eja: add random_instance() method for algebras.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index d787c5fc1366411fe6f6a3b549d8dbd285037d8b..f26766df80f65de8c31fe12ef3eab5d5bd727c7a 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -424,8 +424,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Example 11.11::
 
             sage: set_random_seed()
-            sage: n = ZZ.random_element(1,10)
-            sage: J = JordanSpinEJA(n)
+            sage: J = JordanSpinEJA.random_instance()
             sage: x = J.random_element()
             sage: while not x.is_invertible():
             ....:     x = J.random_element()
@@ -651,8 +650,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         aren't multiples of the identity are regular::
 
             sage: set_random_seed()
-            sage: n = ZZ.random_element(1,10)
-            sage: J = JordanSpinEJA(n)
+            sage: J = JordanSpinEJA.random_instance()
             sage: x = J.random_element()
             sage: x == x.coefficient(0)*J.one() or x.degree() == 2
             True
@@ -735,10 +733,12 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         The minimal polynomial and the characteristic polynomial coincide
         and are known (see Alizadeh, Example 11.11) for all elements of
         the spin factor algebra that aren't scalar multiples of the
-        identity::
+        identity. We require the dimension of the algebra to be at least
+        two here so that said elements actually exist::
 
             sage: set_random_seed()
-            sage: n = ZZ.random_element(2,10)
+            sage: n_max = max(2, JordanSpinEJA._max_test_case_size())
+            sage: n = ZZ.random_element(2, n_max)
             sage: J = JordanSpinEJA(n)
             sage: y = J.random_element()
             sage: while y == y.coefficient(0)*J.one():
@@ -763,8 +763,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         and in particular, a re-scaling of the basis::
 
             sage: set_random_seed()
-            sage: n = ZZ.random_element(1,5)
-            sage: J1 = RealSymmetricEJA(n)
+            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: X = random_matrix(QQ,n)
             sage: X = X*X.transpose()
@@ -916,10 +917,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Alizadeh's Example 11.12::
 
             sage: set_random_seed()
-            sage: n = ZZ.random_element(1,10)
-            sage: J = JordanSpinEJA(n)
-            sage: x = J.random_element()
+            sage: x = JordanSpinEJA.random_instance().random_element()
             sage: x_vec = x.to_vector()
+            sage: n = x_vec.degree()
             sage: x0 = x_vec[0]
             sage: x_bar = x_vec[1:]
             sage: A = matrix(QQ, 1, [x_vec.inner_product(x_vec)])