X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=0953b2f27d67d059e88588fc9adb1f3081fdecc6;hb=ffabf130fc8fa05e68d9b3d55a1f3ccf89f5e390;hp=0f6a47cd4f10efbcb0298725c4ae26537eae6372;hpb=98da0ce1d1102057e34646889c10dfa01fa9faec;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0f6a47c..0953b2f 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -346,6 +346,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  TrivialEJA,
             ....:                                  random_eja)
 
         EXAMPLES::
@@ -364,6 +365,17 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x.det()
             -1
 
+        The determinant of the sole element in the rank-zero trivial
+        algebra is ``1``, by three paths of reasoning. First, its
+        characteristic polynomial is a constant ``1``, so the constant
+        term in that polynomial is ``1``. Second, the characteristic
+        polynomial evaluated at zero is again ``1``. And finally, the
+        (empty) product of its eigenvalues is likewise just unity::
+
+            sage: J = TrivialEJA()
+            sage: J.zero().det()
+            1
+
         TESTS:
 
         An element is invertible if and only if its determinant is
@@ -382,15 +394,21 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x,y = J.random_elements(2)
             sage: (x*y).det() == x.det()*y.det()
             True
-
         """
         P = self.parent()
         r = P.rank()
-        p = P._charpoly_coeff(0)
-        # The _charpoly_coeff function already adds the factor of
-        # -1 to ensure that _charpoly_coeff(0) is really what
-        # appears in front of t^{0} in the charpoly. However,
-        # we want (-1)^r times THAT for the determinant.
+
+        if r == 0:
+            # Special case, since we don't get the a0=1
+            # coefficient when the rank of the algebra
+            # is zero.
+            return P.base_ring().one()
+
+        p = P._charpoly_coefficients()[0]
+        # The _charpoly_coeff function already adds the factor of -1
+        # to ensure that _charpoly_coefficients()[0] is really what
+        # appears in front of t^{0} in the charpoly. However, we want
+        # (-1)^r times THAT for the determinant.
         return ((-1)**r)*p(*self.to_vector())
 
 
@@ -1220,8 +1238,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: l0*c0 + l1*c1 == x
             True
 
+        The spectral decomposition should work in subalgebras, too::
+
+            sage: J = RealSymmetricEJA(4)
+            sage: (e0, e1, e2, e3, e4, e5, e6, e7, e8, e9) = J.gens()
+            sage: A = 2*e5 - 2*e8
+            sage: (lambda1, c1) = A.spectral_decomposition()[1]
+            sage: (J0, J5, J1) = J.peirce_decomposition(c1)
+            sage: (f0, f1, f2) = J1.gens()
+            sage: f0.spectral_decomposition()
+            [(0, 1.000000000000000?*f2), (1, 1.000000000000000?*f0)]
+
         """
-        P = self.parent()
         A = self.subalgebra_generated_by(orthonormalize_basis=True)
         result = []
         for (evalue, proj) in A(self).operator().spectral_decomposition():
@@ -1390,7 +1418,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             # the trace is an empty sum.
             return P.base_ring().zero()
 
-        p = P._charpoly_coeff(r-1)
+        p = P._charpoly_coefficients()[r-1]
         # The _charpoly_coeff function already adds the factor of
         # -1 to ensure that _charpoly_coeff(r-1) is really what
         # appears in front of t^{r-1} in the charpoly. However,