From 858aa3653fd2e4ae8573f472cf3f0d698072c185 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 21 Feb 2021 16:58:05 -0500
Subject: [PATCH] eja: factor out a separate class used by cartesian_product().

---
 mjo/eja/all.py         |  1 +
 mjo/eja/eja_algebra.py | 47 +++++++++++++++++++++---------------------
 2 files changed, 24 insertions(+), 24 deletions(-)

diff --git a/mjo/eja/all.py b/mjo/eja/all.py
index a3b524b..051bd48 100644
--- a/mjo/eja/all.py
+++ b/mjo/eja/all.py
@@ -3,6 +3,7 @@ All imports from mjo.eja modules.
 """
 
 from mjo.eja.eja_algebra import (BilinearFormEJA,
+                                 CartesianProductEJA,
                                  ComplexHermitianEJA,
                                  HadamardEJA,
                                  JordanSpinEJA,
diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 55b8207..1302ca1 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2742,9 +2742,7 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
 
     """
     def __init__(self, modules, **kwargs):
-        CombinatorialFreeModule_CartesianProduct.__init__(self,
-                                                          modules,
-                                                          **kwargs)
+        CombinatorialFreeModule_CartesianProduct.__init__(self, modules)
         field = modules[0].base_ring()
         if not all( J.base_ring() == field for J in modules ):
             raise ValueError("all factors must share the same base field")
@@ -2766,33 +2764,16 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         # some join of the EJA and Cartesian product
         # categories. There's no need to check the field since it
         # already came from an EJA. Likewise the axioms are guaranteed
-        # to be satisfied. We can't orthonormalize by default because
-        # there's no way to pass "orthonormalize=False" to
-        # cartesian_product(...) when the base ring is QQ and
-        # orthonormalizing would give us irrational entries.
-        #
-        # TODO: create a separate constructor that is capable of
-        # orthonormalizing and is only used by the cartesian_product()
-        # thingy.
+        # to be satisfied.
         FiniteDimensionalEJA.__init__(self,
                                       basis,
                                       jordan_product,
                                       inner_product,
                                       field=field,
-                                      orthonormalize=False,
                                       check_field=False,
                                       check_axioms=False,
-                                      category=self.category())
-        # TODO:
-        #
-        # Initialize the FDEJA class, too. Does this override the
-        # initialization that we did for the
-        # CombinatorialFreeModule_CartesianProduct class? If not, we
-        # will probably have to duplicate some of the work (i.e. one
-        # of the constructors).  Since the CartesianProduct one is
-        # smaller, that makes the most sense to copy/paste if it comes
-        # down to that.
-        #
+                                      category=self.category(),
+                                      **kwargs)
 
         self.rank.set_cache(sum(J.rank() for J in modules))
 
@@ -3059,5 +3040,23 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
     Element = FiniteDimensionalEJAElement
 
 
-FiniteDimensionalEJA.CartesianProduct = CartesianProductEJA
+class FiniteDimensionalEJA_CartesianProduct(CartesianProductEJA):
+    r"""
+    A wrapper around the :class:`CartesianProductEJA` class that gets
+    used by the ``cartesian_product`` functor. Its one job is to set
+    ``orthonormalize=False``, since ``cartesian_product()`` can't be
+    made to pass that option through. And if we try to orthonormalize
+    over the rationals, we get conversion errors. If you want a non-
+    standard Jordan product or inner product, or if you want to
+    orthonormalize the basis, use :class:`CartesianProductEJA`
+    directly.
+    """
+    def __init__(self, modules, **options):
+        CombinatorialFreeModule_CartesianProduct.__init__(self,
+                                                          modules,
+                                                          **options)
+        CartesianProductEJA.__init__(self, modules, orthonormalize=False)
+
+
+FiniteDimensionalEJA.CartesianProduct = FiniteDimensionalEJA_CartesianProduct
 random_eja = ConcreteEJA.random_instance
-- 
2.43.2