eja: add "of" to the algebra characteristic_polynomial() method name.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0953b2f27d67d059e88588fc9adb1f3081fdecc6..0be0032751d75b85edf5386b69945dcb7d72b60d 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1,5 +1,3 @@
-# -*- coding: utf-8 -*-
-
 from sage.matrix.constructor import matrix
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
@@ -183,7 +181,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             True
 
         """
-        p = self.parent().characteristic_polynomial()
+        p = self.parent().characteristic_polynomial_of()
         return p(*self.to_vector())
 
 
@@ -438,11 +436,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: while not x.is_invertible():
             ....:     x = J.random_element()
             sage: x_vec = x.to_vector()
-            sage: x0 = x_vec[0]
+            sage: x0 = x_vec[:1]
             sage: x_bar = x_vec[1:]
-            sage: coeff = ~(x0^2 - x_bar.inner_product(x_bar))
-            sage: inv_vec = x_vec.parent()([x0] + (-x_bar).list())
-            sage: x_inverse = coeff*inv_vec
+            sage: coeff = x0.inner_product(x0) - x_bar.inner_product(x_bar)
+            sage: x_inverse = x_vec.parent()(x0.list() + (-x_bar).list())
+            sage: if not coeff.is_zero(): x_inverse = x_inverse/coeff
             sage: x.inverse() == J.from_vector(x_inverse)
             True
 
@@ -796,8 +794,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = JordanSpinEJA.random_instance()
+            sage: n = J.dimension()
             sage: x = J.random_element()
-            sage: x == x.coefficient(0)*J.one() or x.degree() == 2
+            sage: x.degree() == min(n,2) or (x == x.coefficient(0)*J.one())
             True
 
         TESTS:
@@ -875,13 +874,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         TESTS:
 
         The minimal polynomial of the identity and zero elements are
-        always the same::
+        always the same, except in trivial algebras where the minimal
+        polynomial of the unit/zero element is ``1``::
 
             sage: set_random_seed()
-            sage: J = random_eja(nontrivial=True)
-            sage: J.one().minimal_polynomial()
+            sage: J = random_eja()
+            sage: mu = J.one().minimal_polynomial()
+            sage: t = mu.parent().gen()
+            sage: mu + int(J.is_trivial())*(t-2)
             t - 1
-            sage: J.zero().minimal_polynomial()
+            sage: mu = J.zero().minimal_polynomial()
+            sage: t = mu.parent().gen()
+            sage: mu + int(J.is_trivial())*(t-1)
             t
 
         The degree of an element is (by one definition) the degree
@@ -1080,16 +1084,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: x = JordanSpinEJA.random_instance().random_element()
             sage: x_vec = x.to_vector()
+            sage: Q = matrix.identity(x.base_ring(), 0)
             sage: n = x_vec.degree()
-            sage: x0 = x_vec[0]
-            sage: x_bar = x_vec[1:]
-            sage: A = matrix(AA, 1, [x_vec.inner_product(x_vec)])
-            sage: B = 2*x0*x_bar.row()
-            sage: C = 2*x0*x_bar.column()
-            sage: D = matrix.identity(AA, n-1)
-            sage: D = (x0^2 - x_bar.inner_product(x_bar))*D
-            sage: D = D + 2*x_bar.tensor_product(x_bar)
-            sage: Q = matrix.block(2,2,[A,B,C,D])
+            sage: if n > 0:
+            ....:     x0 = x_vec[0]
+            ....:     x_bar = x_vec[1:]
+            ....:     A = matrix(x.base_ring(), 1, [x_vec.inner_product(x_vec)])
+            ....:     B = 2*x0*x_bar.row()
+            ....:     C = 2*x0*x_bar.column()
+            ....:     D = matrix.identity(x.base_ring(), n-1)
+            ....:     D = (x0^2 - x_bar.inner_product(x_bar))*D
+            ....:     D = D + 2*x_bar.tensor_product(x_bar)
+            ....:     Q = matrix.block(2,2,[A,B,C,D])
             sage: Q == x.quadratic_representation().matrix()
             True
 
@@ -1318,12 +1324,13 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         TESTS:
 
         Ensure that we can find an idempotent in a non-trivial algebra
-        where there are non-nilpotent elements::
+        where there are non-nilpotent elements, or that we get the dumb
+        solution in the trivial algebra::
 
             sage: set_random_seed()
-            sage: J = random_eja(nontrivial=True)
+            sage: J = random_eja()
             sage: x = J.random_element()
-            sage: while x.is_nilpotent():
+            sage: while x.is_nilpotent() and not J.is_trivial():
             ....:     x = J.random_element()
             sage: c = x.subalgebra_idempotent()
             sage: c^2 == c