o
    GZhùÀ  ã                   @   sð  d dl mZ d dlmZ d dlmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z% d dl&m'Z' d dl(m)Z)m*Z* d dl+m,Z,m-Z- d dl.m/Z/ d dl0m1Z1m2Z2m3Z3 d d	l4m5Z5 d d
l6m7Z7 d dl8m9Z9 d dl:m;Z;m<Z< d dl=m>Z> dd Z?dd Z@dd ZAdd ZBdd ZCdd ZDdd ZEdd ZFdd ZGd d! ZHd"d# ZId$d% ZJd&d' ZKd(d) ZLe;d*d+ ZMd,d- ZNd.d/ ZOd0d1 ZPd2d3 ZQd4d5 ZRd6d7 ZSd8d9 ZTd:d; ZUd<d= ZVd>d? ZWd@dA ZXdBdC ZYdDdE ZZdFdG Z[dHdI Z\dJdK Z]dLdM Z^dNdO Z_dPdQ Z`dRdS ZadTdU ZbdVdW ZcdXdY ZddZd[ Zed\d] Zfd^d_ Zgd`da Zhdbdc Ziddde Zjdfdg Zkdhdi Zldjdk Zmdldm Zndndo Zodpdq Zpdrds Zqdtdu Zrdvdw Zsdxdy Ztdzd{ Zud|S )}é    )Ú	conjugate)Úexp)!ÚDaggerÚBdÚVarBosonicBasisÚBBraÚBÚBKetÚFixedBosonicBasisÚ
matrix_repÚapply_operatorsÚInnerProductÚ
CommutatorÚKroneckerDeltaÚAnnihilateBosonÚCreateBosonÚBosonicOperatorÚFÚFdÚFKetÚ
BosonStateÚCreateFermionÚAnnihilateFermionÚevaluate_deltasÚAntiSymmetricTensorÚcontractionÚNOÚwicksÚPermutationOperatorÚsimplify_index_permutationsÚ_sort_anticommuting_fermionsÚ_get_ordered_dummiesÚsubstitute_dummiesÚFockStateBosonKetÚ ContractionAppliesOnlyToFermions)ÚSum)ÚFunctionÚexpand)ÚIÚRational)ÚS)ÚDummyÚSymbolÚsymbols)Úsqrt)Úsrepr)Úsimplify)ÚslowÚraises)Úlatexc                  C   s°  t d\} }}}ttd\}}}}t}|| | || || ¡|| ||  ks,J || | || |¡|||  ks?J || | || ¡|| ksOJ || || || || ||||  || ||  || || || ||  ||||  || ||  }	|| ||||g}
t|	|
|| |||| ||  || || || ksºJ t|| |dksÅJ t d\}}t|||dksÖJ d S )Núp,q,r,sZfghizP(pq)zp1,p2zP(p_{1}p_{2}))r-   Úmapr&   r   Zget_permutedr   r3   )ÚpÚqÚrÚsÚfÚgÚhÚiÚPÚexprZpermsÚp1Úp2© rB   úS/var/www/auris/lib/python3.10/site-packages/sympy/physics/tests/test_secondquant.pyÚtest_PermutationOperator   s(   2& ÿþý2ÿrD   c                  C   sV  t d\} }}}t dtd\}}}}ttd\}}	t}
|| |||||| || }t||
| |g|
| ||| ||| ks@J |
| |t|| ||| }|| |||||| || }t||
| |g}|t|ksmJ || |||||| || }t||
| |g}|t|ksJ || ||||	|| || }t||
| |g}||ks©J d S )Núa b c dúp q r s©ÚclsZfg)r-   r+   r5   r&   r   r   r"   )ÚaÚbÚcÚdr6   r7   r8   r9   r:   r;   r>   r?   ÚexpectedÚresultrB   rB   rC   Ú$test_index_permutations_with_dummies/   s(   ÿÿrO   c                  C   sè  t d\} }}}tddksJ tddksJ tdt dt ks$J ttjt d ttdd d ks8J tt|gt|gksFJ ttdt	dksRJ tt	dtdks^J tt|t	|ksjJ tt	|t|ksvJ ttdtd t	dt	d ksJ t|| t|t| ksJ tt|t| t	|t	| ks®J tt|d	 tt|d	 ksÀJ td
tt
d
ksÌJ ttd
t
d
ksØJ ttdt tdt ksèJ t| t| ksòJ d S )Núi,j,n,mé   g      ð?é   éþÿÿÿg      @éÿÿÿÿr   é
   rI   )r-   r   r(   r*   ÚHalfr)   r	   r   r   r   r,   r   r   )r=   ÚjÚnÚmrB   rB   rC   Útest_daggerK   s$   (( ($ rZ   c                  C   sP   t d\} }t| }|j| ksJ |jsJ td}|jdks!J |jr&J d S )Núi,jrQ   )r-   r   ÚstateZis_symbolic)r=   rW   ÚorB   rB   rC   Útest_operator`   s   
r^   c                  C   sÐ   t d\} }}}}t| }t|dksJ tt|dksJ t|ts&J | | |¡}| t¡|hks6J td}| t	|g¡t
|d t	|d g ksQJ t|}| t	|g¡|t	|g ksfJ d S )Nú
i,j,n,m,p1z{b^\dagger_{i}}z{b^\dagger_{p_{1}}}r   rQ   )r-   r   r3   Ú
isinstancer   ÚsubsÚatomsr,   Úapply_operatorr	   r.   ©r=   rW   rX   rY   r@   r]   rB   rB   rC   Útest_createj   s   .&re   c                  C   sÌ   t d\} }}}}t| }t|dksJ tt|dksJ t|ts&J | | |¡}| t¡|hks6J td}| t	|g¡t
