diff options
Diffstat (limited to 'src/algebra/quat.spad.pamphlet')
| -rw-r--r-- | src/algebra/quat.spad.pamphlet | 12 |
1 files changed, 4 insertions, 8 deletions
diff --git a/src/algebra/quat.spad.pamphlet b/src/algebra/quat.spad.pamphlet index 72f99f76..709d9331 100644 --- a/src/algebra/quat.spad.pamphlet +++ b/src/algebra/quat.spad.pamphlet @@ -107,8 +107,7 @@ QuaternionCategory(R: CommutativeRing): Category == coerce(n:Integer) == quatern(n :: R,0$R,0$R,0$R) one? x == --- one? real x and zero? imagI x and - (real x) = 1 and zero? imagI x and + one? real x and zero? imagI x and zero? imagJ x and zero? imagK x zero? x == zero? real x and zero? imagI x and @@ -135,8 +134,7 @@ QuaternionCategory(R: CommutativeRing): Category == y := quatern(0$R,0$R,imagJ(x),imagK(x)) z := part := 'i::OutputForm --- one? imagI(x) => part - (imagI(x) = 1) => part + one? imagI(x) => part (imagI(x) :: OutputForm) * part zero? y => z z + (y :: OutputForm) @@ -145,15 +143,13 @@ QuaternionCategory(R: CommutativeRing): Category == y := quatern(0$R,0$R,0$R,imagK(x)) z := part := 'j::OutputForm --- one? imagJ(x) => part - (imagJ(x) = 1) => part + one? imagJ(x) => part (imagJ(x) :: OutputForm) * part zero? y => z z + (y :: OutputForm) -- we know that the real part and i and j parts are 0 part := 'k::OutputForm --- one? imagK(x) => part - (imagK(x) = 1) => part + one? imagK(x) => part (imagK(x) :: OutputForm) * part if R has Field then |