From: Michael Orlitzky Date: Tue, 9 Mar 2021 16:02:04 +0000 (-0500) Subject: matrix_algebra: fix element construction. X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=a87cbac5c3e1f3a6422b2152609f8209676fb4cb;p=sage.d.git matrix_algebra: fix element construction. --- diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py index cad89ca..57f6578 100644 --- a/mjo/hurwitz.py +++ b/mjo/hurwitz.py @@ -312,19 +312,21 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement): SETUP:: - sage: from mjo.hurwitz import HurwitzMatrixAlgebra + sage: from mjo.hurwitz import ComplexMatrixAlgebra EXAMPLES:: - sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ) + sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ) sage: M = A([ [ I, 2*I], ....: [ 3*I, 4*I] ]) sage: M.conjugate_transpose() +------+------+ - | -1*I | -3*I | + | -I | -3*I | +------+------+ | -2*I | -4*I | +------+------+ + sage: M.conjugate_transpose().to_vector() + (0, -1, 0, -3, 0, -2, 0, -4) """ entries = [ [ self[j,i].conjugate() @@ -337,16 +339,25 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement): SETUP:: - sage: from mjo.hurwitz import HurwitzMatrixAlgebra + sage: from mjo.hurwitz import (ComplexMatrixAlgebra, + ....: HurwitzMatrixAlgebra) EXAMPLES:: - sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ) + sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ) sage: M = A([ [ 0,I], ....: [-I,0] ]) sage: M.is_hermitian() True + :: + + sage: A = HurwitzMatrixAlgebra(2, AA, QQ) + sage: M = A([ [1, 1], + ....: [1, 1] ]) + sage: M.is_hermitian() + True + """ # A tiny bit faster than checking equality with the conjugate # transpose. @@ -649,9 +660,9 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra): (0, 0, 0, 1) """ - from sage.modules.free_module import VectorSpace + from sage.modules.free_module import FreeModule d = len(self.entry_algebra_gens()) - V = VectorSpace(self.entry_algebra().base_ring(), d) + V = FreeModule(self.entry_algebra().base_ring(), d) return V(entry.coefficient_tuple()) class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): @@ -750,7 +761,7 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): (0, 1) """ - from sage.modules.free_module import VectorSpace + from sage.modules.free_module import FreeModule d = len(self.entry_algebra_gens()) - V = VectorSpace(self.entry_algebra().base_ring(), d) + V = FreeModule(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 8491f27..73286ff 100644 --- a/mjo/matrix_algebra.py +++ b/mjo/matrix_algebra.py @@ -205,8 +205,8 @@ class MatrixAlgebra(CombinatorialFreeModule): # lies to us. entry_basis = self.entry_algebra_gens() - basis_indices = [(i,j,e) for j in range(n) - for i in range(n) + basis_indices = [(i,j,e) for i in range(n) + for j in range(n) for e in entry_basis] super().__init__(scalars, @@ -300,9 +300,9 @@ class MatrixAlgebra(CombinatorialFreeModule): if hasattr(entry, 'to_vector'): return entry.to_vector() - from sage.modules.free_module import VectorSpace + from sage.modules.free_module import FreeModule d = len(self.entry_algebra_gens()) - V = VectorSpace(self.entry_algebra().base_ring(), d) + V = FreeModule(self.entry_algebra().base_ring(), d) if hasattr(entry, 'list'): # sage matrices @@ -345,13 +345,16 @@ class MatrixAlgebra(CombinatorialFreeModule): (i,j,e1) = mon1 (k,l,e2) = mon2 if j == k: - # If e1*e2 has a negative sign in front of it, - # then (i,l,e1*e2) won't be a monomial! - p = e1*e2 - if (i,l,p) in self.indices(): - return self.monomial((i,l,p)) - else: - return -self.monomial((i,l,-p)) + # There's no reason to expect e1*e2 to itself be a monomial, + # so we have to do some manual conversion to get one. + p = self._entry_algebra_element_to_vector(e1*e2) + + # We have to convert alpha_g because a priori it lives in the + # base ring of the entry algebra. + R = self.base_ring() + return self.sum( R(alpha_g)*self.monomial( (i,l,g) ) + for (alpha_g, g) + in zip(p, self.entry_algebra_gens())) else: return self.zero() @@ -362,17 +365,20 @@ class MatrixAlgebra(CombinatorialFreeModule): SETUP:: - sage: from mjo.matrix_algebra import MatrixAlgebra + sage: from mjo.hurwitz import ComplexMatrixAlgebra EXAMPLES:: - sage: A = MatrixAlgebra(2, QQbar, ZZ) - sage: A.from_list([[0,I],[-I,0]]) + sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ) + sage: M = A.from_list([[0,I],[-I,0]]) + sage: M +----+---+ | 0 | I | +----+---+ | -I | 0 | +----+---+ + sage: M.to_vector() + (0, 0, 0, 1, 0, -1, 0, 0) """ nrows = len(entries) @@ -400,10 +406,22 @@ class MatrixAlgebra(CombinatorialFreeModule): # Octonions(AA). return self.entry_algebra().from_vector(e_ij.to_vector()) - return sum( (self.monomial( (i,j, convert(entries[i][j])) ) - for i in range(nrows) - for j in range(ncols) ), - self.zero() ) + def entry_to_element(i,j,entry): + # Convert an entry at i,j to a matrix whose only non-zero + # entry is i,j and corresponds to the entry. + p = self._entry_algebra_element_to_vector(entry) + + # We have to convert alpha_g because a priori it lives in the + # base ring of the entry algebra. + R = self.base_ring() + return self.sum( R(alpha_g)*self.monomial( (i,j,g) ) + for (alpha_g, g) + in zip(p, self.entry_algebra_gens())) + + return self.sum( entry_to_element(i,j,entries[i][j]) + for j in range(ncols) + for i in range(nrows) ) + def _element_constructor_(self, elt): if elt in self: