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()
         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()
             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()
         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
             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
         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: 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():
             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()
         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()
             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()
         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: 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)])
             sage: x0 = x_vec[0]
             sage: x_bar = x_vec[1:]
             sage: A = matrix(QQ, 1, [x_vec.inner_product(x_vec)])