where
import Prelude hiding (LT)
-import Test.QuickCheck
import Cardinal
import Comparisons
import Tetrahedron (b0, b1, b2, b3, c, fv,
v0, v1, v2, v3, volume)
-instance Arbitrary Cube where
- arbitrary = do
- (Positive h') <- arbitrary :: Gen (Positive Double)
- i' <- choose (coordmin, coordmax)
- j' <- choose (coordmin, coordmax)
- k' <- choose (coordmin, coordmax)
- fv' <- arbitrary :: Gen FunctionValues
- return (Cube h' i' j' k' fv')
- where
- coordmin = -268435456 -- -(2^29 / 2)
- coordmax = 268435456 -- +(2^29 / 2)
-- Quickcheck tests.
--- | Since the grid size is necessarily positive, all tetrahedrons
+-- | Since the grid size is necessarily positive, all tetrahedra
-- (which comprise cubes of positive volume) must have positive volume
-- as well.
prop_all_volumes_positive :: Cube -> Bool
prop_all_volumes_positive cube =
null nonpositive_volumes
where
- ts = tetrahedrons cube
+ ts = tetrahedra cube
volumes = map volume ts
nonpositive_volumes = filter (<= 0) volumes
-- | In fact, since all of the tetrahedra are identical, we should
-- already know their volumes. There's 24 tetrahedra to a cube, so
-- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron0_volumes_exact :: Cube -> Bool
-prop_tetrahedron0_volumes_exact cube =
- volume (tetrahedron0 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron1_volumes_exact :: Cube -> Bool
-prop_tetrahedron1_volumes_exact cube =
- volume (tetrahedron1 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron2_volumes_exact :: Cube -> Bool
-prop_tetrahedron2_volumes_exact cube =
- volume (tetrahedron2 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron3_volumes_exact :: Cube -> Bool
-prop_tetrahedron3_volumes_exact cube =
- volume (tetrahedron3 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron4_volumes_exact :: Cube -> Bool
-prop_tetrahedron4_volumes_exact cube =
- volume (tetrahedron4 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron5_volumes_exact :: Cube -> Bool
-prop_tetrahedron5_volumes_exact cube =
- volume (tetrahedron5 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron6_volumes_exact :: Cube -> Bool
-prop_tetrahedron6_volumes_exact cube =
- volume (tetrahedron6 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron7_volumes_exact :: Cube -> Bool
-prop_tetrahedron7_volumes_exact cube =
- volume (tetrahedron7 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron8_volumes_exact :: Cube -> Bool
-prop_tetrahedron8_volumes_exact cube =
- volume (tetrahedron8 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron9_volumes_exact :: Cube -> Bool
-prop_tetrahedron9_volumes_exact cube =
- volume (tetrahedron9 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron10_volumes_exact :: Cube -> Bool
-prop_tetrahedron10_volumes_exact cube =
- volume (tetrahedron10 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron11_volumes_exact :: Cube -> Bool
-prop_tetrahedron11_volumes_exact cube =
- volume (tetrahedron11 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron12_volumes_exact :: Cube -> Bool
-prop_tetrahedron12_volumes_exact cube =
- volume (tetrahedron12 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron13_volumes_exact :: Cube -> Bool
-prop_tetrahedron13_volumes_exact cube =
- volume (tetrahedron13 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron14_volumes_exact :: Cube -> Bool
-prop_tetrahedron14_volumes_exact cube =
- volume (tetrahedron14 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron15_volumes_exact :: Cube -> Bool
-prop_tetrahedron15_volumes_exact cube =
- volume (tetrahedron15 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron16_volumes_exact :: Cube -> Bool
-prop_tetrahedron16_volumes_exact cube =
- volume (tetrahedron16 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron17_volumes_exact :: Cube -> Bool
-prop_tetrahedron17_volumes_exact cube =
- volume (tetrahedron17 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron18_volumes_exact :: Cube -> Bool
-prop_tetrahedron18_volumes_exact cube =
- volume (tetrahedron18 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron19_volumes_exact :: Cube -> Bool
-prop_tetrahedron19_volumes_exact cube =
- volume (tetrahedron19 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron20_volumes_exact :: Cube -> Bool
-prop_tetrahedron20_volumes_exact cube =
- volume (tetrahedron20 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron21_volumes_exact :: Cube -> Bool
-prop_tetrahedron21_volumes_exact cube =
- volume (tetrahedron21 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron22_volumes_exact :: Cube -> Bool
-prop_tetrahedron22_volumes_exact cube =
- volume (tetrahedron22 cube) ~~= (1/24)*(delta^(3::Int))
- where
- delta = h cube
-
--- | In fact, since all of the tetrahedra are identical, we should
--- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
-prop_tetrahedron23_volumes_exact :: Cube -> Bool
-prop_tetrahedron23_volumes_exact cube =
- volume (tetrahedron23 cube) ~~= (1/24)*(delta^(3::Int))
+prop_all_volumes_exact :: Cube -> Bool
+prop_all_volumes_exact cube =
+ and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
where
delta = h cube
prop_v0_all_equal :: Cube -> Bool
prop_v0_all_equal cube = (v0 t0) == (v0 t1)
where
- t0 = head (tetrahedrons cube) -- Doesn't matter which two we choose.
