eja: factor out the operator polynomial-matrix construction.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index c0dc408df3a7160a94c7cadcba6a5e35d78ba4fb..dd1bcf2584449f5b80ef13a669a28946948b3d25 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1518,6 +1518,64 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
                       for idx in range(count) )
 
 
+    def operator_polynomial_matrix(self):
+        r"""
+        Return the matrix of polynomials (over this algebra's
+        :meth:`coordinate_polynomial_ring`) that, when evaluated at
+        the basis coordinates of an element `x`, produces the basis
+        representation of `L_{x}`.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (HadamardEJA,
+            ....:                                  JordanSpinEJA)
+
+        EXAMPLES::
+
+            sage: J = HadamardEJA(4)
+            sage: L_x = J.operator_polynomial_matrix()
+            sage: L_x
+            [X0  0  0  0]
+            [ 0 X1  0  0]
+            [ 0  0 X2  0]
+            [ 0  0  0 X3]
+            sage: x = J.one()
+            sage: d = zip(J.coordinate_polynomial_ring().gens(), x.to_vector())
+            sage: L_x.subs(dict(d))
+            [1 0 0 0]
+            [0 1 0 0]
+            [0 0 1 0]
+            [0 0 0 1]
+
+        ::
+
+            sage: J = JordanSpinEJA(4)
+            sage: L_x = J.operator_polynomial_matrix()
+            sage: L_x
+            [X0 X1 X2 X3]
+            [X1 X0  0  0]
+            [X2  0 X0  0]
+            [X3  0  0 X0]
+            sage: x = J.one()
+            sage: d = zip(J.coordinate_polynomial_ring().gens(), x.to_vector())
+            sage: L_x.subs(dict(d))
+            [1 0 0 0]
+            [0 1 0 0]
+            [0 0 1 0]
+            [0 0 0 1]
+
+        """
+        R = self.coordinate_polynomial_ring()
+
+        def L_x_i_j(i,j):
+            # From a result in my book, these are the entries of the
+            # basis representation of L_x.
+            return sum( v*self.monomial(k).operator().matrix()[i,j]
+                        for (k,v) in enumerate(R.gens()) )
+
+        n = self.dimension()
+        return matrix(R, n, n, L_x_i_j)
+
     @cached_method
     def _charpoly_coefficients(self):
         r"""
@@ -1541,16 +1599,9 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         """
         n = self.dimension()
         R = self.coordinate_polynomial_ring()
-        vars = R.gens()
         F = R.fraction_field()
 
-        def L_x_i_j(i,j):
-            # From a result in my book, these are the entries of the
-            # basis representation of L_x.
-            return sum( vars[k]*self.monomial(k).operator().matrix()[i,j]
-                        for k in range(n) )
-
-        L_x = matrix(F, n, n, L_x_i_j)
+        L_x = self.operator_polynomial_matrix()
 
         r = None
         if self.rank.is_in_cache():