eja: add a test for basis-invariance of minimal polynomial.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index e1f75630bf5b3fc33292e4c84fa657fed715828a..03376bda408b8fde98597ca8e8669e7e72a3e81a 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -709,6 +709,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  RealSymmetricEJA,
             ....:                                  random_eja)
 
         TESTS:
@@ -758,6 +759,20 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x.apply_univariate_polynomial(p)
             0
 
+        The minimal polynomial is invariant under a change of basis,
+        and in particular, a re-scaling of the basis::
+
+            sage: set_random_seed()
+            sage: n = ZZ.random_element(1,5).abs()
+            sage: J1 = RealSymmetricEJA(n)
+            sage: J2 = RealSymmetricEJA(n,QQ,False)
+            sage: X = random_matrix(QQ,n)
+            sage: X = X*X.transpose()
+            sage: x1 = J1(X)
+            sage: x2 = J2(X)
+            sage: x1.minimal_polynomial() == x2.minimal_polynomial()
+            True
+
         """
         if self.is_zero():
             # We would generate a zero-dimensional subalgebra
@@ -825,10 +840,37 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         """
         B = self.parent().natural_basis()
-        W = B[0].matrix_space()
+        W = self.parent().natural_basis_space()
         return W.linear_combination(zip(B,self.to_vector()))
 
 
+    def norm(self):
+        """
+        The norm of this element with respect to :meth:`inner_product`.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  RealCartesianProductEJA)
+
+        EXAMPLES::
+
+            sage: J = RealCartesianProductEJA(2)
+            sage: x = sum(J.gens())
+            sage: x.norm()
+            sqrt(2)
+
+        ::
+
+            sage: J = JordanSpinEJA(4)
+            sage: x = sum(J.gens())
+            sage: x.norm()
+            2
+
+        """
+        return self.inner_product(self).sqrt()
+
+
     def operator(self):
         """
         Return the left-multiplication-by-this-element
@@ -912,7 +954,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         Property 2 (multiply on the right for :trac:`28272`):
 
-            sage: alpha = QQ.random_element()
+            sage: alpha = J.base_ring().random_element()
             sage: (alpha*x).quadratic_representation() == Qx*(alpha^2)
             True
 
@@ -1017,7 +1059,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: A = random_eja().zero().subalgebra_generated_by()
             sage: A
-            Euclidean Jordan algebra of dimension 0 over Rational Field
+            Euclidean Jordan algebra of dimension 0 over...
             sage: A.one()
             0
 
@@ -1149,7 +1191,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x = J.random_element()
             sage: y = J.random_element()
             sage: z = J.random_element()
-            sage: a = QQ.random_element();
+            sage: a = J.base_ring().random_element();
             sage: actual = (a*(x+z)).trace_inner_product(y)
             sage: expected = ( a*x.trace_inner_product(y) +
             ....:              a*z.trace_inner_product(y) )
@@ -1177,3 +1219,30 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             raise TypeError("'other' must live in the same algebra")
 
         return (self*other).trace()
+
+
+    def trace_norm(self):
+        """
+        The norm of this element with respect to :meth:`trace_inner_product`.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  RealCartesianProductEJA)
+
+        EXAMPLES::
+
+            sage: J = RealCartesianProductEJA(2)
+            sage: x = sum(J.gens())
+            sage: x.trace_norm()
+            sqrt(2)
+
+        ::
+
+            sage: J = JordanSpinEJA(4)
+            sage: x = sum(J.gens())
+            sage: x.trace_norm()
+            2*sqrt(2)
+
+        """
+        return self.trace_inner_product(self).sqrt()