eja: turn the spin algebra constructor into a subclass.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 24eaf50f381fbab7107bf5f3512354c221148199..579be23b43cb05228991373550ffb599b46d1b7f 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -50,7 +50,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                                  inner_product=inner_product)
 
 
-    def __init__(self, field,
+    def __init__(self,
+                 field,
                  mult_table,
                  names='e',
                  assume_associative=False,
@@ -143,7 +144,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
         ::
 
-            sage: J = JordanSpinSimpleEJA(2)
+            sage: J = JordanSpinAlgebra(2)
             sage: J.basis()
             Family (e0, e1)
             sage: J.natural_basis()
@@ -295,7 +296,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             inner product on `R^n` (this example only works because the
             basis for the Jordan algebra is the standard basis in `R^n`)::
 
-                sage: J = JordanSpinSimpleEJA(3)
+                sage: J = JordanSpinAlgebra(3)
                 sage: x = vector(QQ,[1,2,3])
                 sage: y = vector(QQ,[4,5,6])
                 sage: x.inner_product(y)
@@ -390,12 +391,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             EXAMPLES::
 
-                sage: J = JordanSpinSimpleEJA(2)
+                sage: J = JordanSpinAlgebra(2)
                 sage: e0,e1 = J.gens()
                 sage: x = e0 + e1
                 sage: x.det()
                 0
-                sage: J = JordanSpinSimpleEJA(3)
+                sage: J = JordanSpinAlgebra(3)
                 sage: e0,e1,e2 = J.gens()
                 sage: x = e0 + e1 + e2
                 sage: x.det()
@@ -424,7 +425,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
                 sage: set_random_seed()
                 sage: n = ZZ.random_element(1,10)
-                sage: J = JordanSpinSimpleEJA(n)
+                sage: J = JordanSpinAlgebra(n)
                 sage: x = J.random_element()
                 sage: while x.is_zero():
                 ....:     x = J.random_element()
@@ -554,7 +555,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             The identity element always has degree one, but any element
             linearly-independent from it is regular::
 
-                sage: J = JordanSpinSimpleEJA(5)
+                sage: J = JordanSpinAlgebra(5)
                 sage: J.one().is_regular()
                 False
                 sage: e0, e1, e2, e3, e4 = J.gens() # e0 is the identity
@@ -579,7 +580,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             EXAMPLES::
 
-                sage: J = JordanSpinSimpleEJA(4)
+                sage: J = JordanSpinAlgebra(4)
                 sage: J.one().degree()
                 1
                 sage: e0,e1,e2,e3 = J.gens()
@@ -591,7 +592,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
                 sage: set_random_seed()
                 sage: n = ZZ.random_element(1,10)
-                sage: J = JordanSpinSimpleEJA(n)
+                sage: J = JordanSpinAlgebra(n)
                 sage: x = J.random_element()
                 sage: x == x.coefficient(0)*J.one() or x.degree() == 2
                 True
@@ -623,7 +624,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
                 sage: set_random_seed()
                 sage: n = ZZ.random_element(2,10)
-                sage: J = JordanSpinSimpleEJA(n)
+                sage: J = JordanSpinAlgebra(n)
                 sage: y = J.random_element()
                 sage: while y == y.coefficient(0)*J.one():
                 ....:     y = J.random_element()
@@ -783,7 +784,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
                 sage: set_random_seed()
                 sage: n = ZZ.random_element(1,10)
-                sage: J = JordanSpinSimpleEJA(n)
+                sage: J = JordanSpinAlgebra(n)
                 sage: x = J.random_element()
                 sage: x_vec = x.vector()
                 sage: x0 = x_vec[0]
@@ -930,7 +931,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: c = J.random_element().subalgebra_idempotent()
                 sage: c^2 == c
                 True
-                sage: J = JordanSpinSimpleEJA(5)
+                sage: J = JordanSpinAlgebra(5)
                 sage: c = J.random_element().subalgebra_idempotent()
                 sage: c^2 == c
                 True
@@ -986,7 +987,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             EXAMPLES::
 
