o
    à8VagŒ  ã                   @   s   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#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/m0Z0m1Z1 d dl2m3Z3 dd Z4dd Z5d	d
 Z6dd Z7dd Z8dd Z9dd Z:dd Z;dd Z<dd Z=dd Z>dd Z?dd Z@dd  ZAe0d!d" ZBd#d$ ZCd%d& ZDd'd( ZEd)d* ZFd+d, ZGd-d. ZHd/d0 ZId1d2 ZJd3d4 ZKd5d6 ZLd7d8 ZMd9d: ZNd;d< ZOd=d> ZPd?d@ ZQdAdB ZRdCdD ZSdEdF ZTdGdH ZUdIdJ ZVdKdL ZWdMdN ZXdOdP ZYdQdR ZZdSdT Z[dUdV Z\dWdX Z]dYdZ Z^d[d\ Z_d]d^ Z`d_d` Zadadb Zbdcdd Zcdedf Zddgdh Zedidj Zfdkdl Zgdmdn Zhdodp Zidqdr ZjdsS )té    )!ÚDaggerÚBdÚVarBosonicBasisÚBBraÚBÚBKetÚFixedBosonicBasisÚ
matrix_repÚapply_operatorsÚInnerProductÚ
CommutatorÚKroneckerDeltaÚAnnihilateBosonÚCreateBosonÚBosonicOperatorÚFÚFdÚFKetÚ
BosonStateÚCreateFermionÚAnnihilateFermionÚevaluate_deltasÚAntiSymmetricTensorÚcontractionÚNOÚwicksÚPermutationOperatorÚsimplify_index_permutationsÚ_sort_anticommuting_fermionsÚ_get_ordered_dummiesÚsubstitute_dummiesÚFockStateBosonKetÚ ContractionAppliesOnlyToFermions)ÚDummyÚexpandÚFunctionÚIÚSÚsimplifyÚsqrtÚSumÚSymbolÚsymbolsÚsreprÚRational)ÚslowÚraises)Úlatexc                  C   s  t d\} }}}ttd\}}}}t}|| | || || ¡|| ||  ks,J || | || |¡|||  ks?J || | || ¡|| ksOJ || || || || ||||  || ||  || || || ||  ||||  || ||  }	|| ||||g}
t|	|
|| |||| ||  || || || ksºJ t|| |dksÅJ d S )Núp,q,r,sZfghizP(pq))r,   Úmapr%   r   Zget_permutedr   r1   )ÚpÚqÚrÚsÚfÚgÚhÚiÚPÚexprZperms© r>   úF/usr/lib/python3/dist-packages/sympy/physics/tests/test_secondquant.pyÚtest_PermutationOperator   s$   2& ÿþý2ÿr@   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#   r3   r%   r   r   r    )ÚaÚbÚcÚdr4   r5   r6   r7   r8   r9   r<   r=   ZexpectedÚresultr>   r>   r?   Ú$test_index_permutations_with_dummies%   s(   ÿÿrJ   c                  C   sŽ  t d\} }}}tddksJ tddksJ tdt dt ks$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 d S )Núi,j,n,mé   g      ð?é   éþÿÿÿg      @éÿÿÿÿr   é
   rE   )r,   r   r&   r'   ÚHalfr.   r   r   r   r   r+   )r;   ÚjÚnÚmr>   r>   r?   Útest_daggerA   s    (( ($rU   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,jrL   )r,   r   ÚstateZis_symbolic)r;   rR   Úor>   r>   r?   Útest_operatorT   s   
rY   c                  C   sº   t d\} }}}t| }t|dksJ t|tsJ | | |¡}| t¡|hks+J td}| t	|g¡t
|d t	|d g ksFJ t|}| t	|g¡|t	|g ks[J d S )NrK   z{b^\dagger_{i}}r   rL   )r,   r   r1   Ú
isinstancer   ÚsubsÚatomsr+   Úapply_operatorr   r)   ©r;   rR   rS   rT   rX   r>   r>   r?   Útest_create^   s   .&r_   c                  C   s¶   t d\} }}}t| }t|dksJ t|tsJ | | |¡}| t¡|hks+J td}| t	|g¡t
|t	|d g ksDJ t|}| t	|g¡|t	|g ksYJ d S )NrK   zb_{i}r   rL   )r,   r   r1   rZ   r   r[   r\   r+   r]   r   r)   r^   r>   r>   r?   Útest_annihilatek   s   *&r`   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 )	NrK   )r   rL   rM   é   é   é   r   )rL   rL   rM   ra   rb   rb   )r   rL   rM   ra   ra   rL   )r,   r   ÚlenÚargsÚtupleÚrangeZupZdown)r;   rR   rS   rT   r7   r>   r>   r?   Útest_basic_statex   s   "rh   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 )NrS   r   rL   )r,   r   r   r
   r)   r   )rS   Úer>   r>   r?   Útest_basic_apply   s
   "*rj   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   rL   rO   )r,   r   r   r
   r   r)   r$   )rS   rT   rX   ri   Zanswerr>   r>   r?   Útest_complex_apply   s
    0rl   c                  C   sD   t d} tdtd }t|t| g }|| t| g ks J d S )NrS   r   )r,   r   r   r
   r   )rS   rX   ri   r>   r>   r?   Útest_number_operator   s   rm   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   rL   )r,   r   r   r   r   r   )r;   rR   ÚkÚlÚs1Ús2r6   r>   r>   r?   Útest_inner_product    s   


