From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 8 Dec 2020 15:43:38 +0000 (-0500)
Subject: eja: default to the identity IP matrix when orthonormalizing.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=82b8e49f8f8fae889a64c40139abcbaef71101af

eja: default to the identity IP matrix when orthonormalizing.
---

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 34f8801..9e808ae 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -158,7 +158,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         # Now we actually compute the multiplication and inner-product
         # tables/matrices using the possibly-orthonormalized basis.
-        self._inner_product_matrix = matrix.zero(field, n)
+        self._inner_product_matrix = matrix.identity(field, n)
         self._multiplication_table = [ [0 for j in range(i+1)]
                                        for i in range(n) ]
 
@@ -171,15 +171,20 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
                 q_i = basis[i]
                 q_j = basis[j]
 
-                elt = jordan_product(q_i, q_j)
-                ip = inner_product(q_i, q_j)
-
                 # The jordan product returns a matrixy answer, so we
                 # have to convert it to the algebra coordinates.
+                elt = jordan_product(q_i, q_j)
                 elt = W.coordinate_vector(V(elt.list()))
                 self._multiplication_table[i][j] = self.from_vector(elt)
-                self._inner_product_matrix[i,j] = ip
-                self._inner_product_matrix[j,i] = ip
+
+                if not orthonormalize:
+                    # If we're orthonormalizing the basis with respect
+                    # to an inner-product, then the inner-product
+                    # matrix with respect to the resulting basis is
+                    # just going to be the identity.
+                    ip = inner_product(q_i, q_j)
+                    self._inner_product_matrix[i,j] = ip
+                    self._inner_product_matrix[j,i] = ip
 
         self._inner_product_matrix._cache = {'hermitian': True}
         self._inner_product_matrix.set_immutable()