+
+ @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])
+
+