eja: minor update to HadamardEJA docs.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ca3df5fea55949225a51f8255a2c13a33c37d9f2..c86cdff0e4ab056292ac248289aee6a876332739 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1575,7 +1575,11 @@ class RationalBasisEJA(FiniteDimensionalEJA):
         if check_field:
             # Abuse the check_field parameter to check that the entries of
             # out basis (in ambient coordinates) are in the field QQ.
-            if not all( all(b_i in QQ for b_i in b.list()) for b in basis ):
+            # Use _all2list to get the vector coordinates of octonion
+            # entries and not the octonions themselves (which are not
+            # rational).
+            if not all( all(b_i in QQ for b_i in _all2list(b))
+                        for b in basis ):
                 raise TypeError("basis not rational")
 
         super().__init__(basis,
@@ -1832,7 +1836,7 @@ class RealEmbeddedMatrixEJA(MatrixEJA):
         # as a REAL matrix will be 2*a = 2*Re(z_1). And so forth.
         return (X*Y).trace()/cls.dimension_over_reals()
 
-class RealSymmetricEJA(ConcreteEJA, RationalBasisEJA, MatrixEJA):
+class RealSymmetricEJA(RationalBasisEJA, ConcreteEJA, MatrixEJA):
     """
     The rank-n simple EJA consisting of real symmetric n-by-n
     matrices, the usual symmetric Jordan product, and the trace inner
@@ -2114,7 +2118,7 @@ class ComplexMatrixEJA(RealEmbeddedMatrixEJA):
         return matrix(F, n/d, elements)
 
 
-class ComplexHermitianEJA(ConcreteEJA, RationalBasisEJA, ComplexMatrixEJA):
+class ComplexHermitianEJA(RationalBasisEJA, ConcreteEJA, ComplexMatrixEJA):
     """
     The rank-n simple EJA consisting of complex Hermitian n-by-n
     matrices over the real numbers, the usual symmetric Jordan product,
@@ -2416,8 +2420,8 @@ class QuaternionMatrixEJA(RealEmbeddedMatrixEJA):
         return matrix(Q, n/d, elements)
 
 
-class QuaternionHermitianEJA(ConcreteEJA,
-                             RationalBasisEJA,
+class QuaternionHermitianEJA(RationalBasisEJA,
+                             ConcreteEJA,
                              QuaternionMatrixEJA):
     r"""
     The rank-n simple EJA consisting of self-adjoint n-by-n quaternion
@@ -2586,7 +2590,7 @@ class QuaternionHermitianEJA(ConcreteEJA,
         n = ZZ.random_element(cls._max_random_instance_size() + 1)
         return cls(n, **kwargs)
 
-class OctonionHermitianEJA(ConcreteEJA, MatrixEJA):
+class OctonionHermitianEJA(RationalBasisEJA, ConcreteEJA, MatrixEJA):
     r"""
     SETUP::
 
@@ -2780,7 +2784,7 @@ class AlbertEJA(OctonionHermitianEJA):
 
     SETUP::
 
-        from mjo.eja.eja_algebra import AlbertEJA
+        sage: from mjo.eja.eja_algebra import AlbertEJA
 
     EXAMPLES::
 
@@ -2794,14 +2798,15 @@ class AlbertEJA(OctonionHermitianEJA):
         super().__init__(3, *args, **kwargs)
 
 
-class HadamardEJA(ConcreteEJA, RationalBasisEJA):
+class HadamardEJA(RationalBasisEJA, ConcreteEJA):
     """
-    Return the Euclidean Jordan Algebra corresponding to the set
-    `R^n` under the Hadamard product.
+    Return the Euclidean Jordan algebra on `R^n` with the Hadamard
+    (pointwise real-number multiplication) Jordan product and the
+    usual inner-product.
 
-    Note: this is nothing more than the Cartesian product of ``n``
-    copies of the spin algebra. Once Cartesian product algebras
-    are implemented, this can go.
+    This is nothing more than the Cartesian product of ``n`` copies of
+    the one-dimensional Jordan spin algebra, and is the most common
+    example of a non-simple Euclidean Jordan algebra.
 
     SETUP::
 
@@ -2832,7 +2837,6 @@ class HadamardEJA(ConcreteEJA, RationalBasisEJA):
 
         sage: HadamardEJA(3, prefix='r').gens()
         (r0, r1, r2)
-
     """
     def __init__(self, n, field=AA, **kwargs):
         if n == 0:
@@ -2886,7 +2890,7 @@ class HadamardEJA(ConcreteEJA, RationalBasisEJA):
         return cls(n, **kwargs)
 
 
-class BilinearFormEJA(ConcreteEJA, RationalBasisEJA):
+class BilinearFormEJA(RationalBasisEJA, ConcreteEJA):
     r"""
     The rank-2 simple EJA consisting of real vectors ``x=(x0, x_bar)``
     with the half-trace inner product and jordan product ``x*y =
@@ -3134,7 +3138,7 @@ class JordanSpinEJA(BilinearFormEJA):
         return cls(n, **kwargs)
 
 
-class TrivialEJA(ConcreteEJA, RationalBasisEJA):
+class TrivialEJA(RationalBasisEJA, ConcreteEJA):
     """
     The trivial Euclidean Jordan algebra consisting of only a zero element.