+  ‡i´ ãó`€Rt^RIHtHt^RIHtR.t!RR]4tR]nR]n R#)zHermitian conjugation.)ÚExprÚsympify)ÚadjointÚDaggercó>a€]tRt^ toRt]R4tRRltRtVt R#)raùGeneral Hermitian conjugate operation. Explanation =========== 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. evaluate : bool Whether the resulting expression should be directly evaluated. 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 c ó<€VP^,P#)zHFind the kind of a dagger of something (just the kind of the something).)ÚargsÚkind)Úselfs&Ú|/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/physics/quantum/dagger.pyr Ú Dagger.kindRs€ðy‰y˜|× Ñ Ð ócó*€\VR4'dV'dVP4#\VR4'd9\VR4'd'V'dVP4P4#\P !V\ V44#)rÚ conjugateÚ transpose)ÚhasattrrrrrÚ__new__r)ÚclsÚargÚevaluates&&&r rÚDagger.__new__Wsb€Ü 3˜ × "Ò "§xØ—;‘;“=Ð Ü S˜+× &Ò &¬7°3¸ ×+DÒ+DÏØ—=‘=“?×,Ñ,Ó.Ð .Ü|Š|˜C¤¨£Ó.Ð.r ©N)T) Ú__name__Ú __module__Ú __qualname__Ú__firstlineno__Ú__doc__Úpropertyr rÚ__static_attributes__Ú__classdictcell__)Ú __classdict__s@r rr s*ø‡€ñDðLñ!óð!÷/ò/r cóT€RVPVP^,4,#)z Dagger(%s))Ú_printr)ÚaÚbs&&r Úr%_s€ ,°·±¸!¿&¹&À½)Ó1DÖ"Dr N) rÚ sympy.corerrÚ$sympy.functions.elementary.complexesrÚ__all__rrÚ _sympyreprrr r Úr*s;ðÙç$Ý8ð ð €ô Q/ˆWôQ/ðf€ÔÙD€Ör