X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=dd1bcf2584449f5b80ef13a669a28946948b3d25;hb=6efdc5031a3ae89c16a3184750fb7cf7e26b5fb9;hp=907f40d72135df42d211cdd9bb8923df6bf462e6;hpb=7c21799d680433b62d48ca79cc2ea8f27e1cd8da;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 907f40d..dd1bcf2 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -166,7 +166,8 @@ from sage.modules.free_module import FreeModule, VectorSpace
 from sage.rings.all import (ZZ, QQ, AA, QQbar, RR, RLF, CLF,
                             PolynomialRing,
                             QuadraticField)
-from mjo.eja.eja_element import FiniteDimensionalEJAElement
+from mjo.eja.eja_element import (CartesianProductEJAElement,
+                                 FiniteDimensionalEJAElement)
 from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
 from mjo.eja.eja_utils import _all2list
 
@@ -366,7 +367,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         if orthonormalize:
             # Now "self._matrix_span" is the vector space of our
-            # algebra coordinates. The variables "X1", "X2",...  refer
+            # algebra coordinates. The variables "X0", "X1",...  refer
             # to the entries of vectors in self._matrix_span. Thus to
             # convert back and forth between the orthonormal
             # coordinates and the given ones, we need to stick the
@@ -870,7 +871,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = JordanSpinEJA(3)
             sage: p = J.characteristic_polynomial_of(); p
-            X1^2 - X2^2 - X3^2 + (-2*t)*X1 + t^2
+            X0^2 - X1^2 - X2^2 + (-2*t)*X0 + t^2
             sage: xvec = J.one().to_vector()
             sage: p(*xvec)
             t^2 - 2*t + 1
@@ -919,13 +920,13 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = HadamardEJA(2)
             sage: J.coordinate_polynomial_ring()
-            Multivariate Polynomial Ring in X1, X2...
+            Multivariate Polynomial Ring in X0, X1...
             sage: J = RealSymmetricEJA(3,field=QQ,orthonormalize=False)
             sage: J.coordinate_polynomial_ring()
-            Multivariate Polynomial Ring in X1, X2, X3, X4, X5, X6...
+            Multivariate Polynomial Ring in X0, X1, X2, X3, X4, X5...
 
         """
-        var_names = tuple( "X%d" % z for z in range(1, self.dimension()+1) )
+        var_names = tuple( "X%d" % z for z in range(self.dimension()) )
         return PolynomialRing(self.base_ring(), var_names)
 
     def inner_product(self, x, y):
@@ -1517,6 +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"""
@@ -1540,16 +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():
@@ -1770,7 +1822,7 @@ class RationalBasisEJA(FiniteDimensionalEJA):
 
             sage: J = JordanSpinEJA(3)
             sage: J._charpoly_coefficients()
-            (X1^2 - X2^2 - X3^2, -2*X1)
+            (X0^2 - X1^2 - X2^2, -2*X0)
             sage: a0 = J._charpoly_coefficients()[0]
             sage: J.base_ring()
             Algebraic Real Field
@@ -3089,6 +3141,7 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         sage: actual == expected             # long time
         True
     """
+    Element = CartesianProductEJAElement
     def __init__(self, factors, **kwargs):
         m = len(factors)
         if m == 0: