From 3b8bb4b76e19f857da235759ca413a6ff8d48f71 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 26 Jan 2022 07:41:16 -0500
Subject: [PATCH] hurwitz.py: add is_skew_hermitian() method.

---
 mjo/hurwitz.py | 40 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index ff84b51..43ed8f2 100644
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -359,6 +359,46 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
                     for j in range(self.ncols()) )
 
 
+    def is_skew_hermitian(self):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.hurwitz import (ComplexMatrixAlgebra,
+            ....:                          HurwitzMatrixAlgebra)
+
+        EXAMPLES::
+
+            sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+            sage: M = A([ [ 0,I],
+            ....:         [-I,1] ])
+            sage: M.is_skew_hermitian()
+            False
+
+        ::
+
+            sage: A = HurwitzMatrixAlgebra(2, AA, QQ)
+            sage: M = A([ [1, 1],
+            ....:         [1, 1] ])
+            sage: M.is_skew_hermitian()
+            False
+
+        ::
+
+            sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+            sage: M = A([ [2*I   ,  1 + I],
+            ....:         [-1 + I, -2*I] ])
+            sage: M.is_skew_hermitian()
+            True
+
+        """
+        # A tiny bit faster than checking equality with the conjugate
+        # transpose.
+        return all( self[i,j] == -self[j,i].conjugate()
+                    for i in range(self.nrows())
+                    for j in range(self.ncols()) )
+
+
 class HurwitzMatrixAlgebra(MatrixAlgebra):
     r"""
     A class of matrix algebras whose entries come from a Hurwitz
-- 
2.43.2