From c4a42bd7c60a34353f481f86caeef3f1d1019754 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 2 Feb 2022 13:43:53 -0500
Subject: [PATCH] hurwitz.py: speed up conjugate() and conjugate_transpose().

...by staying as close to the underlying monomial dict as possible.
---
 mjo/hurwitz.py | 66 ++++++++++++++++++++++++++++++++++++++++++++------
 1 file changed, 58 insertions(+), 8 deletions(-)

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index 614804f..07eace6 100644
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -319,11 +319,21 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
             | -3*I | -4*I     |
             +------+----------+
 
+        ::
+
+            sage: A = ComplexMatrixAlgebra(2, QQbar, QQ)
+            sage: M = A([ [ 1, 2],
+            ....:         [ 3, 4] ])
+            sage: M.conjugate() == M
+            True
+            sage: M.to_vector()
+            (1, 0, 2, 0, 3, 0, 4, 0)
+
         """
-        entries = [ [ self[i,j].conjugate()
-                      for j in range(self.ncols())]
-                    for i in range(self.nrows()) ]
-        return self.parent()._element_constructor_(entries)
+        d = self.monomial_coefficients()
+        A = self.parent()
+        new_terms = ( A._conjugate_term((k,v)) for (k,v) in d.items() )
+        return self.parent().sum_of_terms(new_terms)
 
     def conjugate_transpose(self):
         r"""
@@ -348,10 +358,11 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
             (0, -1, 0, -3, 0, -2, 0, -4)
 
         """
-        entries = [ [ self[j,i].conjugate()
-                      for j in range(self.ncols())]
-                    for i in range(self.nrows()) ]
-        return self.parent()._element_constructor_(entries)
+        d = self.monomial_coefficients()
+        A = self.parent()
+        new_terms = ( A._conjugate_term( ((k[1],k[0],k[2]), v) )
+                      for (k,v) in d.items() )
+        return self.parent().sum_of_terms(new_terms)
 
     def is_hermitian(self):
         r"""
@@ -467,6 +478,45 @@ class HurwitzMatrixAlgebra(MatrixAlgebra):
 
         super().__init__(n, entry_algebra, scalars, **kwargs)
 
+
+    @staticmethod
+    def _conjugate_term(t):
+        r"""
+        Conjugate the given ``(index, coefficient)`` term, returning
+        another such term.
+
+        Given a term ``((i,j,e), c)``, it's straightforward to
+        conjugate the entry ``e``, but if ``e``-conjugate is ``-e``,
+        then the resulting ``((i,j,-e), c)`` is not a term, since
+        ``(i,j,-e)`` is not a monomial index! So when we build a sum
+        of these conjugates we can wind up with a nonsense object.
+
+        This function handles the case where ``e``-conjugate is
+        ``-e``, but nothing more complicated. Thus it makes sense in
+        Hurwitz matrix algebras, but not more generally.
+
+        SETUP::
+
+            sage: from mjo.hurwitz import ComplexMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+            sage: M = A([ [ I,   1 + 2*I],
+            ....:         [ 3*I,     4*I] ])
+            sage: t = list(M.monomial_coefficients().items())[1]
+            sage: t
+            ((1, 0, I), 3)
+            sage: A._conjugate_term(t)
+            ((1, 0, I), -3)
+
+        """
+        if t[0][2].conjugate() == t[0][2]:
+            return t
+        else:
+            return (t[0], -t[1])
+
+
     def entry_algebra_gens(self):
         r"""
         Return a tuple of the generators of (that is, a basis for) the
-- 
2.44.2