-- | 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
cube_properties =
testGroup "Cube Properties" [
tp "all volumes positive" prop_all_volumes_positive,
- tp "tetrahedron0 volumes exact" prop_tetrahedron0_volumes_exact,
- tp "tetrahedron1 volumes exact" prop_tetrahedron1_volumes_exact,
- tp "tetrahedron2 volumes exact" prop_tetrahedron2_volumes_exact,
- tp "tetrahedron3 volumes exact" prop_tetrahedron3_volumes_exact,
- tp "tetrahedron4 volumes exact" prop_tetrahedron4_volumes_exact,
- tp "tetrahedron5 volumes exact" prop_tetrahedron5_volumes_exact,
- tp "tetrahedron6 volumes exact" prop_tetrahedron6_volumes_exact,
- tp "tetrahedron7 volumes exact" prop_tetrahedron7_volumes_exact,
- tp "tetrahedron8 volumes exact" prop_tetrahedron8_volumes_exact,
- tp "tetrahedron9 volumes exact" prop_tetrahedron9_volumes_exact,
- tp "tetrahedron10 volumes exact" prop_tetrahedron10_volumes_exact,
- tp "tetrahedron11 volumes exact" prop_tetrahedron11_volumes_exact,
- tp "tetrahedron12 volumes exact" prop_tetrahedron12_volumes_exact,
- tp "tetrahedron13 volumes exact" prop_tetrahedron13_volumes_exact,
- tp "tetrahedron14 volumes exact" prop_tetrahedron14_volumes_exact,
- tp "tetrahedron15 volumes exact" prop_tetrahedron15_volumes_exact,
- tp "tetrahedron16 volumes exact" prop_tetrahedron16_volumes_exact,
- tp "tetrahedron17 volumes exact" prop_tetrahedron17_volumes_exact,
- tp "tetrahedron18 volumes exact" prop_tetrahedron18_volumes_exact,
- tp "tetrahedron19 volumes exact" prop_tetrahedron19_volumes_exact,
- tp "tetrahedron20 volumes exact" prop_tetrahedron20_volumes_exact,
- tp "tetrahedron21 volumes exact" prop_tetrahedron21_volumes_exact,
- tp "tetrahedron22 volumes exact" prop_tetrahedron22_volumes_exact,
- tp "tetrahedron23 volumes exact" prop_tetrahedron23_volumes_exact,
+ tp "all volumes exact" prop_all_volumes_exact,
tp "tetrahedron0 volumes positive" prop_tetrahedron0_volumes_positive,
tp "tetrahedron1 volumes positive" prop_tetrahedron1_volumes_positive,
tp "tetrahedron2 volumes positive" prop_tetrahedron2_volumes_positive,