X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element_subalgebra.py;h=34a63afdc0be38fb34ab95bb211df6d926d9be57;hb=95ae8e7b0ddca840da9631603a2f37cca888468b;hp=dceb3b405a4c5a663c61a966993ce890ed516b49;hpb=4c8f9aac69d1cb4097b60b10e5b198b6372ec55e;p=sage.d.git

diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py
index dceb3b4..34a63af 100644
--- a/mjo/eja/eja_element_subalgebra.py
+++ b/mjo/eja/eja_element_subalgebra.py
@@ -6,43 +6,18 @@ from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra
 
 
 class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra):
-    def __init__(self, elt, orthonormalize=True, **kwargs):
+    def __init__(self, elt, **kwargs):
         superalgebra = elt.parent()
 
-        powers = tuple( elt**k for k in range(superalgebra.dimension()) )
-        power_vectors = ( p.to_vector() for p in powers )
-        P = matrix(superalgebra.base_ring(), power_vectors)
-
-        if orthonormalize:
-            basis = powers # let god sort 'em out
-        else:
-            # Echelonize the matrix ourselves, because otherwise the
-            # call to P.pivot_rows() below can choose a non-optimal
-            # row-reduction algorithm. In particular, scaling can
-            # help over AA because it avoids the RecursionError that
-            # gets thrown when we have to look too hard for a root.
-            #
-            # Beware: QQ supports an entirely different set of "algorithm"
-            # keywords than do AA and RR.
-            algo = None
-            if superalgebra.base_ring() is not QQ:
-                algo = "scaled_partial_pivoting"
-                P.echelonize(algorithm=algo)
-
-                # In this case, we just need to figure out which elements
-                # of the "powers" list are redundant... First compute the
-                # vector subspace spanned by the powers of the given
-                # element.
-
-                # Figure out which powers form a linearly-independent set.
-                ind_rows = P.pivot_rows()
-
-                # Pick those out of the list of all powers.
-                basis = tuple(map(powers.__getitem__, ind_rows))
-
+        # TODO: going up to the superalgebra dimension here is
+        # overkill.  We should append p vectors as rows to a matrix
+        # and continually rref() it until the rank stops going
+        # up. When n=10 but the dimension of the algebra is 1, that
+        # can save a shitload of time (especially over AA).
+        powers = tuple( elt**k for k in range(elt.degree()) )
 
         super().__init__(superalgebra,
-                         basis,
+                         powers,
                          associative=True,
                          **kwargs)
 
@@ -77,7 +52,7 @@ class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra):
             sage: J.one()
             e0 + e1 + e2 + e3 + e4
             sage: x = sum(J.gens())
-            sage: A = x.subalgebra_generated_by()
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: A.one()
             f0
             sage: A.one().superalgebra_element()
@@ -99,7 +74,7 @@ class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra):
 
             sage: set_random_seed()
             sage: x = random_eja().random_element()
-            sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
+            sage: A = x.subalgebra_generated_by()
             sage: x = A.random_element()
             sage: A.one()*x == x and x*A.one() == x
             True
@@ -109,7 +84,7 @@ class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra):
 
             sage: set_random_seed()
             sage: x = random_eja(field=QQ,orthonormalize=False).random_element()
-            sage: A = x.subalgebra_generated_by()
+            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
@@ -120,7 +95,7 @@ class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra):
 
             sage: set_random_seed()
             sage: x = random_eja().random_element()
-            sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
+            sage: A = x.subalgebra_generated_by()
             sage: actual = A.one().operator().matrix()
             sage: expected = matrix.identity(A.base_ring(), A.dimension())
             sage: actual == expected