eja: turn the other simple EJA constructors into classes.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index fa112a373315c21f6b50e6b9edf9ced464923d55..32481621975ab3aabc217eae5ef72d9abf191980 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -133,7 +133,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
         EXAMPLES::
 
-            sage: J = RealSymmetricSimpleEJA(2)
+            sage: J = RealSymmetricEJA(2)
             sage: J.basis()
             Family (e0, e1, e2)
             sage: J.natural_basis()
@@ -181,14 +181,14 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             The identity in `S^n` is converted to the identity in the EJA::
 
-                sage: J = RealSymmetricSimpleEJA(3)
+                sage: J = RealSymmetricEJA(3)
                 sage: I = identity_matrix(QQ,3)
                 sage: J(I) == J.one()
                 True
 
             This skew-symmetric matrix can't be represented in the EJA::
 
-                sage: J = RealSymmetricSimpleEJA(3)
+                sage: J = RealSymmetricEJA(3)
                 sage: A = matrix(QQ,3, lambda i,j: i-j)
                 sage: J(A)
                 Traceback (most recent call last):
@@ -309,7 +309,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             so the inner product of the identity matrix with itself
             should be the `n`::
 
-                sage: J = RealSymmetricSimpleEJA(3)
+                sage: J = RealSymmetricEJA(3)
                 sage: J.one().inner_product(J.one())
                 3
 
@@ -318,13 +318,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             part because the product of Hermitian matrices may not be
             Hermitian::
 
-                sage: J = ComplexHermitianSimpleEJA(3)
+                sage: J = ComplexHermitianEJA(3)
                 sage: J.one().inner_product(J.one())
                 3
 
             Ditto for the quaternions::
 
-                sage: J = QuaternionHermitianSimpleEJA(3)
+                sage: J = QuaternionHermitianEJA(3)
                 sage: J.one().inner_product(J.one())
                 3
 
@@ -670,7 +670,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             EXAMPLES::
 
-                sage: J = ComplexHermitianSimpleEJA(3)
+                sage: J = ComplexHermitianEJA(3)
                 sage: J.one()
                 e0 + e5 + e8
                 sage: J.one().natural_representation()
@@ -683,7 +683,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             ::
 
-                sage: J = QuaternionHermitianSimpleEJA(3)
+                sage: J = QuaternionHermitianEJA(3)
                 sage: J.one()
                 e0 + e9 + e14
                 sage: J.one().natural_representation()
@@ -1086,9 +1086,9 @@ def random_eja():
     n = ZZ.random_element(1,5)
     constructor = choice([eja_rn,
                           JordanSpinEJA,
-                          RealSymmetricSimpleEJA,
-                          ComplexHermitianSimpleEJA,
-                          QuaternionHermitianSimpleEJA])
+                          RealSymmetricEJA,
+                          ComplexHermitianEJA,
+                          QuaternionHermitianEJA])
     return constructor(n, field=QQ)
 
 
@@ -1465,7 +1465,7 @@ def _matrix_ip(X,Y):
     return (X_mat*Y_mat).trace()
 
 
-def RealSymmetricSimpleEJA(n, field=QQ):
+class RealSymmetricEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """
     The rank-n simple EJA consisting of real symmetric n-by-n
     matrices, the usual symmetric Jordan product, and the trace inner
@@ -1473,7 +1473,7 @@ def RealSymmetricSimpleEJA(n, field=QQ):
 
     EXAMPLES::
 
-        sage: J = RealSymmetricSimpleEJA(2)
+        sage: J = RealSymmetricEJA(2)
         sage: e0, e1, e2 = J.gens()
         sage: e0*e0
         e0
@@ -1488,7 +1488,7 @@ def RealSymmetricSimpleEJA(n, field=QQ):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: J = RealSymmetricSimpleEJA(n)
+        sage: J = RealSymmetricEJA(n)
         sage: J.degree() == (n^2 + n)/2
         True
 
@@ -1496,7 +1496,7 @@ def RealSymmetricSimpleEJA(n, field=QQ):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: J = RealSymmetricSimpleEJA(n)
+        sage: J = RealSymmetricEJA(n)
         sage: x = J.random_element()
         sage: y = J.random_element()
         sage: actual = (x*y).natural_representation()
@@ -1509,17 +1509,23 @@ def RealSymmetricSimpleEJA(n, field=QQ):
         True
 
     """
-    S = _real_symmetric_basis(n, field=field)
-    (Qs, T) = _multiplication_table_from_matrix_basis(S)
+    @staticmethod
+    def __classcall_private__(cls, n, field=QQ):
+        S = _real_symmetric_basis(n, field=field)
+        (Qs, T) = _multiplication_table_from_matrix_basis(S)
 
-    return FiniteDimensionalEuclideanJordanAlgebra(field,
-                                                   Qs,
-                                                   rank=n,
-                                                   natural_basis=T,
-                                                   inner_product=_matrix_ip)
+        fdeja = super(RealSymmetricEJA, cls)
+        return fdeja.__classcall_private__(cls,
+                                           field,
+                                           Qs,
+                                           rank=n,
+                                           natural_basis=T)
+
+    def inner_product(self, x, y):
+        return _matrix_ip(x,y)
 