- t1 = head $ tail (tetrahedrons cube)
+ t0 = head (tetrahedra cube) -- Doesn't matter which two we choose.
+ t1 = head $ tail (tetrahedra cube)
-- | This pretty much repeats the prop_all_volumes_positive property,
volume (tetrahedron23 cube) > 0
--- | Given in Sorokina and Zeilfelder, p. 79, (2.6). It appears that
--- the assumptions in sections (2.6) and (2.7) have been
--- switched. From the description, one would expect 'tetrahedron0'
--- and 'tetrahedron3' to share face \<v0,v1,v2\>; however, we have
--- to use 'tetrahedron0' and 'tetahedron1' for all of the tests in
--- section (2.6). Also note that the third and fourth indices of
--- c-t1 have been switched. This is because we store the triangles
--- oriented such that their volume is positive. If T and T-tilde
--- share \<v0,v1,v2\> and v3,v3-tilde point in opposite directions,
--- one of them has to have negative volume!
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the
+-- third and fourth indices of c-t1 have been switched. This is
+-- because we store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
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 1 2) / 2
+ c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
where
t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t3 = tetrahedron3 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
prop_c0120_identity2 :: Cube -> Bool
prop_c0120_identity2 cube =
- c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t2 0 0 1 2) / 2
+ c t1 0 1 2 0 ~= (c t1 0 0 2 1 + c t0 0 0 1 2) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
+-- 'prop_c0120_identity1' with tetrahedrons 1 and 2.
+prop_c0120_identity3 :: Cube -> Bool
+prop_c0120_identity3 cube =
+ c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t1 0 0 1 2) / 2
where
t1 = tetrahedron1 cube
t2 = tetrahedron2 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- 'prop_c0120_identity1' with tetrahedrons 2 and 3.
-prop_c0120_identity3 :: Cube -> Bool
-prop_c0120_identity3 cube =
- c t2 0 1 2 0 ~= (c t2 0 0 2 1 + c t3 0 0 1 2) / 2
+prop_c0120_identity4 :: Cube -> Bool
+prop_c0120_identity4 cube =
+ c t3 0 1 2 0 ~= (c t3 0 0 2 1 + c t2 0 0 1 2) / 2
where
t2 = tetrahedron2 cube
t3 = tetrahedron3 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- 'prop_c0120_identity1' with tetrahedrons 4 and 5.
--- prop_c0120_identity4 :: Cube -> Bool
--- prop_c0120_identity4 cube =
--- sum [trace ("c_t4_0120: " ++ (show tmp1)) tmp1,
--- trace ("c_t5_0012: " ++ (show tmp2)) tmp2,
--- trace ("c_t5_0102: " ++ (show tmp3)) tmp3,
--- trace ("c_t5_1002: " ++ (show tmp4)) tmp4,
--- trace ("c_t5_0120: " ++ (show tmp5)) tmp5,
--- trace ("c_t5_1020: " ++ (show tmp6)) tmp6,
--- trace ("c_t5_1200: " ++ (show tmp7)) tmp7,
--- trace ("c_t5_0021: " ++ (show tmp8)) tmp8,
--- trace ("c_t5_0201: " ++ (show tmp9)) tmp9,
--- trace ("c_t5_2001: " ++ (show tmp10)) tmp10,
--- trace ("c_t5_0210: " ++ (show tmp11)) tmp11,
--- trace ("c_t5_2010: " ++ (show tmp12)) tmp12,
--- trace ("c_t5_2100: " ++ (show tmp13)) tmp13] == 10
--- -- c t4 0 1 2 0 ~= (c t4 0 0 2 1 + c t5 0 0 1 2) / 2
--- where
--- t4 = tetrahedron4 cube
--- t5 = tetrahedron5 cube
--- tmp1 = c t4 0 1 2 0
--- tmp2 = (c t4 0 0 2 1 + c t5 0 0 1 2) / 2
--- tmp3 = (c t4 0 0 2 1 + c t5 0 1 0 2) / 2
--- tmp4 = (c t4 0 0 2 1 + c t5 1 0 0 2) / 2
--- tmp5 = (c t4 0 0 2 1 + c t5 0 1 2 0) / 2
--- tmp6 = (c t4 0 0 2 1 + c t5 1 0 2 0) / 2
--- tmp7 = (c t4 0 0 2 1 + c t5 1 2 0 0) / 2
--- tmp8 = (c t4 0 0 2 1 + c t5 0 0 2 1) / 2
--- tmp9 = (c t4 0 0 2 1 + c t5 0 2 0 1) / 2
--- tmp10 = (c t4 0 0 2 1 + c t5 2 0 0 1) / 2
--- tmp11 = (c t4 0 0 2 1 + c t5 0 2 1 0) / 2
--- tmp12 = (c t4 0 0 2 1 + c t5 2 0 1 0) / 2
--- tmp13 = (c t4 0 0 2 1 + c t5 2 1 0 0) / 2
+prop_c0120_identity5 :: Cube -> Bool
+prop_c0120_identity5 cube =
+ c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t4 0 0 1 2) / 2
+ where
+ t4 = tetrahedron4 cube
+ t5 = tetrahedron5 cube
-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- -- 'prop_c0120_identity1' with tetrahedrons 5 and 6.
