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 9e808ae1cb1c6ec41ca59136c8a6787fd589e61c..83ec50e5a215417811fe09d72c61251081772160 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -133,7 +133,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             deortho_vector_basis = tuple( V(b.list()) for b in basis )
 
             from mjo.eja.eja_utils import gram_schmidt
-            basis = gram_schmidt(basis, inner_product)
+            basis = tuple(gram_schmidt(basis, inner_product))
 
         # Save the (possibly orthonormalized) matrix basis for
         # later...
@@ -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
 
-        The matrix of the unit element's operator is the identity::
+        ::
+
+            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,
+        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.
@@ -1201,6 +1265,7 @@ class RationalBasisEJA(FiniteDimensionalEJA):
             if not all( all(b_i in QQ for b_i in b.list()) for b in basis ):
                 raise TypeError("basis not rational")
 
+        self._rational_algebra = None
         if field is not QQ:
             # There's no point in constructing the extra algebra if this
             # one is already rational.
@@ -1261,7 +1326,14 @@ class RationalBasisEJA(FiniteDimensionalEJA):
         a = ( a_i.change_ring(self.base_ring())
               for a_i in self._rational_algebra._charpoly_coefficients() )
 
-        # Now convert the coordinate variables back to the
+        if self._deortho_matrix is None:
+            # This can happen if our base ring was, say, AA and we
+            # chose not to (or didn't need to) orthonormalize. It's
+            # still faster to do the computations over QQ even if
+            # the numbers in the boxes stay the same.
+            return tuple(a)
+
+        # Otherwise, convert the coordinate variables back to the
         # deorthonormalized ones.
         R = self.coordinate_polynomial_ring()
         from sage.modules.free_module_element import vector