X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=7c4c79ddcd7315e654620a0be8f8bccf5ab9ac11;hb=99ca9f8c24194ad6be7b8e325575e58b53429c2b;hp=276eab040db20d1df1715eed782db7dfe2acd481;hpb=269f872019b616287c4cf1878477879019f8bbd0;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 276eab0..7c4c79d 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1,7 +1,5 @@
 # -*- coding: utf-8 -*-
 
-from itertools import izip
-
 from sage.matrix.constructor import matrix
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
@@ -98,7 +96,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import (RealCartesianProductEJA,
+            sage: from mjo.eja.eja_algebra import (HadamardEJA,
             ....:                                  random_eja)
 
         EXAMPLES::
@@ -106,7 +104,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: R = PolynomialRing(QQ, 't')
             sage: t = R.gen(0)
             sage: p = t^4 - t^3 + 5*t - 2
-            sage: J = RealCartesianProductEJA(5)
+            sage: J = HadamardEJA(5)
             sage: J.one().apply_univariate_polynomial(p) == 3*J.one()
             True
 
@@ -139,7 +137,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import RealCartesianProductEJA
+            sage: from mjo.eja.eja_algebra import HadamardEJA
 
         EXAMPLES:
 
@@ -147,14 +145,14 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         the identity element is `(t-1)` from which it follows that
         the characteristic polynomial should be `(t-1)^3`::
 
-            sage: J = RealCartesianProductEJA(3)
+            sage: J = HadamardEJA(3)
             sage: J.one().characteristic_polynomial()
             t^3 - 3*t^2 + 3*t - 1
 
         Likewise, the characteristic of the zero element in the
         rank-three algebra `R^{n}` should be `t^{3}`::
 
-            sage: J = RealCartesianProductEJA(3)
+            sage: J = HadamardEJA(3)
             sage: J.zero().characteristic_polynomial()
             t^3
 
@@ -164,7 +162,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         to zero on that element::
 
             sage: set_random_seed()
-            sage: x = RealCartesianProductEJA(3).random_element()
+            sage: x = HadamardEJA(3).random_element()
             sage: p = x.characteristic_polynomial()
             sage: x.apply_univariate_polynomial(p)
             0
@@ -172,7 +170,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         The characteristic polynomials of the zero and unit elements
         should be what we think they are in a subalgebra, too::
 
-            sage: J = RealCartesianProductEJA(3)
+            sage: J = HadamardEJA(3)
             sage: p1 = J.one().characteristic_polynomial()
             sage: q1 = J.zero().characteristic_polynomial()
             sage: e0,e1,e2 = J.gens()
@@ -988,7 +986,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         B = self.parent().natural_basis()
         W = self.parent().natural_basis_space()
-        return W.linear_combination(izip(B,self.to_vector()))
+        return W.linear_combination(zip(B,self.to_vector()))
 
 
     def norm(self):
@@ -998,11 +996,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
-            ....:                                  RealCartesianProductEJA)
+            ....:                                  HadamardEJA)
 
         EXAMPLES::
 
-            sage: J = RealCartesianProductEJA(2)
+            sage: J = HadamardEJA(2)
             sage: x = sum(J.gens())
             sage: x.norm()
             sqrt(2)
@@ -1317,7 +1315,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         # will be minimal for some natural number s...
         s = 0
         minimal_dim = J.dimension()
-        for i in xrange(1, minimal_dim):
+        for i in range(1, minimal_dim):
             this_dim = (u**i).operator().matrix().image().dimension()
             if this_dim < minimal_dim:
                 minimal_dim = this_dim
@@ -1352,7 +1350,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
-            ....:                                  RealCartesianProductEJA,
+            ....:                                  HadamardEJA,
             ....:                                  TrivialEJA,
             ....:                                  random_eja)
 
@@ -1370,7 +1368,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         ::
 
-            sage: J = RealCartesianProductEJA(5)
+            sage: J = HadamardEJA(5)
             sage: J.one().trace()
             5
 
@@ -1448,11 +1446,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
-            ....:                                  RealCartesianProductEJA)
+            ....:                                  HadamardEJA)
 
         EXAMPLES::
 
-            sage: J = RealCartesianProductEJA(2)
+            sage: J = HadamardEJA(2)
             sage: x = sum(J.gens())
             sage: x.trace_norm()
             sqrt(2)