X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fhurwitz.py;h=ff84b51f8e3923ef7a8a93cb7d42ea1cfe6e3d32;hb=928b7d49fda98ff105c92293b5797bb7a2b9873a;hp=cad89ca177cbdcfbc065682d4a64af43aad6917a;hpb=f721f283cea741c54e4a2b26d63094dd6c396c6a;p=sage.d.git

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index cad89ca..ff84b51 100644
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -23,7 +23,6 @@ class Octonion(IndexedFreeModuleElement):
 
         Conjugating twice gets you the original element::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: x = O.random_element()
             sage: x.conjugate().conjugate() == x
@@ -58,7 +57,6 @@ class Octonion(IndexedFreeModuleElement):
 
         This method is idempotent::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: x = O.random_element()
             sage: x.real().real() == x.real()
@@ -91,7 +89,6 @@ class Octonion(IndexedFreeModuleElement):
 
         This method is idempotent::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: x = O.random_element()
             sage: x.imag().imag() == x.imag()
@@ -121,7 +118,6 @@ class Octonion(IndexedFreeModuleElement):
 
         The norm is nonnegative and belongs to the base field::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: n = O.random_element().norm()
             sage: n >= 0 and n in O.base_ring()
@@ -129,7 +125,6 @@ class Octonion(IndexedFreeModuleElement):
 
         The norm is homogeneous::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: x = O.random_element()
             sage: alpha = O.base_ring().random_element()
@@ -167,7 +162,6 @@ class Octonion(IndexedFreeModuleElement):
 
         TESTS::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: x = O.random_element()
             sage: x.is_zero() or ( x*x.inverse() == O.one() )
@@ -241,7 +235,6 @@ class Octonions(CombinatorialFreeModule):
 
         This gives the correct unit element::
 
-            sage: set_random_seed()
             sage: O = Octonions()
             sage: x = O.random_element()
             sage: x*O.one() == x and O.one()*x == x
@@ -312,19 +305,21 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
 
         SETUP::
 
-            sage: from mjo.hurwitz import HurwitzMatrixAlgebra
+            sage: from mjo.hurwitz import ComplexMatrixAlgebra
 
         EXAMPLES::
 
-            sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ)
+            sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
             sage: M = A([ [ I,   2*I],
             ....:         [ 3*I, 4*I] ])
             sage: M.conjugate_transpose()
             +------+------+
-            | -1*I | -3*I |
+            | -I   | -3*I |
             +------+------+
             | -2*I | -4*I |
             +------+------+
+            sage: M.conjugate_transpose().to_vector()
+            (0, -1, 0, -3, 0, -2, 0, -4)
 
         """
         entries = [ [ self[j,i].conjugate()
@@ -337,16 +332,25 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
 
         SETUP::
 
-            sage: from mjo.hurwitz import HurwitzMatrixAlgebra
+            sage: from mjo.hurwitz import (ComplexMatrixAlgebra,
+            ....:                          HurwitzMatrixAlgebra)
 
         EXAMPLES::
 
-            sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ)
+            sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
             sage: M = A([ [ 0,I],
             ....:         [-I,0] ])
             sage: M.is_hermitian()
             True
 
+        ::
+
+            sage: A = HurwitzMatrixAlgebra(2, AA, QQ)
+            sage: M = A([ [1, 1],
+            ....:         [1, 1] ])
+            sage: M.is_hermitian()
+            True
+
         """
         # A tiny bit faster than checking equality with the conjugate
         # transpose.
@@ -518,7 +522,6 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra):
 
     TESTS::
 
-        sage: set_random_seed()
         sage: A = OctonionMatrixAlgebra(ZZ.random_element(10))
         sage: x = A.random_element()
         sage: x*A.one() == x and A.one()*x == x
@@ -611,7 +614,6 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra):
 
     TESTS::
 
-        sage: set_random_seed()
         sage: A = QuaternionMatrixAlgebra(ZZ.random_element(10))
         sage: x = A.random_element()
         sage: x*A.one() == x and A.one()*x == x
@@ -649,9 +651,9 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra):
             (0, 0, 0, 1)
 
         """
-        from sage.modules.free_module import VectorSpace
+        from sage.modules.free_module import FreeModule
         d = len(self.entry_algebra_gens())
-        V = VectorSpace(self.entry_algebra().base_ring(), d)
+        V = FreeModule(self.entry_algebra().base_ring(), d)
         return V(entry.coefficient_tuple())
 
 class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
@@ -704,11 +706,11 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
         sage: (I,) = A.entry_algebra().gens()
         sage: A([ [1+I, 1],
         ....:     [-1, -I] ])
-        +-------+----+
-        | I + 1 | 1  |
-        +-------+----+
-        | -1    | -I |
-        +-------+----+
+        +---------+------+
+        | 1 + 1*I | 1    |
+        +---------+------+
+        | -1      | -1*I |
+        +---------+------+
 
     ::
 
@@ -721,7 +723,6 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
 
     TESTS::
 
-        sage: set_random_seed()
         sage: A = ComplexMatrixAlgebra(ZZ.random_element(10))
         sage: x = A.random_element()
         sage: x*A.one() == x and A.one()*x == x
@@ -750,7 +751,7 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
             (0, 1)
 
         """
-        from sage.modules.free_module import VectorSpace
+        from sage.modules.free_module import FreeModule
         d = len(self.entry_algebra_gens())
-        V = VectorSpace(self.entry_algebra().base_ring(), d)
+        V = FreeModule(self.entry_algebra().base_ring(), d)
         return V((entry.real(), entry.imag()))