From bc418347d7267c8eaee6f3989db000b2f3b77165 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 8 Dec 2020 21:34:54 -0500
Subject: [PATCH] eja: factor out the complex/quaternion extension fields.

---
 mjo/eja/eja_algebra.py | 75 +++++++++++++++++++++++++++++-------------
 1 file changed, 53 insertions(+), 22 deletions(-)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 5deb5c9..58d5ce0 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1667,6 +1667,38 @@ class RealSymmetricEJA(ConcreteEJA, RealMatrixEJA):
 
 
 class ComplexMatrixEJA(MatrixEJA):
+    # A manual dictionary-cache for the complex_extension() method,
+    # since apparently @classmethods can't also be @cached_methods.
+    _complex_extension = {}
+
+    @classmethod
+    def complex_extension(cls,field):
+        r"""
+        The complex field that we embed/unembed, as an extension
+        of the given ``field``.
+        """
+        if field in cls._complex_extension:
+            return cls._complex_extension[field]
+
+        # Sage doesn't know how to adjoin the complex "i" (the root of
+        # x^2 + 1) to a field in a general way. Here, we just enumerate
+        # all of the cases that I have cared to support so far.
+        if field is AA:
+            # Sage doesn't know how to embed AA into QQbar, i.e. how
+            # to adjoin sqrt(-1) to AA.
+            F = QQbar
+        elif not field.is_exact():
+            # RDF or RR
+            F = field.complex_field()
+        else:
+            # Works for QQ and... maybe some other fields.
+            R = PolynomialRing(field, 'z')
+            z = R.gen()
+            F = field.extension(z**2 + 1, 'I', embedding=CLF(-1).sqrt())
+
+        cls._complex_extension[field] = F
+        return F
+
     @staticmethod
     def dimension_over_reals():
         return 2
@@ -1763,26 +1795,7 @@ class ComplexMatrixEJA(MatrixEJA):
         super(ComplexMatrixEJA,cls).real_unembed(M)
         n = ZZ(M.nrows())
         d = cls.dimension_over_reals()
-
-        # If "M" was normalized, its base ring might have roots
-        # adjoined and they can stick around after unembedding.
-        field = M.base_ring()
-        R = PolynomialRing(field, 'z')
-        z = R.gen()
-
-        # Sage doesn't know how to adjoin the complex "i" (the root of
-        # x^2 + 1) to a field in a general way. Here, we just enumerate
-        # all of the cases that I have cared to support so far.
-        if field is AA:
-            # Sage doesn't know how to embed AA into QQbar, i.e. how
-            # to adjoin sqrt(-1) to AA.
-            F = QQbar
-        elif not field.is_exact():
-            # RDF or RR
-            F = field.complex_field()
-        else:
-            # Works for QQ and... maybe some other fields.
-            F = field.extension(z**2 + 1, 'I', embedding=CLF(-1).sqrt())
+        F = cls.complex_extension(M.base_ring())
         i = F.gen()
 
         # Go top-left to bottom-right (reading order), converting every
@@ -1951,6 +1964,25 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
         return cls(n, **kwargs)
 
 class QuaternionMatrixEJA(MatrixEJA):
+
+    # A manual dictionary-cache for the quaternion_extension() method,
+    # since apparently @classmethods can't also be @cached_methods.
+    _quaternion_extension = {}
+
+    @classmethod
+    def quaternion_extension(cls,field):
+        r"""
+        The quaternion field that we embed/unembed, as an extension
+        of the given ``field``.
+        """
+        if field in cls._quaternion_extension:
+            return cls._quaternion_extension[field]
+
+        Q = QuaternionAlgebra(field,-1,-1)
+
+        cls._quaternion_extension[field] = Q
+        return Q
+
     @staticmethod
     def dimension_over_reals():
         return 4
@@ -2055,8 +2087,7 @@ class QuaternionMatrixEJA(MatrixEJA):
 
         # Use the base ring of the matrix to ensure that its entries can be
         # multiplied by elements of the quaternion algebra.
-        field = M.base_ring()
-        Q = QuaternionAlgebra(field,-1,-1)
+        Q = cls.quaternion_extension(M.base_ring())
         i,j,k = Q.gens()
 
         # Go top-left to bottom-right (reading order), converting every
-- 
2.44.2