-                sage: J = JordanSpinSimpleEJA(3)
+                sage: J = JordanSpinAlgebra(3)
                 sage: e0,e1,e2 = J.gens()
                 sage: x = e0 + e1 + e2
                 sage: x.trace()
@@ -1084,7 +1085,7 @@ def random_eja():
     """
     n = ZZ.random_element(1,5)
     constructor = choice([eja_rn,
-                          JordanSpinSimpleEJA,
+                          JordanSpinAlgebra,
                           RealSymmetricSimpleEJA,
                           ComplexHermitianSimpleEJA,
                           QuaternionHermitianSimpleEJA])
@@ -1633,7 +1634,7 @@ def OctonionHermitianSimpleEJA(n):
     n = 3
     pass
 
-def JordanSpinSimpleEJA(n, field=QQ):
+class JordanSpinAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
     """
     The rank-2 simple EJA consisting of real vectors ``x=(x0, x_bar)``
     with the usual inner product and jordan product ``x*y =
@@ -1644,7 +1645,7 @@ def JordanSpinSimpleEJA(n, field=QQ):
 
     This multiplication table can be verified by hand::
 
-        sage: J = JordanSpinSimpleEJA(4)
+        sage: J = JordanSpinAlgebra(4)
         sage: e0,e1,e2,e3 = J.gens()
         sage: e0*e0
         e0
@@ -1661,31 +1662,34 @@ def JordanSpinSimpleEJA(n, field=QQ):
         sage: e2*e3
         0
 
-    In one dimension, this is the reals under multiplication::
+    """
+    @staticmethod
+    def __classcall_private__(cls, n, field=QQ):
+        Qs = []
+        id_matrix = identity_matrix(field, n)
+        for i in xrange(n):
+            ei = id_matrix.column(i)
+            Qi = zero_matrix(field, n)
+            Qi.set_row(0, ei)
+            Qi.set_column(0, ei)
+            Qi += diagonal_matrix(n, [ei[0]]*n)
+            # The addition of the diagonal matrix adds an extra ei[0] in the
+            # upper-left corner of the matrix.
+            Qi[0,0] = Qi[0,0] * ~field(2)
+            Qs.append(Qi)
+
+        fdeja = super(JordanSpinAlgebra, cls)
+        return fdeja.__classcall_private__(cls, field, Qs)
 
-        sage: J1 = JordanSpinSimpleEJA(1)
-        sage: J2 = eja_rn(1)
-        sage: J1 == J2
-        True
+    def rank(self):
+        """
+        Return the rank of this Jordan Spin Algebra.
 
-    """
-    Qs = []
-    id_matrix = identity_matrix(field, n)
-    for i in xrange(n):
-        ei = id_matrix.column(i)
-        Qi = zero_matrix(field, n)
-        Qi.set_row(0, ei)
-        Qi.set_column(0, ei)
-        Qi += diagonal_matrix(n, [ei[0]]*n)
-        # The addition of the diagonal matrix adds an extra ei[0] in the
-        # upper-left corner of the matrix.
-        Qi[0,0] = Qi[0,0] * ~field(2)
-        Qs.append(Qi)
-
-    # The rank of the spin factor algebra is two, UNLESS we're in a
-    # one-dimensional ambient space (the rank is bounded by the
-    # ambient dimension).
-    return FiniteDimensionalEuclideanJordanAlgebra(field,
-                                                   Qs,
-                                                   rank=min(n,2),
-                                                   inner_product=_usual_ip)
+        The rank of the spin algebra is two, unless we're in a
+        one-dimensional ambient space (because the rank is bounded by
+        the ambient dimension).
+        """
+        return min(self.dimension(),2)
+
+    def inner_product(self, x, y):
+        return _usual_ip(x,y)