X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fhurwitz.py;h=10b308d2bfa602373e0924e390e7e10453eff221;hb=ba5106550a9a614c6b6f7a2941ddce91ab592934;hp=ccc8219b1a92036c6ac92f118339c160a885977b;hpb=d0c6baf5cd567617f96a2a598123052409b33c94;p=sage.d.git diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py index ccc8219..10b308d 100644 --- a/mjo/hurwitz.py +++ b/mjo/hurwitz.py @@ -306,22 +306,61 @@ class Octonions(CombinatorialFreeModule): class HurwitzMatrixAlgebraElement(MatrixAlgebraElement): + def conjugate_transpose(self): + r""" + Return the conjugate-transpose of this matrix. + + SETUP:: + + sage: from mjo.hurwitz import ComplexMatrixAlgebra + + EXAMPLES:: + + sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ) + sage: M = A([ [ I, 2*I], + ....: [ 3*I, 4*I] ]) + sage: M.conjugate_transpose() + +------+------+ + | -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() + for j in range(self.ncols())] + for i in range(self.nrows()) ] + return self.parent()._element_constructor_(entries) + def is_hermitian(self): r""" 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. return all( self[i,j] == self[j,i].conjugate() for i in range(self.nrows()) for j in range(self.ncols()) ) @@ -599,6 +638,32 @@ 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 FreeModule + d = len(self.entry_algebra_gens()) + V = FreeModule(self.entry_algebra().base_ring(), d) + return V(entry.coefficient_tuple()) class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): r""" @@ -650,11 +715,11 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra): sage: (I,) = A.entry_algebra().gens() sage: A([ [1+I, 1], ....: [-1, -I] ]) - +-------+----+ - | I + 1 | 1 | - +-------+----+ - | -1 | -I | - +-------+----+ + +---------+------+ + | 1 + 1*I | 1 | + +---------+------+ + | -1 | -1*I | + +---------+------+ :: @@ -679,3 +744,24 @@ 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 FreeModule + d = len(self.entry_algebra_gens()) + V = FreeModule(self.entry_algebra().base_ring(), d) + return V((entry.real(), entry.imag()))