eja: don't waste time computing the unit element in subalgebras.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 5e782cf4a69b13d0d6c2e36beb5b190d81ddb3b4..7451e47bdbbbf2d58ce598aa3bb4e17ec42d5dae 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -99,28 +99,12 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         # matrix for the successive basis elements b0, b1,... of
         # that subspace.
         field = superalgebra.base_ring()
-        mult_table = []
-        for b_right in superalgebra_basis:
-                b_right_rows = []
-                # The first row of the right-multiplication matrix by
-                # b1 is what we get if we apply that matrix to b1. The
-                # second row of the right multiplication matrix by b1
-                # is what we get when we apply that matrix to b2...
-                #
-                # IMPORTANT: this assumes that all vectors are COLUMN
-                # vectors, unlike our superclass (which uses row vectors).
-                for b_left in superalgebra_basis:
-                    # Multiply in the original EJA, but then get the
-                    # coordinates from the subalgebra in terms of its
-                    # basis.
-                    this_row = W.coordinates((b_left*b_right).to_vector())
-                    b_right_rows.append(this_row)
-                b_right_matrix = matrix(field, b_right_rows)
-                mult_table.append(b_right_matrix)
-
-        for m in mult_table:
-            m.set_immutable()
-        mult_table = tuple(mult_table)
+        n = len(superalgebra_basis)
+        mult_table = [[W.zero() for i in range(n)] for j in range(n)]
+        for i in range(n):
+            for j in range(n):
+                product = superalgebra_basis[i]*superalgebra_basis[j]
+                mult_table[i][j] = W.coordinate_vector(product.to_vector())
 
         # TODO: We'll have to redo this and make it unique again...
         prefix = 'f'
@@ -178,6 +162,62 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             return self.from_vector(coords)
 
 
+    def one_basis(self):
+        """
+        Return the basis-element-index of this algebra's unit element.
+        """
+        return 0
+
+
+    def one(self):
+        """
+        Return the multiplicative identity element of this algebra.
+
+        The superclass method computes the identity element, which is
+        beyond overkill in this case: the algebra identity should be our
+        first basis element. We implement this via :meth:`one_basis`
+        because that method can optionally be used by other parts of the
+        category framework.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (RealCartesianProductEJA,
+            ....:                                  random_eja)
+
+        EXAMPLES::
+
+            sage: J = RealCartesianProductEJA(5)
+            sage: J.one()
+            e0 + e1 + e2 + e3 + e4
+            sage: x = sum(J.gens())
+            sage: A = x.subalgebra_generated_by()
+            sage: A.one()
+            f0
+            sage: A.one().superalgebra_element()
+            e0 + e1 + e2 + e3 + e4
+
+        TESTS:
+
+        The identity element acts like the identity::
+
+            sage: set_random_seed()
+            sage: J = random_eja().random_element().subalgebra_generated_by()
+            sage: x = J.random_element()
+            sage: J.one()*x == x and x*J.one() == x
+            True
+
+        The matrix of the unit element's operator is the identity::
+
+            sage: set_random_seed()
+            sage: J = random_eja().random_element().subalgebra_generated_by()
+            sage: actual = J.one().operator().matrix()
+            sage: expected = matrix.identity(J.base_ring(), J.dimension())
+            sage: actual == expected
+            True
+        """
+        return self.monomial(self.one_basis())
+
+
     def superalgebra(self):
         """
         Return the superalgebra that this algebra was generated from.