eja: fix alphabetical ordering of element methods.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 59e1537854a09f7058498cdd0959bbc82ccbde8d..8d9b27e974fff75f769579853d7ac60716d26298 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -461,6 +461,91 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             return self.span_of_powers().dimension()
 
 
+        def minimal_polynomial(self):
+            """
+            EXAMPLES::
+
+                sage: set_random_seed()
+                sage: x = random_eja().random_element()
+                sage: x.degree() == x.minimal_polynomial().degree()
+                True
+
+            ::
+
+                sage: set_random_seed()
+                sage: x = random_eja().random_element()
+                sage: x.degree() == x.minimal_polynomial().degree()
+                True
+
+            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::
+
+                sage: set_random_seed()
+                sage: n = ZZ.random_element(2,10)
+                sage: J = JordanSpinSimpleEJA(n)
+                sage: y = J.random_element()
+                sage: while y == y.coefficient(0)*J.one():
+                ....:     y = J.random_element()
+                sage: y0 = y.vector()[0]
+                sage: y_bar = y.vector()[1:]
+                sage: actual = y.minimal_polynomial()
+                sage: x = SR.symbol('x', domain='real')
+                sage: expected = x^2 - 2*y0*x + (y0^2 - norm(y_bar)^2)
+                sage: bool(actual == expected)
+                True
+
+            """
+            # The element we're going to call "minimal_polynomial()" on.
+            # Either myself, interpreted as an element of a finite-
+            # dimensional algebra, or an element of an associative
+            # subalgebra.
+            elt = None
+
+            if self.parent().is_associative():
+                elt = FiniteDimensionalAlgebraElement(self.parent(), self)
+            else:
+                V = self.span_of_powers()
+                assoc_subalg = self.subalgebra_generated_by()
+                # Mis-design warning: the basis used for span_of_powers()
+                # and subalgebra_generated_by() must be the same, and in
+                # the same order!
+                elt = assoc_subalg(V.coordinates(self.vector()))
+
+            # Recursive call, but should work since elt lives in an
+            # associative algebra.
+            return elt.minimal_polynomial()
+
+
+        def natural_representation(self):
+            """
+            Return a more-natural representation of this element.
+
+            Every finite-dimensional Euclidean Jordan Algebra is a
+            direct sum of five simple algebras, four of which comprise
+            Hermitian matrices. This method returns the original
+            "natural" representation of this element as a Hermitian
+            matrix, if it has one. If not, you get the usual representation.
+
+            EXAMPLES::
+
+                sage: J = ComplexHermitianSimpleEJA(3)
+                sage: J.one()
+                e0 + e5 + e8
+                sage: J.one().natural_representation()
+                [1 0 0 0 0 0]
+                [0 1 0 0 0 0]
+                [0 0 1 0 0 0]
+                [0 0 0 1 0 0]
+                [0 0 0 0 1 0]
+                [0 0 0 0 0 1]
+
+            """
+            B = self.parent().natural_basis()
+            W = B[0].matrix_space()
+            return W.linear_combination(zip(self.vector(), B))
+
 
         def operator_matrix(self):
             """
@@ -529,92 +614,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             return fda_elt.matrix().transpose()
 
 
-        def natural_representation(self):
-            """
-            Return a more-natural representation of this element.
-
-            Every finite-dimensional Euclidean Jordan Algebra is a
-            direct sum of five simple algebras, four of which comprise
-            Hermitian matrices. This method returns the original
-            "natural" representation of this element as a Hermitian
-            matrix, if it has one. If not, you get the usual representation.
-
-            EXAMPLES::
-
-                sage: J = ComplexHermitianSimpleEJA(3)
-                sage: J.one()
-                e0 + e5 + e8
-                sage: J.one().natural_representation()
-                [1 0 0 0 0 0]
-                [0 1 0 0 0 0]
-                [0 0 1 0 0 0]
-                [0 0 0 1 0 0]
-                [0 0 0 0 1 0]
-                [0 0 0 0 0 1]
-
-            """
-            B = self.parent().natural_basis()
-            W = B[0].matrix_space()
-            return W.linear_combination(zip(self.vector(), B))
-
-
-        def minimal_polynomial(self):
-            """
-            EXAMPLES::
-
-                sage: set_random_seed()
-                sage: x = random_eja().random_element()
-                sage: x.degree() == x.minimal_polynomial().degree()
-                True
-
-            ::
-
-                sage: set_random_seed()
-                sage: x = random_eja().random_element()
-                sage: x.degree() == x.minimal_polynomial().degree()
-                True
-
-            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::
-
-                sage: set_random_seed()
-                sage: n = ZZ.random_element(2,10)
-                sage: J = JordanSpinSimpleEJA(n)
-                sage: y = J.random_element()
-                sage: while y == y.coefficient(0)*J.one():
-                ....:     y = J.random_element()
-                sage: y0 = y.vector()[0]
-                sage: y_bar = y.vector()[1:]
-                sage: actual = y.minimal_polynomial()
-                sage: x = SR.symbol('x', domain='real')
-                sage: expected = x^2 - 2*y0*x + (y0^2 - norm(y_bar)^2)
-                sage: bool(actual == expected)
-                True
-
-            """
-            # The element we're going to call "minimal_polynomial()" on.
-            # Either myself, interpreted as an element of a finite-
-            # dimensional algebra, or an element of an associative
-            # subalgebra.
-            elt = None
-
-            if self.parent().is_associative():
-                elt = FiniteDimensionalAlgebraElement(self.parent(), self)
-            else:
-                V = self.span_of_powers()
-                assoc_subalg = self.subalgebra_generated_by()
-                # Mis-design warning: the basis used for span_of_powers()
-                # and subalgebra_generated_by() must be the same, and in
-                # the same order!
-                elt = assoc_subalg(V.coordinates(self.vector()))
-
-            # Recursive call, but should work since elt lives in an
-            # associative algebra.
-            return elt.minimal_polynomial()
-
-
         def quadratic_representation(self, other=None):
             """
             Return the quadratic representation of this element.