From 4bca351aed81d3ee621b530e7e802122b08bd2a6 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 22 Nov 2020 10:50:19 -0500
Subject: [PATCH] eja: cache the unit element immediately where it is known.

---
 mjo/eja/eja_algebra.py | 28 +++++++++++++++++++++++++++-
 1 file changed, 27 insertions(+), 1 deletion(-)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ec692e4..e436bf1 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -588,6 +588,16 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             sage: actual == expected
             True
 
+        Ensure that the cached unit element (often precomputed by
+        hand) agrees with the computed one::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: cached = J.one()
+            sage: J.one.clear_cache()
+            sage: J.one() == cached
+            True
+
         """
         # We can brute-force compute the matrices of the operators
         # that correspond to the basis elements of this algebra.
@@ -1108,7 +1118,8 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
         # time to ensure that it isn't a generator expression.
         basis = tuple(basis)
 
-        if len(basis) > 1 and normalize_basis:
+        algebra_dim = len(basis)
+        if algebra_dim > 1 and normalize_basis:
             # We'll need sqrt(2) to normalize the basis, and this
             # winds up in the multiplication table, so the whole
             # algebra needs to be over the field extension.
@@ -1129,6 +1140,14 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
                                                            natural_basis=basis,
                                                            **kwargs)
 
+        if algebra_dim == 0:
+            self.one.set_cache(self.zero())
+        else:
+            n = basis[0].nrows()
+            # The identity wrt (A,B) -> (AB + BA)/2 is independent of the
+            # details of this algebra.
+            self.one.set_cache(self(matrix.identity(field,n)))
+
 
     @cached_method
     def _charpoly_coefficients(self):
@@ -2051,6 +2070,7 @@ class HadamardEJA(RationalBasisEuclideanJordanAlgebra):
                                           check_axioms=False,
                                           **kwargs)
         self.rank.set_cache(n)
+        self.one.set_cache( sum(self.gens()) )
 
     @staticmethod
     def _max_random_instance_size():
@@ -2191,6 +2211,11 @@ class BilinearFormEJA(RationalBasisEuclideanJordanAlgebra):
                                               **kwargs)
         self.rank.set_cache(min(n,2))
 
+        if n == 0:
+            self.one.set_cache( self.zero() )
+        else:
+            self.one.set_cache( self.monomial(0) )
+
     @staticmethod
     def _max_random_instance_size():
         return 5
@@ -2354,6 +2379,7 @@ class TrivialEJA(FiniteDimensionalEuclideanJordanAlgebra):
         # The rank is zero using my definition, namely the dimension of the
         # largest subalgebra generated by any element.
         self.rank.set_cache(0)
+        self.one.set_cache( self.zero() )
 
     @classmethod
     def random_instance(cls, field=AA, **kwargs):
-- 
2.44.2