|t	|d g ksOJ t|}| t	|g¡|t	|g ksdJ d S )Nr_   zb_{i}z	b_{p_{1}}r   rQ   )r-   r   r3   r`   r   ra   rb   r,   rc   r	   r.   rd   rB   rB   rC   Útest_annihilatex   s   *&rf   c                  C   s  t d\} }}}tg d¢}t|dksJ |jd ttdks#J | d¡tg d¢ks0J | d¡tg d¢ks=J tdD ]} | | ¡ | ¡|ksOJ qA| d¡dksYJ tdD ]
} ||  | ksgJ q]t||g}| d¡t|d |gks}J | d¡t|d |gksJ d S )	NrP   )r   rQ   rR   é   é   é   r   )rQ   rQ   rR   rg   rh   rh   )r   rQ   rR   rg   rg   rQ   )r-   r   ÚlenÚargsÚtupleÚrangeÚupZdown)r=   rW   rX   rY   r9   rB   rB   rC   Útest_basic_state   s   "ro   c                  C   sx   t d} tdt| g }t|t| t| d g ksJ tdt| g }t|t| d t| d g ks:J d S )NrX   r   rQ   )r-   r   r	   r   r.   r   )rX   ÚerB   rB   rC   Útest_basic_apply   s
   "*rq   c                  C   s   t d\} }tdtd td td }t|t| |g }t| t|d  d|   td|  d| g }t|t|ksBJ d S )Nún,mr   rQ   rT   )r-   r   r   r   r	   r.   r'   )rX   rY   r]   rp   ZanswerrB   rB   rC   Útest_complex_apply   s
    0rs   c                  C   sD   t d} tdtd }t|t| g }|| t| g ks J d S )NrX   r   )r-   r   r   r   r	   )rX   r]   rp   rB   rB   rC   Útest_number_operator§   s   rt   c                  C   s   t d\} }}}tdg}tdg}t|t|dksJ t||dks&J t| |g}t||g}t||}|t| |t|| ksEJ d S )Núi,j,k,lr   rQ   )r-   r   r	   r   r   r   )r=   rW   ÚkÚlÚs1Ús2r8   rB   rB   rC   Útest_inner_product®   s   


 rz   c                  C   sZ   t d\} }t| g}t|g}td}t|| | }|t|t| |d  ks+J d S )Nrr   r   rQ   )r-   r   r	   r   r   r.   r   )rX   rY   rx   ry   r]   rp   rB   rB   rC   Útest_symbolic_matrix_elementsº   s   

"r{   c                  C   s   t d} td}t|| }tdD ]}|||d f t|d ks#J qtd}t|| }tdD ]}||d |f t|d ksCJ q1d S )Nri   r   rh   rQ   )r   r   r   rm   r.   r   )rJ   r]   rY   r=   rB   rB   rC   Útest_matrix_elementsÃ   s   
"
"ÿr|   c                  C   s   t dd} |  d¡}|tdksJ |  |¡dksJ |  d¡| d ks&J t| dks.J t| dks6J t| dks>J t| dksFJ d S )NrR   rQ   )rQ   rQ   rg   z9[FockState((2, 0)), FockState((1, 1)), FockState((0, 2))])r
   r\   r#   Úindexrj   ÚstrÚreprr/   )rJ   r\   rB   rB   rC   Útest_fixed_bosonic_basisÏ   s   

r   c                  C   s   t d\} }t| t|  | tj  }t|| ddf}|jdd}tdd}t||}g d¢}t	t
|D ]}|| |||f ksCJ q5d S )	Nrr   r   ri   F)ÚdeeprR   é   )rQ   rR   rg   rg   rh   ri   rh   ri   r   é   ri   r   r   é   é	   r   r   r   r   rU   é   )r-   r   r   r*   rV   r%   Údoitr
   r   rm   rj   )rX   rY   Zh_nÚHr]   rJ   Zdiagr=   rB   rB   rC   Útest_shoÜ   s   

ÿr   c                  C   s0  t ddd\} }ttdtd}|dksJ ttdtd}|dks&J tt| td}|t| dks8J ttdtd}|dksGJ ttdtd}tt|t| g }|t| gksdJ ttdtd}tt|t| |g }|dksJ tt|t	|}|ddt
t	|t|   ksJ tt	|t|}| ¡ ddt
t	|t|   ks·J t}t dd	d
\}}}|||||dksÎJ |||||dksÚJ |||||dksæJ t ddd\}}	}
}t ddd\}}}}t d\}}}}t}|t	|t|dt
t|t	|  ksJ |t	|	t
