eja: speed up the computation of element powers.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index f26766df80f65de8c31fe12ef3eab5d5bd727c7a..7c861834723344ea6403f9f5da289af8aa299ae7 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -78,7 +78,7 @@ 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):
@@ -243,9 +243,8 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
-            sage: x.inner_product(y) in RR
+            sage: x,y = J.random_elements(2)
+            sage: x.inner_product(y) in RLF
             True
 
         """
@@ -280,9 +279,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Test Lemma 1 from Chapter III of Koecher::
 
             sage: set_random_seed()
-            sage: J = random_eja()
-            sage: u = J.random_element()
-            sage: v = J.random_element()
+            sage: u,v = random_eja().random_elements(2)
             sage: lhs = u.operator_commutes_with(u*v)
             sage: rhs = v.operator_commutes_with(u^2)
             sage: lhs == rhs
@@ -292,9 +289,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Chapter III, or from Baes (2.3)::
 
             sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
+            sage: x,y = random_eja().random_elements(2)
             sage: Lx = x.operator()
             sage: Ly = y.operator()
             sage: Lxx = (x*x).operator()
@@ -306,10 +301,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Baes (2.4)::
 
             sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
-            sage: z = J.random_element()
+            sage: x,y,z = random_eja().random_elements(3)
             sage: Lx = x.operator()
             sage: Ly = y.operator()
             sage: Lz = z.operator()
@@ -323,10 +315,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Baes (2.5)::
 
             sage: set_random_seed()
-            sage: J = random_eja()
-            sage: u = J.random_element()
-            sage: y = J.random_element()
-            sage: z = J.random_element()
+            sage: u,y,z = random_eja().random_elements(3)
             sage: Lu = u.operator()
             sage: Ly = y.operator()
             sage: Lz = z.operator()
@@ -388,8 +377,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = random_eja().random_element().subalgebra_generated_by()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
+            sage: x,y = J.random_elements(2)
             sage: (x*y).det() == x.det()*y.det()
             True
 
@@ -885,8 +873,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
+            sage: x,y = J.random_elements(2)
             sage: x.operator()(y) == x*y
             True
             sage: y.operator()(x) == x*y
@@ -936,8 +923,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
+            sage: x,y = J.random_elements(2)
             sage: Lx = x.operator()
             sage: Lxx = (x*x).operator()
             sage: Qx = x.quadratic_representation()
@@ -1039,9 +1025,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: x0 = random_eja().random_element()
             sage: A = x0.subalgebra_generated_by()
-            sage: x = A.random_element()
-            sage: y = A.random_element()
-            sage: z = A.random_element()
+            sage: x,y,z = A.random_elements(3)
             sage: (x*y)*z == x*(y*z)
             True
 
@@ -1152,7 +1136,7 @@ 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
 
         """
@@ -1181,9 +1165,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = random_eja()
-            sage: x = J.random_element();
-            sage: y = J.random_element()
-            sage: z = J.random_element()
+            sage: x,y,z = J.random_elements(3)
             sage: # commutative
             sage: x.trace_inner_product(y) == y.trace_inner_product(x)
             True