eja: factor out MatrixEJA initialization.

[sage.d.git] / mjo / eja / eja_element.py

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 52933e2decdcf3d9dc1218a568bf29bcff6cf5f1..c98d9a2b64651562928a6489ef88e03fdd2b0dc9 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -167,8 +167,8 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: J = HadamardEJA(3)
             sage: p1 = J.one().characteristic_polynomial()
             sage: q1 = J.zero().characteristic_polynomial()
-            sage: e0,e1,e2 = J.gens()
-            sage: A = (e0 + 2*e1 + 3*e2).subalgebra_generated_by() # dim 3
+            sage: b0,b1,b2 = J.gens()
+            sage: A = (b0 + 2*b1 + 3*b2).subalgebra_generated_by() # dim 3
             sage: p2 = A.one().characteristic_polynomial()
             sage: q2 = A.zero().characteristic_polynomial()
             sage: p1 == p2
@@ -348,7 +348,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         EXAMPLES::
 
             sage: J = JordanSpinEJA(2)
-            sage: e0,e1 = J.gens()
             sage: x = sum( J.gens() )
             sage: x.det()
             0
@@ -356,7 +355,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         ::
 
             sage: J = JordanSpinEJA(3)
-            sage: e0,e1,e2 = J.gens()
             sage: x = sum( J.gens() )
             sage: x.det()
             -1
@@ -391,7 +389,7 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: (x*y).det() == x.det()*y.det()
             True
 
-        The determinant in matrix algebras is just the usual determinant::
+        The determinant in real matrix algebras is the usual determinant::
 
             sage: set_random_seed()
             sage: X = matrix.random(QQ,3)
@@ -406,21 +404,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: actual2 == expected
             True
 
-        ::
-
-            sage: set_random_seed()
-            sage: J1 = ComplexHermitianEJA(2)
-            sage: J2 = ComplexHermitianEJA(2,field=QQ,orthonormalize=False)
-            sage: X = matrix.random(GaussianIntegers(), 2)
-            sage: X = X + X.H
-            sage: expected = AA(X.det())
-            sage: actual1 = J1(J1.real_embed(X)).det()
-            sage: actual2 = J2(J2.real_embed(X)).det()
-            sage: expected == actual1
-            True
-            sage: expected == actual2
-            True
-
         """
         P = self.parent()
         r = P.rank()
@@ -793,7 +776,9 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: J = JordanSpinEJA(5)
             sage: J.one().is_regular()
             False
-            sage: e0, e1, e2, e3, e4 = J.gens() # e0 is the identity
+            sage: b0, b1, b2, b3, b4 = J.gens()
+            sage: b0 == J.one()
+            True
             sage: for x in J.gens():
             ....:     (J.one() + x).is_regular()
             False
@@ -843,8 +828,8 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: J = JordanSpinEJA(4)
             sage: J.one().degree()
             1
-            sage: e0,e1,e2,e3 = J.gens()
-            sage: (e0 - e1).degree()
+            sage: b0,b1,b2,b3 = J.gens()
+            sage: (b0 - b1).degree()
             2
 
         In the spin factor algebra (of rank two), all elements that
@@ -1096,29 +1081,27 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
             sage: J = ComplexHermitianEJA(3)
             sage: J.one()
-            e0 + e3 + e8
+            b0 + b3 + b8
             sage: J.one().to_matrix()
-            [1 0 0 0 0 0]
-            [0 1 0 0 0 0]
-            [0 0 1 0 0 0]
-            [0 0 0 1 0 0]
-            [0 0 0 0 1 0]
-            [0 0 0 0 0 1]
+            +---+---+---+
+            | 1 | 0 | 0 |
+            +---+---+---+
+            | 0 | 1 | 0 |
+            +---+---+---+
+            | 0 | 0 | 1 |
+            +---+---+---+
 
         ::
 
             sage: J = QuaternionHermitianEJA(2)
             sage: J.one()
-            e0 + e5
+            b0 + b5
             sage: J.one().to_matrix()
-            [1 0 0 0 0 0 0 0]
-            [0 1 0 0 0 0 0 0]
-            [0 0 1 0 0 0 0 0]
-            [0 0 0 1 0 0 0 0]
-            [0 0 0 0 1 0 0 0]
-            [0 0 0 0 0 1 0 0]
-            [0 0 0 0 0 0 1 0]
-            [0 0 0 0 0 0 0 1]
+            +---+---+
+            | 1 | 0 |
+            +---+---+
+            | 0 | 1 |
+            +---+---+
 
         This also works in Cartesian product algebras::
 
@@ -1355,11 +1338,11 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
             sage: J = RealSymmetricEJA(3)
             sage: J.one()
-            e0 + e2 + e5
+            b0 + b2 + b5
             sage: J.one().spectral_decomposition()
-            [(1, e0 + e2 + e5)]
+            [(1, b0 + b2 + b5)]
             sage: J.zero().spectral_decomposition()
-            [(0, e0 + e2 + e5)]
+            [(0, b0 + b2 + b5)]
 
         TESTS::
 
@@ -1384,13 +1367,13 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         The spectral decomposition should work in subalgebras, too::
 
             sage: J = RealSymmetricEJA(4)
-            sage: (e0, e1, e2, e3, e4, e5, e6, e7, e8, e9) = J.gens()
-            sage: A = 2*e5 - 2*e8
+            sage: (b0, b1, b2, b3, b4, b5, b6, b7, b8, b9) = J.gens()
+            sage: A = 2*b5 - 2*b8
             sage: (lambda1, c1) = A.spectral_decomposition()[1]
             sage: (J0, J5, J1) = J.peirce_decomposition(c1)
             sage: (f0, f1, f2) = J1.gens()
             sage: f0.spectral_decomposition()
-            [(0, f2), (1, f0)]
+            [(0, c2), (1, c0)]
 
         """
         A = self.subalgebra_generated_by(orthonormalize=True)