import Cardinal
import Comparisons
-import Cube
+import Cube hiding (i, j, k)
import FunctionValues
import Misc (all_equal)
import Tests.FunctionValues ()
-- 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! We also switch the third and fourth vertices of t6, but
--- as of now, why this works is a mystery.
+-- volume!
prop_c3000_identity :: Cube -> Bool
prop_c3000_identity cube =
c t0 3 0 0 0 ~= c t0 2 1 0 0 + c t6 2 1 0 0
- ((c t0 2 0 1 0 + c t0 2 0 0 1)/ 2)
where
t0 = tetrahedron0 cube
- t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
+ t6 = tetrahedron6 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
- ((c t0 1 0 2 0 + c t0 1 0 1 1)/ 2)
where
t0 = tetrahedron0 cube
- t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
+ t6 = tetrahedron6 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
- ((c t0 1 0 0 2 + c t0 1 0 1 1)/ 2)
where
t0 = tetrahedron0 cube
- t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
+ t6 = tetrahedron6 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
- ((c t0 0 0 3 0 + c t0 0 0 2 1)/ 2)
where
t0 = tetrahedron0 cube
- t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
+ t6 = tetrahedron6 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
- ((c t0 0 0 0 3 + c t0 0 0 1 2)/ 2)
where
t0 = tetrahedron0 cube
- t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
+ t6 = tetrahedron6 cube
-- | Given in Sorokina and Zeilfelder, p. 79, (2.8). See
((c t0 0 0 1 2 + c t0 0 0 2 1)/ 2)
where
t0 = tetrahedron0 cube
- t6 = (tetrahedron6 cube) { v2 = (v3 t6), v3 = (v2 t6) }
+ t6 = tetrahedron6 cube
-- | Given in Sorokina and Zeilfelder, p. 78.
--- prop_cijk1_identity :: Cube -> Bool
--- prop_cijk1_identity cube =
--- and [ c t0 i j k 1 ~=
--- (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
--- (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
--- (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
--- (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
--- j <- [0..2],
--- k <- [0..2],
--- i + j + k == 2]
--- where
--- t0 = tetrahedron0 cube
--- t1 = tetrahedron1 cube
-
+prop_cijk1_identity :: Cube -> Bool
+prop_cijk1_identity cube =
+ and [ c t0 i j k 1 ~=
+ (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
+ (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
+ (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
+ (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ i + j + k == 2]
+ where
+ t0 = tetrahedron0 cube
+ t1 = tetrahedron1 cube
-- | The function values at the interior should be the same for all tetrahedra.
i9, i10, i11, i12, i13, i14, i15, i16,
i17, i18, i19, i20, i21, i22, i23]
where
- i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) $ I
- i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) $ I
- i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) $ I
- i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) $ I
- i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) $ I
- i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) $ I
- i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) $ I
- i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) $ I
- i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) $ I
- i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) $ I
- i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) $ I
- i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) $ I
- i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) $ I
- i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) $ I
- i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) $ I
- i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) $ I
- i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) $ I
- i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) $ I
- i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) $ I
- i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) $ I
- i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) $ I
- i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) $ I
- i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) $ I
- i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) $ I
+ i0 = eval (Tetrahedron.fv (tetrahedron0 cube)) I
+ i1 = eval (Tetrahedron.fv (tetrahedron1 cube)) I
+ i2 = eval (Tetrahedron.fv (tetrahedron2 cube)) I
+ i3 = eval (Tetrahedron.fv (tetrahedron3 cube)) I
+ i4 = eval (Tetrahedron.fv (tetrahedron4 cube)) I
+ i5 = eval (Tetrahedron.fv (tetrahedron5 cube)) I
+ i6 = eval (Tetrahedron.fv (tetrahedron6 cube)) I
+ i7 = eval (Tetrahedron.fv (tetrahedron7 cube)) I
+ i8 = eval (Tetrahedron.fv (tetrahedron8 cube)) I
+ i9 = eval (Tetrahedron.fv (tetrahedron9 cube)) I
+ i10 = eval (Tetrahedron.fv (tetrahedron10 cube)) I
+ i11 = eval (Tetrahedron.fv (tetrahedron11 cube)) I
+ i12 = eval (Tetrahedron.fv (tetrahedron12 cube)) I
+ i13 = eval (Tetrahedron.fv (tetrahedron13 cube)) I
+ i14 = eval (Tetrahedron.fv (tetrahedron14 cube)) I
+ i15 = eval (Tetrahedron.fv (tetrahedron15 cube)) I
+ i16 = eval (Tetrahedron.fv (tetrahedron16 cube)) I
+ i17 = eval (Tetrahedron.fv (tetrahedron17 cube)) I
+ i18 = eval (Tetrahedron.fv (tetrahedron18 cube)) I
+ i19 = eval (Tetrahedron.fv (tetrahedron19 cube)) I
+ i20 = eval (Tetrahedron.fv (tetrahedron20 cube)) I
+ i21 = eval (Tetrahedron.fv (tetrahedron21 cube)) I
+ i22 = eval (Tetrahedron.fv (tetrahedron22 cube)) I
+ i23 = eval (Tetrahedron.fv (tetrahedron23 cube)) I
-- | We know what (c t6 2 1 0 0) should be from Sorokina and Zeilfelder, p. 87.