t	|t| jdd||	| t	| ks<J |t	|t| t	|t|	 jdddksVJ tt|t	|}t ||¡dksjJ tt	|t| t	|t|	 }t|dksJ t|dksJ t|dksJ d S )Nrr   T©Úabove_fermir   rQ   rT   rR   zX,Y,ZF)Zcommutativeru   ©Úbelow_fermiúa,b,c,dr4   rS   )r   z8\left[{a^\dagger_{a}} a_{i},{a^\dagger_{b}} a_{j}\right]zWCommutator(CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j))zM[CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j)])r-   r   r   r   r   r0   r   r	   r   r   r   r'   r   Úevalr3   r   r~   )rX   rY   rK   rp   ÚCÚXÚYÚZr=   rW   rv   rw   rI   rJ   rL   r6   r7   r8   r9   ÚDÚc1rB   rB   rC   Útest_commutationë   sJ   $(0@4"r   c                  C   s   t d\} }}}t| }t|tsJ | | |¡}| t¡|hks#J td}| t|g¡td|gks7J | t|g¡t|dg ksHJ t|}| tg ¡t|gksZJ tg dd}|tg ddksjJ t ddd\} }}}t ddd	\}}	}
}t d
\}}}}t d}t|  t| ||gd¡t||gdks J t| t| |	|gd¡t|| |	|gdksžJ t	t
| |¡|t| ksÉJ tt|dksÓJ tt|dksÝJ tt|dksçJ tt|dksñJ tt|| gddksþJ tt|| |	|gddksJ d S )NrP   rQ   rh   )Zfermi_levelru   Tr   r   r   r4   r@   zCreateFermion(p)zCreateFermion(Symbol('p'))z{a^\dagger_{p}}z{a^\dagger_{p_{1}}}z(\left|\left( a, \  i\right)\right\ranglerR   z4\left|\left( a, \  b, \  i, \  j\right)\right\rangle)r-   r   r`   r   ra   rb   r,   rc   r   r   r   r   r   r/   r3   )r=   rW   rX   rY   r]   Zvacuumrv   rw   rI   rJ   rK   rL   r6   r7   r8   r9   r@   rB   rB   rC   Útest_create_f  s2    ",0"$r   c                  C   sò  t d\} }}}t| }t|tsJ | | |¡}| t¡|hks#J td}| td|g¡t|gks7J | t|dg¡t|g ksHJ t|}| t|g¡tg ksZJ t ddd\} }}}t ddd\}}}	}
t d\}}}}t d	}t|  t| ||gd
¡dksJ t| t| ||gd
¡dksJ t| t| ||gd¡dks­J t| t| ||gd
¡t|| ||gd
ksÅJ t	t|dksÏJ t
t|dksÙJ tt|dksãJ tt|dksíJ tt|dks÷J d S )NrP   rQ   ru   Tr   r   r   r4   r@   rh   r   rg   zf(p)zAnnihilateFermion(p)zAnnihilateFermion(Symbol('p'))za_{p}z	a_{p_{1}})r-   r   r`   r   ra   rb   r,   rc   r   r~   r   r/   r3   )r=   rW   rX   rY   r]   rv   rw   rI   rJ   rK   rL   r6   r7   r8   r9   r@   rB   rB   rC   Útest_annihilate_f8  s.    """"0r   c                  C   sª   t d\} }}}t| }t|tsJ | | |¡}| t¡|hks#J td}| t|g¡t	|d t|d g ks>J t|}| t|g¡|t|g ksSJ d S )NrP   r   rQ   )
r-   r   r`   r   ra   rb   r,   rc   r	   r.   ©r=   rW   rX   rY   r]   rB   rB   rC   Útest_create_bT  s   .&r   c                  C   sR   t d\} }}}t| }t|tsJ | | |¡}| t¡|hks#J td}d S )NrP   r   )r-   r   r`   r   ra   rb   r,   r   rB   rB   rC   Útest_annihilate_b`  s   r   c                  C   sP  t ddd\} }}}t| t| }t|tt| t| t| | ks'J t| t| }t|tt| t| ks?J t| t| t| t| }t|}tt| |t|| t| |t| t|  t||t|  t|  t| |t| t|  t| t| t| t|  }||ksJ | | |  ¡ t| | | ks®J ||  | d  ¡ t||  | d ksÄJ t ddt	d\}}}	}
t ddt	d\}}}}t d	t	d
\} }}}tt|tt|t|  t| tt|t| t| t| t||tt|t|   ksJ tt|tt|t| t|	  t| tt|t| t| t|	 t| t||tt|t| t|	   ks`J tt|tt|t|	  t|
 }|t||	 tt|t|
  t||
tt|t|	   t||	t||
  t||
tt|t|	   tt|t| t|	 t|
  ksÃJ tt|tt|t|  t| }|t|| tt|t|  t||tt|t|   t||t||  t||tt|t|   tt|t| t| t|  ks&J d S )Nr4   Tr   rR   úi j k l©r   rH   rE   ©r   rH   rF   rG   )
r-   r   r   r   r   r   r   r   r'   r+   )r6   r7   r8   r9   r~   ZnstrZfasitr=   rW   rv   rw   rI   rJ   rK   rL   r?   rB   rB   rC   Ú
test_wicksi  st   *  ÿþýüÿ$,&"ÿ
ÿ.*$ÿ
ÿ(ÿþý"ü
ÿ(ÿþý"üÿr   c                     s  t ddd\} }}}t ddd\}}}}t dtd\ }}	tt t t|t|  tt t tt|t|  ksFJ tt| tt|t|  tt| t| t| ksfJ tddksnJ t| | ksvJ tt|t| t|t|  tt|t| t| tt|t| t|  ksŠJ tt|t|  ¡ t|t| ksŒJ tt|t|   ¡ t|t|  ksÒJ tt t  t t|t|  ¡tt|t tt| t  ksþJ tt t  tt|t|  ¡tt t| tt t|   ks+J tt t  ¡ }