--- prop_c0120_identity5 :: Cube -> Bool
--- prop_c0120_identity5 cube =
--- c t5 0 1 2 0 ~= (c t5 0 0 2 1 + c t6 0 0 1 2) / 2
--- where
--- t5 = tetrahedron5 cube
--- t6 = tetrahedron6 cube
+prop_c0120_identity6 :: Cube -> Bool
+prop_c0120_identity6 cube =
+ c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2
+ where
+ t5 = tetrahedron5 cube
+ t6 = tetrahedron6 cube
-- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats
-- -- 'prop_c0120_identity1' with tetrahedrons 6 and 7.
--- prop_c0120_identity6 :: Cube -> Bool
--- prop_c0120_identity6 cube =
--- c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t7 0 0 1 2) / 2
--- where
--- t6 = tetrahedron6 cube
--- t7 = tetrahedron7 cube
+prop_c0120_identity7 :: Cube -> Bool
+prop_c0120_identity7 cube =
+ c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2
+ where
+ t6 = tetrahedron6 cube
+ t7 = tetrahedron7 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
-- 'prop_c0120_identity1'.
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
+ c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
where
t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t3 = tetrahedron3 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
-- 'prop_c0120_identity1'.
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 1 0) / 2
+ c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
where
t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t3 = tetrahedron3 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
-- 'prop_c0120_identity1'.
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
+ c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
where
t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t3 = tetrahedron3 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
-- 'prop_c0120_identity1'.
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 1 0) / 2
+ c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
where
t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t3 = tetrahedron3 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). See
-- 'prop_c0120_identity1'.
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 1 0) / 2
+ c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
where
t0 = tetrahedron0 cube
- t1 = tetrahedron1 cube
+ t3 = tetrahedron3 cube
--- | Given in Sorokina and Zeilfelder, p. 79, (2.7). It appears that
--- the assumptions in sections (2.6) and (2.7) have been
--- switched. From the description, one would expect 'tetrahedron0'
--- and 'tetrahedron1' to share face \<v0,v1,v3\>; however, we have
--- to use 'tetrahedron0' and 'tetahedron3' for all of the tests in
--- section (2.7). Also note that the third and fourth indices of
--- c-t3 have been switched. This is because we store the triangles
--- oriented such that their volume is positive. If T and T-tilde
--- share \<v0,v1,v2\> and v3,v3-tilde point in opposite directions,
--- one of them has to have negative volume!
+-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). Note that the
+-- third and fourth indices of c-t3 have been switched. This is
+-- because we store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share \<v0,v1,v2\> and v3,v3-tilde
+-- point in opposite directions, one of them has to have negative
+-- volume!
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 2 1) / 2
+ c t0 0 1 0 2 ~= (c t0 0 0 1 2 + c t1 0 0 2 1) / 2
where
t0 = tetrahedron0 cube
- t3 = tetrahedron3 cube
+ t1 = tetrahedron1 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
-- 'prop_c0102_identity1'.
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
+ c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
where
t0 = tetrahedron0 cube
- t3 = tetrahedron3 cube
+ t1 = tetrahedron1 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
-- 'prop_c0102_identity1'.
prop_c0300_identity2 :: Cube -> Bool
prop_c0300_identity2 cube =
- c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t3 0 2 0 1) / 2
+ c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
where
t0 = tetrahedron0 cube
- t3 = tetrahedron3 cube
+ t1 = tetrahedron1 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
-- 'prop_c0102_identity1'.
prop_c1101_identity :: Cube -> Bool
prop_c1101_identity cube =
- c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+ c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
where
t0 = tetrahedron0 cube
- t3 = tetrahedron3 cube
+ t1 = tetrahedron1 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
-- 'prop_c0102_identity1'.
prop_c1200_identity2 :: Cube -> Bool
prop_c1200_identity2 cube =
- c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t3 1 1 0 1) / 2
+ c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
where
t0 = tetrahedron0 cube
- t3 = tetrahedron3 cube
+ t1 = tetrahedron1 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.7). See
-- 'prop_c0102_identity1'.
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 0 1) / 2
+ c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
where
t0 = tetrahedron0 cube
- t3 = tetrahedron3 cube
+ t1 = tetrahedron1 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). The third and