eja: eliminate the special element subalgebra class.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 3bc296446da3021ea8913996fa9932580e022934..83ec50e5a215417811fe09d72c61251081772160 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -750,23 +750,57 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: from mjo.eja.eja_algebra import (HadamardEJA,
             ....:                                  random_eja)
 
-        EXAMPLES::
+        EXAMPLES:
+
+        We can compute unit element in the Hadamard EJA::
+
+            sage: J = HadamardEJA(5)
+            sage: J.one()
+            e0 + e1 + e2 + e3 + e4
+
+        The unit element in the Hadamard EJA is inherited in the
+        subalgebras generated by its elements::
 
             sage: J = HadamardEJA(5)
             sage: J.one()
             e0 + e1 + e2 + e3 + e4
+            sage: x = sum(J.gens())
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
+            sage: A.one()
+            f0
+            sage: A.one().superalgebra_element()
+            e0 + e1 + e2 + e3 + e4
 
         TESTS:
 
-        The identity element acts like the identity::
+        The identity element acts like the identity, regardless of
+        whether or not we orthonormalize::
 
             sage: set_random_seed()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: J.one()*x == x and x*J.one() == x
             True
+            sage: A = x.subalgebra_generated_by()
+            sage: y = A.random_element()
+            sage: A.one()*y == y and y*A.one() == y
+            True
+
+        ::
+
+            sage: set_random_seed()
+            sage: J = random_eja(field=QQ, orthonormalize=False)
+            sage: x = J.random_element()
+            sage: J.one()*x == x and x*J.one() == x
+            True
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
+            sage: y = A.random_element()
+            sage: A.one()*y == y and y*A.one() == y
+            True
 
-        The matrix of the unit element's operator is the identity::
+        The matrix of the unit element's operator is the identity,
+        regardless of the base field and whether or not we
+        orthonormalize::
 
             sage: set_random_seed()
             sage: J = random_eja()
@@ -774,6 +808,27 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: expected = matrix.identity(J.base_ring(), J.dimension())
             sage: actual == expected
             True
+            sage: x = J.random_element()
+            sage: A = x.subalgebra_generated_by()
+            sage: actual = A.one().operator().matrix()
+            sage: expected = matrix.identity(A.base_ring(), A.dimension())
+            sage: actual == expected
+            True
+
+        ::
+
+            sage: set_random_seed()
+            sage: J = random_eja(field=QQ, orthonormalize=False)
+            sage: actual = J.one().operator().matrix()
+            sage: expected = matrix.identity(J.base_ring(), J.dimension())
+            sage: actual == expected
+            True
+            sage: x = J.random_element()
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
+            sage: actual = A.one().operator().matrix()
+            sage: expected = matrix.identity(A.base_ring(), A.dimension())
+            sage: actual == expected
+            True
 
         Ensure that the cached unit element (often precomputed by
         hand) agrees with the computed one::
@@ -785,6 +840,15 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: J.one() == cached
             True
 
+        ::
+
+            sage: set_random_seed()
+            sage: J = random_eja(field=QQ, orthonormalize=False)
+            sage: cached = J.one()
+            sage: J.one.clear_cache()
+            sage: J.one() == cached
+            True
+
         """
         # We can brute-force compute the matrices of the operators
         # that correspond to the basis elements of this algebra.