t|
t|
ksBJ tt|t| tt|t|  ksZJ tt|t|  t| t| }t| 	¡ }|d	dgks{J t| 
¡ }|d
dgksJ tt|t|  }|jdksJ |jdks€J t|dks­J t|dks¶J t|dks¿J tt fdd d S )Nr   Tr   rE   r   rF   rG   rQ   r   rg   rR   rT   z#:CreateFermion(a)*CreateFermion(i):z%NO(CreateFermion(a)*CreateFermion(i))z.\left\{{a^\dagger_{a}} {a^\dagger_{i}}\right\}c                      s   t t t S ©N)r   r   r   rB   ©r6   r7   rB   rC   Ú<lambda>Ã  s    ztest_NO.<locals>.<lambda>)r-   r+   r   r   r   Z_remove_bracketsra   r   ÚlistZiter_q_creatorsZiter_q_annihilatorsZhas_q_creatorsZhas_q_annihilatorsr~   r   r3   r2   ÚNotImplementedError)r=   rW   rv   rw   rI   rJ   rK   rL   r8   r9   r?   ÚnoÚl1Úl2rB   r¡   rC   Útest_NO  sN   "&ÿÿ"ÿÿ,,*&ÿ*&
ÿ0$rš   c                  C   sl  t ddd\} }t ddd\}}t d\}}tt|t|gt|t|gdfks,J tt|t|gt|t|gdfksBJ tt|t| gt|t| gdfksXJ tt| t|gt|t| gdfksnJ tt|t| gt|t| gdfksJ tt| t|gt|t| gdfksJ tt|t| gt| t|gdfks°J tt| t|gt| t|gdfksÆJ tt|t| gt| t|gdfksÜJ tt| t|gt| t|gdfksòJ tt|t|gt|t|gdfks	J tt|t|gt|t|gdfks J tt|t|gt|t|gdfks7J tt|t|gt|t|gdfksNJ tt|t|gt|t|gdfkseJ tt|t|gt|t|gdfks|J tt|t|gt|t|gdfksJ tt|t|gt|t|gdfksªJ tt| t|gt| t|gdfksÁJ tt|t| gt| t|gdfksØJ tt|t| gt|t| gdfksïJ tt| t|gt|t| gdfksJ tt|t| gt| t|gdfksJ tt| t|gt| t|gdfks4J d S )	Nr[   Tr   za,br   zp,qr   rQ   )r-   r    r   r   )r=   rW   rI   rJ   r6   r7   rB   rB   rC   Útest_sortingÆ  s6   ,,,,,,,,,,.............2r©   c                     sX  t ddd\} }}}t ddd\ }}t d\}}}}	tt| t|t| |ks,J tt tt ks<J tt t| dksIJ tt t| dksVJ tt| t dkscJ tt| t dkspJ tt| t|t| |ksJ ttt|t|}
|
jsJ ttt|t|}
|
js J tt	 fdd	 d S )
Nru   Tr   r   r   r4   r   c                      s   t t tS r    )r   r   r   rB   ©rI   rJ   rB   rC   r¢   û  s    z"test_contraction.<locals>.<lambda>)
r-   r   r   r   r   r   Zis_only_below_fermiZis_only_above_fermir2   r$   )r=   rW   rv   rw   rK   rL   r6   r7   r8   r9   ÚrestrrB   rª   rC   Útest_contractionì  s      

r¬   c                  C   s*  t d\} }}t| |t|| }t|t| |ksJ t| dt|| }t|t| dt|| ks6J td|t|| }t|td|ksKJ t|dt|| }t|td|ks`J t| dt| | t|d }t|dkswJ td| td| td| td| }t|dksJ d S )Nzi,j,kr   rQ   rR   )r-   r   r   )r=   rW   rv   r8   rB   rB   rC   Útest_evaluate_deltasþ  s"    ÿÿr­   c                  C   sô  t ddtd\} }}}t ddtd\}}}}t d\}}	}
}t}|d||f| |f|d||f| |f ks7J |d||f| |f|d||f|| fksMJ |d||f| |f|d||f|| f ksdJ |d||f| |fdksrJ |d||f| | fdksJ |d|||f| |f|d|||f| |f ksJ |d|||f| ||f|d|||f| ||fks³J |d||f| |f}| |¡sÄJ | |¡sËJ | | ¡sÒJ | |¡sÙJ | ||¡|d||f| |fksëJ d	|  | |¡d	|d||f||f ksJ |jtdksJ t|d
ksJ t|dksJ |d||f| |f ||¡|d||f| |fks9J |d|| f||f ||¡|d|| f||fksTJ t d\}}}}td||f||f}t|dksoJ t|dksxJ d S )Nr   Tr   rE   r   rF   Útr   rR   z{t^{ab}_{ij}}zt((_a, _b),(_i, _j))zalpha1:5Úuz1{u^{\alpha_{1}\alpha_{2}}_{\alpha_{3}\alpha_{4}}}z$u((alpha1, alpha2),(alpha3, alpha4)))	r-   r+   r   Úhasra   Úsymbolr,   r3   r~   )r=   rW   rv   rw   rI   rJ   rK   rL   r6   r7   r8   r9   ÚATZtabijZa1Za2Úa3Za4Zu_alpha1234rB   rB   rC   Útest_Tensors  s6   .,.24$.66rŽ   c                  C   s(  t ddd\} }}}t ddd\}}}}t dtd\}}	}
