+-- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-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 t1 0 0 2 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0201_identity1 :: Cube -> Bool
+prop_c0201_identity1 cube =
+ c t0 0 2 0 1 ~= (c t0 0 1 1 1 + c t1 0 1 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0300_identity2 :: Cube -> Bool
+prop_c0300_identity2 cube =
+ c t0 0 3 0 0 ~= (c t0 0 2 1 0 + c t1 0 2 0 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1101_identity :: Cube -> Bool
+prop_c1101_identity cube =
+ c t0 1 1 0 1 ~= (c t0 1 0 1 1 + c t1 1 0 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1200_identity2 :: Cube -> Bool
+prop_c1200_identity2 cube =
+ c t0 1 2 0 0 ~= (c t0 1 1 1 0 + c t1 1 1 0 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. 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,v3> and v2,v2-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c2100_identity2 :: Cube -> Bool
+prop_c2100_identity2 cube =
+ c t0 2 1 0 0 ~= (c t0 2 0 1 0 + c t1 2 0 0 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
+
+
+
-- | Given in Sorokina and Zeilfelder, p. 78.
-- prop_cijk1_identity :: Cube -> Bool
-- prop_cijk1_identity cube =
--- -- | 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.
putStr "prop_c2100_identity1... "
quickCheckWith qc_args TC.prop_c2100_identity1
- -- putStrLn "\np. 79, (2.7)\n"
+ putStrLn "\np. 79, (2.7)\n"
- -- putStr "prop_c0102_identity1... "
- -- quickCheckWith qc_args TF.prop_c0102_identity1
+ putStr "prop_c0102_identity1... "
+ quickCheckWith qc_args TC.prop_c0102_identity1
- -- putStr "prop_c0201_identity1... "
- -- quickCheckWith qc_args TF.prop_c0201_identity1
+ putStr "prop_c0201_identity1... "
+ quickCheckWith qc_args TC.prop_c0201_identity1
- -- putStr "prop_c0300_identity2... "
- -- quickCheckWith qc_args TF.prop_c0300_identity2
+ putStr "prop_c0300_identity2... "
+ quickCheckWith qc_args TC.prop_c0300_identity2
- -- putStr "prop_c1101_identity... "
- -- quickCheckWith qc_args TF.prop_c1101_identity
+ putStr "prop_c1101_identity... "
+ quickCheckWith qc_args TC.prop_c1101_identity
- -- putStr "prop_c1200_identity2... "
- -- quickCheckWith qc_args TF.prop_c1200_identity2
+ putStr "prop_c1200_identity2... "
+ quickCheckWith qc_args TC.prop_c1200_identity2
- -- putStr "prop_c2100_identity2... "
- -- quickCheckWith qc_args TF.prop_c2100_identity2
+ putStr "prop_c2100_identity2... "
+ quickCheckWith qc_args TC.prop_c2100_identity2
-- putStrLn "\np. 79, (2.8)\n"