X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=832e7a19d5857fcd429a11b8693565aa781ba617;hb=02c754829b2f2e8378561e6afd7cbfab2577f3f4;hp=3855f0ef41e0e95efcadb359d6c7b908960a13b2;hpb=13a49fd59d57cf34b026460ace004ddbd60d4b68;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 3855f0e..832e7a1 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -404,6 +404,29 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         return x.trace_inner_product(y)
 
 
+    def is_trivial(self):
+        """
+        Return whether or not this algebra is trivial.
+
+        A trivial algebra contains only the zero element.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import ComplexHermitianEJA
+
+        EXAMPLES::
+
+            sage: J = ComplexHermitianEJA(3)
+            sage: J.is_trivial()
+            False
+            sage: A = J.zero().subalgebra_generated_by()
+            sage: A.is_trivial()
+            True
+
+        """
+        return self.dimension() == 0
+
+
     def multiplication_table(self):
         """
         Return a visual representation of this algebra's multiplication
@@ -546,6 +569,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         return self.linear_combination(zip(self.gens(), coeffs))
 
 
+    def random_element(self):
+        # Temporary workaround for https://trac.sagemath.org/ticket/28327
+        if self.is_trivial():
+            return self.zero()
+        else:
+            s = super(FiniteDimensionalEuclideanJordanAlgebra, self)
+            return s.random_element()
+
+
     def rank(self):
         """
         Return the rank of this EJA.
@@ -659,14 +691,21 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: e2*e2
         e2
 
+    TESTS:
+
+    We can change the generator prefix::
+
+        sage: RealCartesianProductEJA(3, prefix='r').gens()
+        (r0, r1, r2)
+
     """
-    def __init__(self, n, field=QQ):
+    def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
         mult_table = [ [ V.gen(i)*(i == j) for j in range(n) ]
                        for i in range(n) ]
 
         fdeja = super(RealCartesianProductEJA, self)
-        return fdeja.__init__(field, mult_table, rank=n)
+        return fdeja.__init__(field, mult_table, rank=n, **kwargs)
 
     def inner_product(self, x, y):
         return _usual_ip(x,y)
@@ -1145,8 +1184,13 @@ class RealSymmetricEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: J(expected) == x*y
         True
 
+    We can change the generator prefix::
+
+        sage: RealSymmetricEJA(3, prefix='q').gens()
+        (q0, q1, q2, q3, q4, q5)
+
     """
-    def __init__(self, n, field=QQ):
+    def __init__(self, n, field=QQ, **kwargs):
         S = _real_symmetric_basis(n, field=field)
         Qs = _multiplication_table_from_matrix_basis(S)
 
@@ -1154,7 +1198,8 @@ class RealSymmetricEJA(FiniteDimensionalEuclideanJordanAlgebra):
         return fdeja.__init__(field,
                               Qs,
                               rank=n,
-                              natural_basis=S)
+                              natural_basis=S,
+                              **kwargs)
 
     def inner_product(self, x, y):
         return _matrix_ip(x,y)
@@ -1197,8 +1242,13 @@ class ComplexHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: J(expected) == x*y
         True
 
+    We can change the generator prefix::
+
+        sage: ComplexHermitianEJA(2, prefix='z').gens()
+        (z0, z1, z2, z3)
+
     """
-    def __init__(self, n, field=QQ):
+    def __init__(self, n, field=QQ, **kwargs):
         S = _complex_hermitian_basis(n)
         Qs = _multiplication_table_from_matrix_basis(S)
 
@@ -1206,7 +1256,8 @@ class ComplexHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
         return fdeja.__init__(field,
                               Qs,
                               rank=n,
-                              natural_basis=S)
+                              natural_basis=S,
+                              **kwargs)
 
 
     def inner_product(self, x, y):
@@ -1257,8 +1308,13 @@ class QuaternionHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: J(expected) == x*y
         True
 
+    We can change the generator prefix::
+
+        sage: QuaternionHermitianEJA(2, prefix='a').gens()
+        (a0, a1, a2, a3, a4, a5)
+
     """
-    def __init__(self, n, field=QQ):
+    def __init__(self, n, field=QQ, **kwargs):
         S = _quaternion_hermitian_basis(n)
         Qs = _multiplication_table_from_matrix_basis(S)
 
@@ -1266,7 +1322,8 @@ class QuaternionHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
         return fdeja.__init__(field,
                               Qs,
                               rank=n,
-                              natural_basis=S)
+                              natural_basis=S,
+                              **kwargs)
 
     def inner_product(self, x, y):
         # Since a+bi+cj+dk on the diagonal is represented as
@@ -1313,8 +1370,13 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: e2*e3
         0
 
+    We can change the generator prefix::
+
+        sage: JordanSpinEJA(2, prefix='B').gens()
+        (B0, B1)
+
     """
-    def __init__(self, n, field=QQ):
+    def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
         mult_table = [[V.zero() for j in range(n)] for i in range(n)]
         for i in range(n):
@@ -1335,7 +1397,7 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra):
         # one-dimensional ambient space (because the rank is bounded by
         # the ambient dimension).
         fdeja = super(JordanSpinEJA, self)
-        return fdeja.__init__(field, mult_table, rank=min(n,2))
+        return fdeja.__init__(field, mult_table, rank=min(n,2), **kwargs)
 
     def inner_product(self, x, y):
         return _usual_ip(x,y)