 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80.
+prop_c0120_identity2 :: Cube -> Bool
+prop_c0120_identity2 cube =
+ c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron0 (face2 (top cube))
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80.
+prop_c0102_identity2 :: Cube -> Bool
+prop_c0102_identity2 cube =
+ c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron0 (face2 (top cube))
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80.
+prop_c0111_identity :: Cube -> Bool
+prop_c0111_identity cube =
+ c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron0 (face2 (top cube))
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80.
+prop_c0210_identity2 :: Cube -> Bool
+prop_c0210_identity2 cube =
+ c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron0 (face2 (top cube))
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80.
+prop_c0201_identity2 :: Cube -> Bool
+prop_c0201_identity2 cube =
+ c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron0 (face2 (top cube))
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80.
+prop_c0300_identity3 :: Cube -> Bool
+prop_c0300_identity3 cube =
+ c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron0 (face2 (top cube))
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
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