eja: define subalgebra_generated_by() to contain the identity.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 430f233114b09f36361322e5f2d4b4e408fd2aeb..658957556cf382a62d0d252359ce735019996973 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -16,12 +16,9 @@ from sage.misc.cachefunc import cached_method
 from sage.misc.prandom import choice
 from sage.misc.table import table
 from sage.modules.free_module import FreeModule, VectorSpace
-from sage.rings.integer_ring import ZZ
-from sage.rings.number_field.number_field import QuadraticField
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import QQ
-from sage.rings.real_lazy import CLF, RLF
-
+from sage.rings.all import (ZZ, QQ, RR, RLF, CLF,
+                            PolynomialRing,
+                            QuadraticField)
 from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement
 from mjo.eja.eja_utils import _mat2vec
 
@@ -40,11 +37,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
                  rank,
                  prefix='e',
                  category=None,
-                 natural_basis=None):
+                 natural_basis=None,
+                 check=True):
         """
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import random_eja
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA, random_eja)
 
         EXAMPLES:
 
@@ -56,7 +54,23 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             sage: x*y == y*x
             True
 
+        TESTS:
+
+        The ``field`` we're given must be real::
+
+            sage: JordanSpinEJA(2,QQbar)
+            Traceback (most recent call last):
+            ...
+            ValueError: field is not real
+
         """
+        if check:
+            if not field.is_subring(RR):
+                # Note: this does return true for the real algebraic
+                # field, and any quadratic field where we've specified
+                # a real embedding.
+                raise ValueError('field is not real')
+
         self._rank = rank
         self._natural_basis = natural_basis
 
@@ -435,9 +449,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             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
@@ -611,14 +622,6 @@ 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 random_elements(self, count):
         """
         Return ``count`` random elements as a tuple.
@@ -838,7 +841,7 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra,
         return x.to_vector().inner_product(y.to_vector())
 
 
-def random_eja():
+def random_eja(field=QQ):
     """
     Return a "random" finite-dimensional Euclidean Jordan Algebra.
 
@@ -875,7 +878,7 @@ def random_eja():
 
     """
     classname = choice(KnownRankEJA.__subclasses__())
-    return classname.random_instance()
+    return classname.random_instance(field=field)