X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FCube.hs;h=46b2530ab82053fae93fcf68de6e839ed8cf6304;hb=b36cb982a689fa31b1d0c4e3e9994f36cc4b26b2;hp=b5e771b2684c50df9658f49ce7d76c9258dc5084;hpb=7bfd79b7cc06dfd0b08cf14794d7659a940b8f08;p=spline3.git diff --git a/src/Tests/Cube.hs b/src/Tests/Cube.hs index b5e771b..46b2530 100644 --- a/src/Tests/Cube.hs +++ b/src/Tests/Cube.hs @@ -2,7 +2,6 @@ module Tests.Cube where import Prelude hiding (LT) -import Test.QuickCheck import Cardinal import Comparisons @@ -13,246 +12,27 @@ import Tests.FunctionValues () 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 @@ -260,8 +40,8 @@ prop_tetrahedron23_volumes_exact 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, @@ -409,38 +189,42 @@ prop_tetrahedron23_volumes_positive cube = 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 \; 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 \ 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 \ 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 @@ -448,176 +232,146 @@ prop_c0120_identity3 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 \; 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 \ 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 \ 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