}td|f|	ftt|t|	  }td	||	f|
|ftt|t|	 t| t|
  d
 }ttt| t| | ddd}|td|f| fkskJ ttt| t| t| t| | ddd}|td	||f| |fksJ d S )Nr   Tr   rE   r   rF   rG   r:   Úvrh   )Zkeep_only_fully_contractedZsimplify_kronecker_deltas)r-   r+   r   r   r   r   r   )r=   rW   rv   rw   rI   rJ   rK   rL   r6   r7   r8   r9   ZFockÚVZFaiZVabijrB   rB   rC   Útest_fully_contracted8  s*   ÿ"ÿÿþ(þ r·   c                  C   sX   t d\} }tt| |d t| |d ksJ tt| |d t| |d ks*J d S )Nr[   rR   rQ   )r-   r"   Úatt©r=   rW   rB   rB   rC   Ú'test_substitute_dummies_without_dummiesL  s   $(rº   c                  C   s\   t dtd\} }tt| |tt| t|  t|| tt|t|    dks,J d S ©Núi jrG   r   )r-   r+   r"   rž   r   r   r   r¹   rB   rB   rC   Ú#test_substitute_dummies_NO_operatorR  s   ÿÿrœ   c                  C   sT   t dtd\} }tt| |t|  t| t|| t| t|   dks(J d S r»   )r-   r+   r"   rž   r   r   r¹   rB   rB   rC   Ú#test_substitute_dummies_SQ_operatorX  s   ÿÿrŸ   c                  C   sh   t ddtd\} }t ddtd\}}t dtd\}}td}t|| |||||| dd	d
ks2J d S )NrŒ   Tr   úa br   úp qrG   r:   )Znew_indicesr   )r-   r+   r&   r"   )r=   rW   rI   rJ   r6   r7   r:   rB   rB   rC   Ú#test_substitute_dummies_new_indices^  s
   ,rÁ   c                  C   sh   t ddtd\} }}}td}ddlm} || |||gdD ]}t|| || ||| dks1J qd S )Nr   Tr   r:   r   ©Ú
variationsrh   )r-   r+   r&   Úsympy.utilities.iterablesrÃ   r"   )r=   rW   rv   rw   r:   rÃ   ÚpermutrB   rB   rC   Ú*test_substitute_dummies_substitution_orderf  s   $ÿrÆ   c                  C   sB  t ddd} t ddd}t ddtd\}}t ddtd	\}}td
}td}t}||||||||  ||| ||| ||||||||  ||| ||| ||||||||  ||| ||| ||||||||  ||| ||| g}	|	dd  D ]}
||	d ||
ksJ t|	d t|
ksJ qd S )Nr=   Tr   rI   r   úk lr   úc dr   rµ   r®   rQ   r   ©r-   r+   r&   r!   r"   )ÚiiÚaarv   rw   rK   rL   rµ   r®   ÚdumsÚexprsrÅ   rB   rB   rC   Ú*test_dummy_order_inner_outer_lines_VT1T1T1n  s    ****úþrÎ   c                  C   sª  t ddd\} }t ddd\}}t ddtd\}}t ddtd	\}}td
}td}	t}
||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| g}|dd  D ]}|
|d |
|ksªJ t|d t|ks¶J q||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| g}|dd  D ]}|
|d |
|ks6J t|d t|ksCJ q'||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| g}|dd  D ]}|
|d |
|ksÄJ t|d t|ksÑJ qµd S ©NrŒ   Tr   r¿   r   rÇ   r   rÈ   r   rµ   r®   rQ   r   rÉ   ©rÊ   ÚjjrË   Úbbrv   rw   rK   rL   rµ   r®   rÌ   rÍ   rÅ   rB   rB   rC   Ú,test_dummy_order_inner_outer_lines_VT1T1T1T1  s@   4444ú4
444ô4444ù	þrÓ   c                  C   sÀ   t d\} }}tt| t| t|  d¡tt| t| ks$J tt| t| t|  d¡tt|t| ksAJ tt| t| t|  d¡tt| t| ks^J d S )Nzp,q,rrQ   r   rR   )r-   r   r   Z	get_subNO)r6   r7   r8   rB   rB   rC   Útest_get_subNOŒ  s   ::>rÔ   c                  C   sÂ  t ddtd\} }}}t ddtd\}}}}td}td}	t}
|| ||||	||  |	|| ||| |||	||  |	|| || ||||	||  |	|| g}|dd  D ]}|
|d	 |
|ksfJ t|d	 t|ksrJ qX|| ||||	||  |	|| ||| |||	||  |	|| g}|dd  D ]}|
|d	 |
|ks©J t|d	 t|ksµJ q|| ||||	||  |	|| || ||||	||  |	|| g}|dd  D ]}|
|d	 |
|ksìJ t|d	 t|ksøJ qÞ|| ||||	||  |	|| ||| |||	|| |	||  || ||||	||  |	|| ||| |||	|| |	||  g}|dd  D ]}|
