eja: move the element constructor into the parent algebra class.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 4ed0a59216e7d07eaba9a6aec1b43e91902d3513..5b9142496f434be0a7c4dc014816302262eb33a5 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -25,69 +25,6 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
                       dir(self.__class__) )
 
 
-    def __init__(self, A, elt):
-        """
-
-        SETUP::
-
-            sage: from mjo.eja.eja_algebra import (RealSymmetricEJA,
-            ....:                                  random_eja)
-
-        EXAMPLES:
-
-        The identity in `S^n` is converted to the identity in the EJA::
-
-            sage: J = RealSymmetricEJA(3)
-            sage: I = matrix.identity(QQ,3)
-            sage: J(I) == J.one()
-            True
-
-        This skew-symmetric matrix can't be represented in the EJA::
-
-            sage: J = RealSymmetricEJA(3)
-            sage: A = matrix(QQ,3, lambda i,j: i-j)
-            sage: J(A)
-            Traceback (most recent call last):
-            ...
-            ArithmeticError: vector is not in free module
-
-        TESTS:
-
-        Ensure that we can convert any element of the parent's
-        underlying vector space back into an algebra element whose
-        vector representation is what we started with::
-
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: v = J.vector_space().random_element()
-            sage: J(v).to_vector() == v
-            True
-
-        """
-        # Goal: if we're given a matrix, and if it lives in our
-        # parent algebra's "natural ambient space," convert it
-        # into an algebra element.
-        #
-        # The catch is, we make a recursive call after converting
-        # the given matrix into a vector that lives in the algebra.
-        # This we need to try the parent class initializer first,
-        # to avoid recursing forever if we're given something that
-        # already fits into the algebra, but also happens to live
-        # in the parent's "natural ambient space" (this happens with
-        # vectors in R^n).
-        ifme = super(FiniteDimensionalEuclideanJordanAlgebraElement, self)
-        try:
-            ifme.__init__(A, elt)
-        except ValueError:
-            natural_basis = A.natural_basis()
-            if elt in natural_basis[0].matrix_space():
-                # Thanks for nothing! Matrix spaces aren't vector
-                # spaces in Sage, so we have to figure out its
-                # natural-basis coordinates ourselves.
-                V = VectorSpace(elt.base_ring(), elt.nrows()**2)
-                W = V.span( _mat2vec(s) for s in natural_basis )
-                coords =  W.coordinate_vector(_mat2vec(elt))
-                ifme.__init__(A, coords)
 
 
     def __pow__(self, n):
@@ -808,7 +745,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: J = ComplexHermitianEJA(3)
             sage: J.one()
-            e0 + e5 + e8
+            e0 + e3 + e8
             sage: J.one().natural_representation()
             [1 0 0 0 0 0]
             [0 1 0 0 0 0]
@@ -821,7 +758,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: J = QuaternionHermitianEJA(3)
             sage: J.one()
-            e0 + e9 + e14
+            e0 + e5 + e14
             sage: J.one().natural_representation()
             [1 0 0 0 0 0 0 0 0 0 0 0]
             [0 1 0 0 0 0 0 0 0 0 0 0]