From c1a571e4ac42dbc6949a06d43dca502563fd9096 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 26 Jul 2019 12:12:41 -0400
Subject: [PATCH] eja: new class
 FiniteDimensionalEuclideanJordanAlgebraMorphism.

This is the first step towards implementing left-multiplication
operators and quadratic-representations properly.
---
 mjo/eja/euclidean_jordan_algebra.py | 71 +++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 8bd10cc..fcaf100 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -11,6 +11,77 @@ from sage.structure.category_object import normalize_names
 
 from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra import FiniteDimensionalAlgebra
 from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement
+from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism import FiniteDimensionalAlgebraMorphism
+
+
+class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMorphism):
+    """
+    A very thin wrapper around FiniteDimensionalAlgebraMorphism that
+    does only two things:
+
+      1. Avoids the ``unitary`` and ``check`` arguments to the constructor
+         that will always be ``False``. This is necessary because these
+         are homomorphisms with respect to ADDITION, but the SageMath
+         machinery wants to check that they're homomorphisms with respect
+         to (Jordan) MULTIPLICATION. That obviously doesn't work.
+
+      2. Inputs and outputs the underlying matrix with respect to COLUMN
+         vectors, unlike the parent class.
+
+    If this seems a bit heavyweight, it is. I would have been happy to
+    use a the ring morphism that underlies the finite-dimensional
+    algebra morphism, but they don't seem to be callable on elements of
+    our EJA.
+    """
+    def __init__(self, parent, f):
+        FiniteDimensionalAlgebraMorphism.__init__(self,
+                                                  parent,
+                                                  f.transpose(),
+                                                  unitary=False,
+                                                  check=False)
+
+
+    def _repr_(self):
+        """
+        We override only the representation that is shown to the user,
+        because we want the matrix to be with respect to COLUMN vectors.
+
+        TESTS:
+
+        Ensure that we see the transpose of the underlying matrix object:
+
+            sage: J = RealSymmetricEJA(3)
+            sage: x = J.linear_combination(zip(range(len(J.gens())), J.gens()))
+            sage: L = x.operator()
+            sage: L
+            Morphism from Euclidean Jordan algebra of degree 6 over Rational
+            Field to Euclidean Jordan algebra of degree 6 over Rational Field
+            given by matrix
+            [  0   1   2   0   0   0]
+            [1/2 3/2   2 1/2   1   0]
+            [  1   2 5/2   0 1/2   1]
+            [  0   1   0   3   4   0]
+            [  0   1 1/2   2   4   2]
+            [  0   0   2   0   4   5]
+            sage: L._matrix
+            [  0 1/2   1   0   0   0]
+            [  1 3/2   2   1   1   0]
+            [  2   2 5/2   0 1/2   2]
+            [  0 1/2   0   3   2   0]
+            [  0   1 1/2   4   4   4]
+            [  0   0   1   0   2   5]
+
+        """
+        return "Morphism from {} to {} given by matrix\n{}".format(
+            self.domain(), self.codomain(), self.matrix())
+
+    def matrix(self):
+        """
+        Return the matrix of this morphism with respect to a left-action
+        on column vectors.
+        """
+        return FiniteDimensionalAlgebraMorphism.matrix(self).transpose()
+
 
 class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
     @staticmethod
-- 
2.44.2