|d	 |
|ksPJ t|d	 t|ks]J qAd S ©
Nr   Tr   rE   r   rµ   r®   rQ   r   rÉ   ©r=   rW   rv   rw   rI   rJ   rK   rL   rµ   r®   rÌ   rÍ   rÅ   rB   rB   rC   Ú$test_equivalent_internal_lines_VT1T1Ã  sB      ý  þ  þ    üþr×   c                  C   s(  t ddtd\} }}}}}t ddtd\}}}}	}
}t ddtd\}}}}t ddtd\}}}}dd	lm} td
}td}t}||||||||| | || ||| }|||||	gd}| t||||gt|¡}|D ]$}t||||g|}| |¡}||||ksJ t	|t	|ksJ qn||||||||||  ||| || }|||||	gd}| t||||gt|¡}|D ]$}t||||g|}| |¡}||||ksÛJ t	|t	|ksåJ qÁ||||||||| | ||| || }|||||	gd}| t||||gt|¡}|D ]'}t||||g|}| |¡}||||ks/J t	|t	|ks:J q||||||||||  || ||| }|||||	gd}| t||||gt|¡}|D ]'}t||||g|}| |¡}||||ksJ t	|t	|ksJ qjd S ©Núi j k l m nTr   úa b c d e fr   úp1 p2 p3 p4úh1 h2 h3 h4r   rÂ   rµ   r®   rh   ©
r-   r+   rÄ   rÃ   r&   r!   ra   ÚzipÚnextr"   ©r=   rW   rv   rw   rY   rX   rI   rJ   rK   rL   rp   r:   r@   rA   Úp3Úp4Úh1Úh2Úh3Úh4rÃ   rµ   r®   rÌ   ÚtemplateÚ
permutatorÚbaserÅ   Úsubslistr?   rB   rB   rC   Ú(test_equivalent_internal_lines_VT2conjT2ï  sR   *
*
*
*
ürë   c                  C   sÐ  t ddtd\} }}}}}t ddtd\}}}}	}
}t ddtd\}}}}t ddtd\}}}}dd	lm} td
}td}t}||||||||| | |||| | }|||||	gd}| t||||gt|¡}|D ]$}t||||g|}| |¡}||||ksJ t	|t	|ksJ qn||||||||||  |||| | }|||||	gd}| t||||gt|¡}|D ]$}t||||g|}| |¡}||||ksÛJ t	|t	|ksåJ qÁd S rØ   rÝ   rà   rB   rB   rC   Ú8test_equivalent_internal_lines_VT2conjT2_ambiguous_order!  s2   *
*
ürì   c               	   C   sT  t ddtd\} }}}t ddtd\}}}}td}td}	t}
|| ||||	||| | ||| |||	||| | || ||||	||| | ||| |||	||| | g}|dd  D ]}|
|d	 |
|ksjJ t|d	 t|ksvJ q\|| ||||	||| | || ||||	||| | || ||||	||||  || ||||	||||  g}|dd  D ]}|
|d	 |
|ksÁJ t|d	 t|ksÍJ q³|| ||||	||| | ||| |||	||||  || ||||	||| | ||| |||	||||  g}|dd  D ]}|
|d	 |
|ksJ t|d	 t|ks&J q
d S rÕ   rÉ   rÖ   rB   rB   rC   Ú"test_equivalent_internal_lines_VT2B  s<   òûüþrí   c               	   C   s  t ddd\} }t ddd\}}t ddtd\}}t ddtd	\}}td
}td}	t}
||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| g}|dd  D ]}|
|d |
|ksJ t|d t|ksJ q||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| g}|dd  D ]}|
|d |
|ksJ t|d t|ksJ q÷||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| g}|dd  D ]}|
|d |
|ks{J t|d t|ksJ qld S rÏ   rÉ   rÐ   rB   rB   rC   Útest_internal_external_VT2T2s  s@   ((((ü((((ü((((üþrî   c               	   C   s6  t d\} }t d\}}t dtd\}}t dtd\}}td}td}	t}
||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| g}|dd  D ]}|
|d	 |
|ksJ t|d	 t|ksJ q~d S )
NrŒ   r¿   rÇ   rG   rÈ   rµ   r®   rQ   r   rÉ   rÐ   rB   rB   rC   Útest_internal_external_pqrs  s    ((((üþrï   c                  C   sL  t ddd\} }t ddtd\}}}t ddtd\}}t dtd	\}}td
}	td}
td}t}||	|||
|| ||gksCJ ||	|||
|| ||gksUJ ||	|||
|| ||gksgJ ||	|||
|| ||gksyJ ||	|||
|| ||| |||gksJ ||	|||
|| ||| |||gks©J ||	|||
|| ||| |||gksÁJ ||	|||
|| ||| |||gksÙJ ||	|||
|| ||| |||gksñJ ||	|||
|| ||| |||gks
J ||	|||
|| ||| |||gks#J ||	|||
|| ||| |||gks<J ||	|| ||	||| |	||| |||gksXJ ||	|| ||	||| |	||| |||gkstJ ||	|| ||	||| |	||| |||gksJ ||	|| ||	||| |	||| |||gks¬J ||	|| ||	||| |	||| |||gksÈJ ||	|| ||	||| |	||| |||gksäJ ||	|| ||	||| |	||| |||gks J ||	|| ||	||| |	||| |||gksJ ||	||||
