eja: move the "field" argument to (usually passed through) kwargs.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 110b049573bbc8d8aeaaab768e9cebceadbf3c7e..e7308ea34b9a36aef09a84069a1289e072487ec7 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -11,14 +11,14 @@ class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclide
 
     TESTS::
 
-    The natural representation of an element in the subalgebra is
-    the same as its natural representation in the superalgebra::
+    The matrix representation of an element in the subalgebra is
+    the same as its matrix representation in the superalgebra::
 
         sage: set_random_seed()
         sage: A = random_eja().random_element().subalgebra_generated_by()
         sage: y = A.random_element()
-        sage: actual = y.natural_representation()
-        sage: expected = y.superalgebra_element().natural_representation()
+        sage: actual = y.to_matrix()
+        sage: expected = y.superalgebra_element().to_matrix()
         sage: actual == expected
         True
 
@@ -27,7 +27,7 @@ class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclide
     our basis::
 
         sage: set_random_seed()
-        sage: x = random_eja(AA).random_element()
+        sage: x = random_eja(field=AA).random_element()
         sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
         sage: y = A.random_element()
         sage: y.operator()(A.one()) == y
@@ -121,11 +121,11 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         sage: E22 = matrix(AA, [ [0,0],
         ....:                    [0,1] ])
         sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
-        sage: K1.one().natural_representation()
+        sage: K1.one().to_matrix()
         [1 0]
         [0 0]
         sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),))
-        sage: K2.one().natural_representation()
+        sage: K2.one().to_matrix()
         [0 0]
         [0 1]
 
@@ -173,12 +173,25 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         # If our superalgebra is a subalgebra of something else, then
         # these vectors won't have the right coordinates for
         # V.span_of_basis() unless we use V.from_vector() on them.
-        W = V.span_of_basis( V.from_vector(b.to_vector()) for b in basis )
+        W = V.span_of_basis( (V.from_vector(b.to_vector()) for b in basis),
+                             check=check_axioms)
 
         n = len(basis)
-        mult_table = [[W.zero() for i in range(n)] for j in range(n)]
+        if check_axioms:
+            # The tables are square if we're verifying that they
+            # are commutative.
+            mult_table = [[W.zero() for j in range(n)] for i in range(n)]
+            ip_table = [ [ self._superalgebra.inner_product(basis[i],basis[j])
+                           for j in range(n) ]
+                         for i in range(n) ]
+        else:
+            mult_table = [[W.zero() for j in range(i+1)] for i in range(n)]
+            ip_table = [ [ self._superalgebra.inner_product(basis[i],basis[j])
+                           for j in range(i+1) ]
+                         for i in range(n) ]
+
         for i in range(n):
-            for j in range(n):
+            for j in range(i+1):
                 product = basis[i]*basis[j]
                 # product.to_vector() might live in a vector subspace
                 # if our parent algebra is already a subalgebra. We
@@ -186,8 +199,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
                 # that case.
                 product_vector = V.from_vector(product.to_vector())
                 mult_table[i][j] = W.coordinate_vector(product_vector)
+                if check_axioms:
+                    mult_table[j][i] = mult_table[i][j]
 
-        natural_basis = tuple( b.natural_representation() for b in basis )
+        matrix_basis = tuple( b.to_matrix() for b in basis )
 
 
         self._vector_space = W
@@ -195,9 +210,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         fdeja = super(FiniteDimensionalEuclideanJordanSubalgebra, self)
         fdeja.__init__(field,
                        mult_table,
+                       ip_table,
                        prefix=prefix,
                        category=category,
-                       natural_basis=natural_basis,
+                       matrix_basis=matrix_basis,
                        check_field=False,
                        check_axioms=check_axioms)
 
@@ -251,16 +267,16 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
 
 
 
-    def natural_basis_space(self):
+    def matrix_space(self):
         """
-        Return the natural basis space of this algebra, which is identical
-        to that of its superalgebra.
+        Return the matrix space of this algebra, which is identical to
+        that of its superalgebra.
 
-        This is correct "by definition," and avoids a mismatch when the
-        subalgebra is trivial (with no natural basis to infer anything
-        from) and the parent is not.
+        This is correct "by definition," and avoids a mismatch when
+        the subalgebra is trivial (with no matrix basis elements to
+        infer anything from) and the parent is not.
         """
-        return self.superalgebra().natural_basis_space()
+        return self.superalgebra().matrix_space()
 
 
     def superalgebra(self):