From f721f283cea741c54e4a2b26d63094dd6c396c6a Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Tue, 9 Mar 2021 10:15:48 -0500 Subject: [PATCH] matrix_algebra: add _entry_algebra_element_to_vector() method. --- mjo/hurwitz.py | 47 +++++++++++++++++++++++++++ mjo/matrix_algebra.py | 75 +++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 122 insertions(+) diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py index e280034..cad89ca 100644 --- a/mjo/hurwitz.py +++ b/mjo/hurwitz.py @@ -627,6 +627,32 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): entry_algebra = QuaternionAlgebra(scalars,-1,-1) super().__init__(n, entry_algebra, scalars, **kwargs) + def _entry_algebra_element_to_vector(self, entry): + r""" + + SETUP:: + + sage: from mjo.hurwitz import QuaternionMatrixAlgebra + + EXAMPLES:: + + sage: A = QuaternionMatrixAlgebra(2) + sage: u = A.entry_algebra().one() + sage: A._entry_algebra_element_to_vector(u) + (1, 0, 0, 0) + sage: i,j,k = A.entry_algebra().gens() + sage: A._entry_algebra_element_to_vector(i) + (0, 1, 0, 0) + sage: A._entry_algebra_element_to_vector(j) + (0, 0, 1, 0) + sage: A._entry_algebra_element_to_vector(k) + (0, 0, 0, 1) + + """ + from sage.modules.free_module import VectorSpace + d = len(self.entry_algebra_gens()) + V = VectorSpace(self.entry_algebra().base_ring(), d) + return V(entry.coefficient_tuple()) class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): r""" @@ -707,3 +733,24 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): from sage.rings.all import QQbar entry_algebra = QQbar super().__init__(n, entry_algebra, scalars, **kwargs) + + def _entry_algebra_element_to_vector(self, entry): + r""" + + SETUP:: + + sage: from mjo.hurwitz import ComplexMatrixAlgebra + + EXAMPLES:: + + sage: A = ComplexMatrixAlgebra(2, QQbar, QQ) + sage: A._entry_algebra_element_to_vector(QQbar(1)) + (1, 0) + sage: A._entry_algebra_element_to_vector(QQbar(I)) + (0, 1) + + """ + from sage.modules.free_module import VectorSpace + d = len(self.entry_algebra_gens()) + V = VectorSpace(self.entry_algebra().base_ring(), d) + return V((entry.real(), entry.imag())) diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py index 84aa8d2..8491f27 100644 --- a/mjo/matrix_algebra.py +++ b/mjo/matrix_algebra.py @@ -240,6 +240,81 @@ class MatrixAlgebra(CombinatorialFreeModule): """ return self.entry_algebra().gens() + def _entry_algebra_element_to_vector(self, entry): + r""" + Return a vector representation (of length equal to the cardinality + of :meth:`entry_algebra_gens`) of the given ``entry``. + + This can be overridden in subclasses to work around the fact that + real numbers, complex numbers, quaternions, et cetera, all require + different incantations to turn them into a vector. + + It only makes sense to "guess" here in the superclass when no + subclass that overrides :meth:`entry_algebra_gens` exists. So + if you have a special subclass for your annoying entry algebra, + override this with the correct implementation there instead of + adding a bunch of awkward cases to this superclass method. + + SETUP:: + + sage: from mjo.hurwitz import Octonions + sage: from mjo.matrix_algebra import MatrixAlgebra + + EXAMPLES: + + Real numbers:: + + sage: A = MatrixAlgebra(1, AA, QQ) + sage: A._entry_algebra_element_to_vector(AA(17)) + (17) + + Octonions:: + + sage: A = MatrixAlgebra(1, Octonions(), QQ) + sage: e = A.entry_algebra_gens() + sage: A._entry_algebra_element_to_vector(e[0]) + (1, 0, 0, 0, 0, 0, 0, 0) + sage: A._entry_algebra_element_to_vector(e[1]) + (0, 1, 0, 0, 0, 0, 0, 0) + sage: A._entry_algebra_element_to_vector(e[2]) + (0, 0, 1, 0, 0, 0, 0, 0) + sage: A._entry_algebra_element_to_vector(e[3]) + (0, 0, 0, 1, 0, 0, 0, 0) + sage: A._entry_algebra_element_to_vector(e[4]) + (0, 0, 0, 0, 1, 0, 0, 0) + sage: A._entry_algebra_element_to_vector(e[5]) + (0, 0, 0, 0, 0, 1, 0, 0) + sage: A._entry_algebra_element_to_vector(e[6]) + (0, 0, 0, 0, 0, 0, 1, 0) + sage: A._entry_algebra_element_to_vector(e[7]) + (0, 0, 0, 0, 0, 0, 0, 1) + + Sage matrices:: + + sage: MS = MatrixSpace(QQ,2) + sage: A = MatrixAlgebra(1, MS, QQ) + sage: A._entry_algebra_element_to_vector(MS([[1,2],[3,4]])) + (1, 2, 3, 4) + + """ + if hasattr(entry, 'to_vector'): + return entry.to_vector() + + from sage.modules.free_module import VectorSpace + d = len(self.entry_algebra_gens()) + V = VectorSpace(self.entry_algebra().base_ring(), d) + + if hasattr(entry, 'list'): + # sage matrices + return V(entry.list()) + + # This works in AA, and will crash if it doesn't know what to + # do, and that's fine because then I don't know what to do + # either. + return V((entry,)) + + + def nrows(self): return self._nrows ncols = nrows -- 2.44.2