||| |||gks2J ||	||||
||| |||gksHJ ||	||||
||| |||gks^J ||	||||
||| |||gkstJ ||	||||
||| |||gksJ ||	||||
||| |||gks J ||
||||	||| |||gks¶J ||
||||	||| |||gksÌJ ||
||||	||| |||gksâJ ||
||||	||| |||gksøJ ||
||||	||| |||gksJ ||
||||	||| |||gks$J d S )Nr¿   Tr   zk l mr   rÈ   r   rÀ   rG   ÚAr   r   )r-   r+   r&   r!   )rË   rÒ   rv   rw   rY   rK   rL   r6   r7   rð   r   r   rÌ   rB   rB   rC   Útest_dummy_order_well_defined¯  sP   $$$$0000022288888888,,,,,,,,,,,0rñ   c            '      C   s¢  t ddd\} }t ddtd\}}}}}t ddtd\}}}	}
}t dtd	\}}t d
dtd\}}}}t ddtd\}}}}t ddtd\}}}}t ddtd\}}}}td}td}ddlm}  |||||| ||| ||| ||| }!| |||	|
|gd}"|! t|||||gt|"¡}#|"D ]}$t|||||g|$}%|! |%¡}&t|&t|#ks±J q|||||| ||| ||| ||| }!| |||	|
|gd}"|! t|||||gt|"¡}#|"D ]}$t|||||g|$}%|! |%¡}&t|&t|#ksJ qæ|||||||||| ||| }!| |||	|
|gd}"|! t|||||gt|"¡}#|"D ]}$t|||||g|$}%|! |%¡}&t|&t|#ksMJ q1d S )Nr¿   Tr   z	i j k l mr   z	a b c d er   rÀ   rG   rÛ   zp5 p6 p7 p8rÜ   zh5 h6 h7 h8rð   r   r   rÂ   ri   )	r-   r+   r&   rÄ   rÃ   ra   rÞ   rß   r"   )'rË   rÒ   r=   rW   rv   rw   rY   rI   rJ   rK   rL   rp   r6   r7   r@   rA   rá   râ   Zp5Zp6Zp7Zp8rã   rä   rå   ræ   Zh5Zh6Zh7Zh8rð   r   rÃ   rç   rè   ré   rÅ   rê   r?   rB   rB   rC   Útest_dummy_order_ambiguousç  sB   2
2
&
ýrò   c                  G   s   t d| d d | dd  S )Nrµ   rR   )r   ©rk   rB   rB   rC   Úatv  s   rô   c                  G   sP   t | dkrtd| d d | dd  S t | dkr&td| d f| d fS d S )Nrh   r®   rR   r   rQ   )rj   r   ró   rB   rB   rC   rž     s
   ÿrž   c                  C   s  t ddd} t ddd}t ddtd\}}t ddtd	\}}t||||t||  t|| t|| t||||t||  t|| t|| t||||t||  t|| t|| t||||t||  t|| t|| g}|d
d  D ]}t|d t|ksJ qzd S )Nr=   Tr   rI   r   rÇ   r   rÈ   r   rQ   r   ©r-   r+   rô   rž   r"   )rÊ   rË   rv   rw   rK   rL   rÍ   rÅ   rB   rB   rC   Ú-test_dummy_order_inner_outer_lines_VT1T1T1_AT  s   ****úÿrö   c            
      C   sª  t ddd\} }t ddd\}}t ddtd\}}t ddtd	\}}t||||t||  t|| t|| t|| t||||t|| t||  t|| t|| t||||t||  t|| t|| t|| g}|d
d  D ]}	t|d t|	 ksJ qxt||||t||  t|| t|| t|| t||||t|| t||  t|| t|| g}|d
d  D ]}	t|d t|	ksÒJ qÄd S ©NrŒ   Tr   r¿   r   rÇ   r   rÈ   r   rQ   r   rõ   ©
rÊ   rÑ   rË   rÒ   rv   rw   rK   rL   rÍ   rÅ   rB   rB   rC   Ú/test_dummy_order_inner_outer_lines_VT1T1T1T1_AT1  s    444ü44ýÿrù   c            
      C   sL  t ddtd\} }}}t ddtd\}}}}t| |||t||  t|| t|| ||t||  t|| t| |||t||  t|| g}|dd  D ]}	t|d t|	ks\J qNt| |||t||  t|| t|| ||t||  t|| g}|dd  D ]}	t|d t|	ksJ qt| |||t||  t|| t| |||t||  t|| g}|dd  D ]}	t|d t|	ksÊJ qŒt| |||t||  t|| t|| ||t|| t||  t| |||t||  t|| t|| ||t|| t||  g}|dd  D ]}	t|d t|	ks"J qd S ©Nr   Tr   rE   r   rQ   r   rõ   ©
r=   rW   rv   rw   rI   rJ   rK   rL   rÍ   rÅ   rB   rB   rC   Ú'test_equivalent_internal_lines_VT1T1_ATL  s4      ý  þ  þ    üÿrü   c                  C   sŸ  t ddtd\} }}}}}t ddtd\}}}}	}
}t ddtd\}}}}t ddtd\}}}}dd	lm} t||||t||| | t| ||| }|||||	gd
}| t||||gt|¡}|D ]}t||||g|}| |¡}t	|t	|ks~J qdt||||t||||  t|| || }|||||	gd
