ó ¡¼™\c@ stdZddlmZmZddlmZddlmZdgZdefd„ƒYZ de_ d„e_ dS( sHermitian conjugation.iÿÿÿÿ(tprint_functiontdivision(tExpr(tadjointtDaggercB seZdZd„ZRS(sQGeneral Hermitian conjugate operation. Take the Hermetian conjugate of an argument [1]_. For matrices this operation is equivalent to transpose and complex conjugate [2]_. Parameters ========== arg : Expr The sympy expression that we want to take the dagger of. Examples ======== Daggering various quantum objects: >>> from sympy.physics.quantum.dagger import Dagger >>> from sympy.physics.quantum.state import Ket, Bra >>> from sympy.physics.quantum.operator import Operator >>> Dagger(Ket('psi')) >> Dagger(Bra('phi')) |phi> >>> Dagger(Operator('A')) Dagger(A) Inner and outer products:: >>> from sympy.physics.quantum import InnerProduct, OuterProduct >>> Dagger(InnerProduct(Bra('a'), Ket('b'))) >>> Dagger(OuterProduct(Ket('a'), Bra('b'))) |b>>> A = Operator('A') >>> B = Operator('B') >>> Dagger(A*B) Dagger(B)*Dagger(A) >>> Dagger(A+B) Dagger(A) + Dagger(B) >>> Dagger(A**2) Dagger(A)**2 Dagger also seamlessly handles complex numbers and matrices:: >>> from sympy import Matrix, I >>> m = Matrix([[1,I],[2,I]]) >>> m Matrix([ [1, I], [2, I]]) >>> Dagger(m) Matrix([ [ 1, 2], [-I, -I]]) References ========== .. [1] https://en.wikipedia.org/wiki/Hermitian_adjoint .. [2] https://en.wikipedia.org/wiki/Hermitian_transpose cC sqt|dƒr|jƒ}n3t|dƒrQt|dƒrQ|jƒjƒ}n|dk ra|Stj||ƒS(NRt conjugatet transpose(thasattrRRRtNoneRt__new__(tclstargtobj((s;lib/python2.7/site-packages/sympy/physics/quantum/dagger.pyR Os (t__name__t __module__t__doc__R (((s;lib/python2.7/site-packages/sympy/physics/quantum/dagger.pyR s@cC sd|j|jdƒS(Ns Dagger(%s)i(t_printtargs(tatb((s;lib/python2.7/site-packages/sympy/physics/quantum/dagger.pytYtN( Rt __future__RRt sympy.coreRt$sympy.functions.elementary.complexesRt__all__RR t _sympyrepr(((s;lib/python2.7/site-packages/sympy/physics/quantum/dagger.pyts K