From a2cfe216f45da307ed6d1f75ffaa9d48565dc33e Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 13 Nov 2020 10:23:49 -0500
Subject: [PATCH] eja: add inclusion maps for DirectSumEJA.

---
 mjo/eja/eja_algebra.py | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 3f91ee3..183e4cb 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2399,3 +2399,44 @@ class DirectSumEJA(FiniteDimensionalEuclideanJordanAlgebra):
         pi_left  = lambda x: J1.from_vector(x.to_vector()[:n])
         pi_right = lambda x: J2.from_vector(x.to_vector()[n:])
         return (pi_left, pi_right)
+
+    def inclusions(self):
+        r"""
+        Return the pair of inclusion maps from our factors into us.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  RealSymmetricEJA,
+            ....:                                  DirectSumEJA)
+
+        EXAMPLES::
+
+            sage: J1 = JordanSpinEJA(3)
+            sage: J2 = RealSymmetricEJA(2)
+            sage: J = DirectSumEJA(J1,J2)
+            sage: (iota_left, iota_right) = J.inclusions()
+            sage: iota_left(J1.zero()) == J.zero()
+            True
+            sage: iota_right(J2.zero()) == J.zero()
+            True
+            sage: J1.one().to_vector()
+            (1, 0, 0)
+            sage: iota_left(J1.one()).to_vector()
+            (1, 0, 0, 0, 0, 0)
+            sage: J2.one().to_vector()
+            (1, 0, 1)
+            sage: iota_right(J2.one()).to_vector()
+            (0, 0, 0, 1, 0, 1)
+            sage: J.one().to_vector()
+            (1, 0, 0, 1, 0, 1)
+
+        """
+        (J1,J2) = self.factors()
+        n = J1.dimension()
+        V_basis = self.vector_space().basis()
+        I1 = matrix.column(self.base_ring(), V_basis[:n])
+        I2 = matrix.column(self.base_ring(), V_basis[n:])
+        iota_left = lambda x: self.from_vector(I1*x.to_vector())
+        iota_right = lambda x: self.from_vector(I2*+x.to_vector())
+        return (iota_left, iota_right)
-- 
2.43.2