}| t||||gt|¡}|D ]}t||||g|}| |¡}t	|t	|ksÇJ q­t||||t||| | t|| || }|||||	gd
}| t||||gt|¡}|D ]}t||||g|}| |¡}t	|t	|ksJ qöt||||t||||  t| ||| }|||||	gd
}| t||||gt|¡}|D ]}t||||g|}| |¡}t	|t	|ks[J q@d S ©NrÙ   Tr   rÚ   r   rÛ   rÜ   r   rÂ   rh   ©
r-   r+   rÄ   rÃ   rô   rž   ra   rÞ   rß   r"   ©r=   rW   rv   rw   rY   rX   rI   rJ   rK   rL   rp   r:   r@   rA   rá   râ   rã   rä   rå   ræ   rÃ   rç   rè   ré   rÅ   rê   r?   rB   rB   rC   Ú+test_equivalent_internal_lines_VT2conjT2_ATp  sD   *
*
*
*
ýr   c                  C   s  t ddtd\} }}}}}t ddtd\}}}}	}
}t ddtd\}}}}t ddtd\}}}}dd	lm} t||||t||| | t||| | }|||||	gd
}| t||||gt|¡}|D ]}t||||g|}| |¡}t	|t	|ks~J qdt||||t||||  t||| | }|||||	gd
}| t||||gt|¡}|D ]}t||||g|}| |¡}t	|t	|ksÇJ q­d S rý   rþ   rÿ   rB   rB   rC   Ú;test_equivalent_internal_lines_VT2conjT2_ambiguous_order_AT  s(   *
*
ýr  c            
   	   C   sŸ  t ddtd\} }}}t ddtd\}}}}t| |||t||| | t|| ||t||| | t| |||t||| | g}|dd  D ]}	t|d t|	ksSJ qEt| |||t||| | t| |||t||| | t| |||t||||  g}|dd  D ]}	t|d t|	ksJ qt| |||t||| | t|| ||t||||  t| |||t||| | t|| ||t||||  g}|dd  D ]}	t|d t|	ksÜJ qÎd S rú   rõ   rû   rB   rB   rC   Ú%test_equivalent_internal_lines_VT2_ATµ  s,   üüüÿr  c            
   	   C   s¶  t ddd\} }t ddd\}}t ddtd\}}t ddtd	\}}t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| g}|d
d  D ]}	t|d t|	ksJ qzt||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| g}|d
d  D ]}	t|d t|	ksïJ qát||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| g}|d
d  D ]}	t|d t|	ksWJ qHd S r÷   rõ   rø   rB   rB   rC   Útest_internal_external_VT2T2_ATÕ  s4   ((((ü((((ü((((üÿr  c            
   	   C   s
  t d\} }t d\}}t dtd\}}t dtd\}}t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| g}|dd  D ]}	t|d t|	ksJ qtd S )NrŒ   r¿   rÇ   rG   rÈ   rQ   r   rõ   rø   rB   rB   rC   Útest_internal_external_pqrs_ATõ  s   ((((üÿr  c                  C   s.   t d} ttt| d t| dksJ d S )NÚ0rR   z(- \left[b_{0},{b^\dagger_{0}}^{2}\right])r,   r3   r   r   r   )rI   rB   rB   rC   Útest_issue_19661  s   ÿr  c                  C   s^   t d} t ddtd\}}t ddtd\}}t| ||f||ft| ||f||f ks-J d S )Nrµ   )rK   rL   Tr   )rv   rw   r   )r-   r+   r   )rµ   rK   rL   rv   rw   rB   rB   rC   Ú+test_canonical_ordering_AntiSymmetricTensor  s   
ÿ
ÿÿr  N)vZ$sympy.functions.elementary.complexesr   Z&sympy.functions.elementary.exponentialr   Zsympy.physics.secondquantr   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   Zsympy.concrete.summationsr%   Zsympy.core.functionr&   r'   Zsympy.core.numbersr(   r)   Zsympy.core.singletonr*   Zsympy.core.symbolr+   r,   r-   Z(sympy.functions.elementary.miscellaneousr.   Zsympy.printing.reprr/   Zsympy.simplify.simplifyr0   Zsympy.testing.pytestr1   r2   Zsympy.printing.latexr3   rD   rO   rZ   r^   re   rf   ro   rq   rs   rt   rz   r{   r|   r   r   r   r   r   r   r   r   rš   r©   r¬   r­   rŽ   r·   rº   rœ   rŸ   rÁ   rÆ   rÎ   rÓ   rÔ   r×   rë   rì   rí   rî   rï   rñ   rò   rô   rž   rö   rù   rü   r   r  r  r  r  r  r  rB   rB   rB   rC   Ú<module>   s    
	
- 	3*&#5,2!1'8+$*  