 
-def ComplexHermitianSimpleEJA(n, field=QQ):
+class ComplexHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """
     The rank-n simple EJA consisting of complex Hermitian n-by-n
     matrices over the real numbers, the usual symmetric Jordan product,
@@ -1532,7 +1538,7 @@ def ComplexHermitianSimpleEJA(n, field=QQ):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: J = ComplexHermitianSimpleEJA(n)
+        sage: J = ComplexHermitianEJA(n)
         sage: J.degree() == n^2
         True
 
@@ -1540,7 +1546,7 @@ def ComplexHermitianSimpleEJA(n, field=QQ):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: J = ComplexHermitianSimpleEJA(n)
+        sage: J = ComplexHermitianEJA(n)
         sage: x = J.random_element()
         sage: y = J.random_element()
         sage: actual = (x*y).natural_representation()
@@ -1553,26 +1559,30 @@ def ComplexHermitianSimpleEJA(n, field=QQ):
         True
 
     """
-    S = _complex_hermitian_basis(n)
-    (Qs, T) = _multiplication_table_from_matrix_basis(S)
+    @staticmethod
+    def __classcall_private__(cls, n, field=QQ):
+        S = _complex_hermitian_basis(n)
+        (Qs, T) = _multiplication_table_from_matrix_basis(S)
 
-    # Since a+bi on the diagonal is represented as
-    #
-    #   a + bi  = [  a  b  ]
-    #             [ -b  a  ],
-    #
-    # we'll double-count the "a" entries if we take the trace of
-    # the embedding.
-    ip = lambda X,Y: _matrix_ip(X,Y)/2
+        fdeja = super(ComplexHermitianEJA, cls)
+        return fdeja.__classcall_private__(cls,
+                                           field,
+                                           Qs,
+                                           rank=n,
+                                           natural_basis=T)
 
-    return FiniteDimensionalEuclideanJordanAlgebra(field,
-                                                   Qs,
-                                                   rank=n,
-                                                   natural_basis=T,
-                                                   inner_product=ip)
+    def inner_product(self, x, y):
+        # Since a+bi on the diagonal is represented as
+        #
+        #   a + bi  = [  a  b  ]
+        #             [ -b  a  ],
+        #
+        # we'll double-count the "a" entries if we take the trace of
+        # the embedding.
+        return _matrix_ip(x,y)/2
 
 
-def QuaternionHermitianSimpleEJA(n, field=QQ):
+class QuaternionHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """
     The rank-n simple EJA consisting of self-adjoint n-by-n quaternion
     matrices, the usual symmetric Jordan product, and the
@@ -1585,7 +1595,7 @@ def QuaternionHermitianSimpleEJA(n, field=QQ):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: J = QuaternionHermitianSimpleEJA(n)
+        sage: J = QuaternionHermitianEJA(n)
         sage: J.degree() == 2*(n^2) - n
         True
 
@@ -1593,7 +1603,7 @@ def QuaternionHermitianSimpleEJA(n, field=QQ):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: J = QuaternionHermitianSimpleEJA(n)
+        sage: J = QuaternionHermitianEJA(n)
         sage: x = J.random_element()
         sage: y = J.random_element()
         sage: actual = (x*y).natural_representation()
@@ -1606,33 +1616,30 @@ def QuaternionHermitianSimpleEJA(n, field=QQ):
         True
 
     """
-    S = _quaternion_hermitian_basis(n)
-    (Qs, T) = _multiplication_table_from_matrix_basis(S)
+    @staticmethod
+    def __classcall_private__(cls, n, field=QQ):
+        S = _quaternion_hermitian_basis(n)
+        (Qs, T) = _multiplication_table_from_matrix_basis(S)
 
-    # Since a+bi+cj+dk on the diagonal is represented as
-    #
-    #   a + bi +cj + dk = [  a  b  c  d]
-    #                     [ -b  a -d  c]
-    #                     [ -c  d  a -b]
-    #                     [ -d -c  b  a],
-    #
-    # we'll quadruple-count the "a" entries if we take the trace of
-    # the embedding.
-    ip = lambda X,Y: _matrix_ip(X,Y)/4
-
-    return FiniteDimensionalEuclideanJordanAlgebra(field,
-                                                   Qs,
-                                                   rank=n,
-                                                   natural_basis=T,
-                                                   inner_product=ip)
+        fdeja = super(QuaternionHermitianEJA, cls)
+        return fdeja.__classcall_private__(cls,
+                                           field,
+                                           Qs,
+                                           rank=n,
+                                           natural_basis=T)
 
+    def inner_product(self, x, y):
+        # Since a+bi+cj+dk on the diagonal is represented as
+        #
+        #   a + bi +cj + dk = [  a  b  c  d]
+        #                     [ -b  a -d  c]
+        #                     [ -c  d  a -b]
+        #                     [ -d -c  b  a],
+        #
+        # we'll quadruple-count the "a" entries if we take the trace of
+        # the embedding.
+        return _matrix_ip(x,y)/4
 
-def OctonionHermitianSimpleEJA(n):
-    """
-    This shit be crazy. It has dimension 27 over the reals.
-    """
-    n = 3
-    pass
 
 class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """