From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 14 Jun 2019 14:20:05 +0000 (-0400)
Subject: WIP: euclidean jordan algebras.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=1067cbcb46e31220c619ff61e66c3b1c3386b86b;p=sage.d.git

WIP: euclidean jordan algebras.
---

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
new file mode 100644
index 0000000..5ccf2f2
--- /dev/null
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -0,0 +1,23 @@
+"""
+Euclidean Jordan Algebras. These are formally-real Jordan Algebras;
+specifically those where u^2 + v^2 = 0 implies that u = v = 0. They
+are used in optimization, and have some additional nice methods beyond
+what can be supported in a general Jordan Algebra.
+"""
+
+from sage.all import *
+
+def eja_rn(dimension, field=QQ):
+    """
+    Return the Euclidean Jordan Algebra corresponding to the set
+    `R^n` under the Hadamard product.
+    """
+    # The FiniteDimensionalAlgebra constructor takes a list of
+    # matrices, the ith representing right multiplication by the ith
+    # basis element in the vector space. So if e_1 = (1,0,0), then
+    # right (Hadamard) multiplication of x by e_1 picks out the first
+    # component of x; and likewise for the ith basis element e_i.
+    Qs = [ matrix(field, dimension, dimension, lambda k,j: 1*(k == j == i))
+           for i in xrange(dimension) ]
+    A = FiniteDimensionalAlgebra(QQ,Qs,assume_associative=True)
+    return JordanAlgebra(A)