From d0c6baf5cd567617f96a2a598123052409b33c94 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 8 Mar 2021 22:02:25 -0500 Subject: [PATCH] hurwitz: fix Hurwitz matrix algebra generators. --- mjo/hurwitz.py | 45 +++++++++++++++++++++++++++++++++++++++++++ mjo/matrix_algebra.py | 19 ++++++++++++++++-- 2 files changed, 62 insertions(+), 2 deletions(-) diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py index a1a6af0..ccc8219 100644 --- a/mjo/hurwitz.py +++ b/mjo/hurwitz.py @@ -440,6 +440,31 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra): +---------------------+ | 1.00000000000000*e0 | +---------------------+ + sage: A.gens() + (+---------------------+ + | 1.00000000000000*e0 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e1 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e2 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e3 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e4 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e5 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e6 | + +---------------------+, + +---------------------+ + | 1.00000000000000*e7 | + +---------------------+) :: @@ -519,6 +544,19 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): +-----+ | 1.0 | +-----+ + sage: A.gens() + (+-----+ + | 1.0 | + +-----+, + +---+ + | i | + +---+, + +---+ + | j | + +---+, + +---+ + | k | + +---+) :: @@ -598,6 +636,13 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): +------------------+ | 1.00000000000000 | +------------------+ + sage: A.gens() + (+------------------+ + | 1.00000000000000 | + +------------------+, + +--------------------+ + | 1.00000000000000*I | + +--------------------+) :: diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py index c38e855..d67347b 100644 --- a/mjo/matrix_algebra.py +++ b/mjo/matrix_algebra.py @@ -201,11 +201,15 @@ class MatrixAlgebra(CombinatorialFreeModule): I = range(n) J = range(n) self._entry_algebra = entry_algebra - entry_basis = entry_algebra.gens() + + # Needs to make the (overridden) method call when, for example, + # the entry algebra is the complex numbers and its gens() method + # lies to us. + entry_basis = self.entry_algebra_gens() basis_indices = [(i,j,e) for i in range(n) for j in range(n) - for e in entry_algebra.gens()] + for e in entry_basis] super().__init__(scalars, basis_indices, @@ -227,6 +231,17 @@ class MatrixAlgebra(CombinatorialFreeModule): """ return self._entry_algebra + def entry_algebra_gens(self): + r""" + Return a tuple of the generators of (that is, a basis for) the + entries of this matrix algebra. + + This can be overridden in subclasses to work around the + inconsistency in the ``gens()`` methods of the various + entry algebras. + """ + return self.entry_algebra().gens() + def nrows(self): return self._nrows ncols = nrows -- 2.43.2