eja: add a WIP gram-schmidt for EJA elements.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 8a17c25d4a0d52d98c063f856d888207e2ca74ea..c2f9fe652851fa4dc2ce519856160efc221debcc 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1,3 +1,5 @@
+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
@@ -78,7 +80,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         elif n == 1:
             return self
         else:
-            return (self.operator()**(n-1))(self)
+            return (self**(n-1))*self
 
 
     def apply_univariate_polynomial(self, p):
@@ -244,7 +246,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: J = random_eja()
             sage: x,y = J.random_elements(2)
-            sage: x.inner_product(y) in RR
+            sage: x.inner_product(y) in RLF
             True
 
         """
@@ -754,7 +756,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: n_max = RealSymmetricEJA._max_test_case_size()
             sage: n = ZZ.random_element(1, n_max)
             sage: J1 = RealSymmetricEJA(n,QQ)
-            sage: J2 = RealSymmetricEJA(n,QQ,False)
+            sage: J2 = RealSymmetricEJA(n,QQ,normalize_basis=False)
             sage: X = random_matrix(QQ,n)
             sage: X = X*X.transpose()
             sage: x1 = J1(X)
@@ -830,7 +832,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         B = self.parent().natural_basis()
         W = self.parent().natural_basis_space()
-        return W.linear_combination(zip(B,self.to_vector()))
+        return W.linear_combination(izip(B,self.to_vector()))
 
 
     def norm(self):
@@ -968,10 +970,10 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: not x.is_invertible() or (
             ....:   x.quadratic_representation(x.inverse())*Qx
             ....:   ==
-            ....:   2*x.operator()*Qex - Qx )
+            ....:   2*Lx*Qex - Qx )
             True
 
-            sage: 2*x.operator()*Qex - Qx == Lxx
+            sage: 2*Lx*Qex - Qx == Lxx
             True
 
         Property 5:
@@ -1009,7 +1011,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
 
 
-    def subalgebra_generated_by(self):
+    def subalgebra_generated_by(self, orthonormalize_basis=False):
         """
         Return the associative subalgebra of the parent EJA generated
         by this element.
@@ -1048,7 +1050,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             0
 
         """
-        return FiniteDimensionalEuclideanJordanElementSubalgebra(self)
+        return FiniteDimensionalEuclideanJordanElementSubalgebra(self, orthonormalize_basis)
 
 
     def subalgebra_idempotent(self):
@@ -1136,7 +1138,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = random_eja()
-            sage: J.random_element().trace() in J.base_ring()
+            sage: J.random_element().trace() in RLF
             True
 
         """
@@ -1160,8 +1162,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         TESTS:
 
-        The trace inner product is commutative, bilinear, and satisfies
-        the Jordan axiom:
+        The trace inner product is commutative, bilinear, and associative::
 
             sage: set_random_seed()
             sage: J = random_eja()
@@ -1181,7 +1182,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             ....:              a*x.trace_inner_product(z) )
             sage: actual == expected
             True
-            sage: # jordan axiom
+            sage: # associative
             sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z)
             True