 rs   c                  C   sZ   t d\} }t| g}t|g}td}t|| | }|t|t| |d  ks+J d S )Nrk   r   rL   )r,   r   r   r   r
   r)   r   )rS   rT   rq   rr   rX   ri   r>   r>   r?   Útest_symbolic_matrix_elements¬   s   

"rt   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 )Nrc   r   rb   rL   )r   r   r	   rg   r)   r   )rF   rX   rT   r;   r>   r>   r?   Útest_matrix_elementsµ   s   
"
"ÿru   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 )NrM   rL   )rL   rL   ra   z9[FockState((2, 0)), FockState((1, 1)), FockState((0, 2))])r   rW   r!   Úindexrd   ÚstrÚreprr-   )rF   rW   r>   r>   r?   Útest_fixed_bosonic_basisÁ   s   

ry   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 )	Nrk   r   rc   F)ZdeeprM   é   )rL   rM   ra   ra   rb   rc   rb   rc   rz   é   rc   rz   r{   é   é	   rz   r{   r|   r}   rP   é   )r,   r   r   r'   rQ   r*   Údoitr   r	   rg   rd   )rS   rT   Zh_nÚHrX   rF   Zdiagr;   r>   r>   r?   Útest_shoÎ   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 )Nrk   T©Úabove_fermir   rL   rO   rM   zX,Y,ZF)Zcommutativern   ©Úbelow_fermiúa,b,c,dr2   rN   )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   r(   r
   r   r   r   r   r$   r   Úevalr1   rx   rw   )rS   rT   rG   ri   ÚCÚXÚYÚZr;   rR   ro   rp   rE   rF   rH   r4   r5   r6   r7   ÚDZc1r>   r>   r?   Útest_commutationÝ   sJ   $(0@4"r   c                  C   sÊ  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|  t| ||gd¡t||gdksJ t| t| |	|gd¡t|| |	|gdksŽJ t	t
| |¡|t| ksÅJ tt|dksÏJ tt|dksÙJ tt|dksãJ d S )NrK   rL   rb   )Zfermi_levelrn   Tr   r   r   r2   zCreateFermion(p)zCreateFermion(Symbol('p'))z{a^\dagger_{p}})r,   r   rZ   r   r[   r\   r+   r]   r   r   r   r   rx   r-   r1   )r;   rR   rS   rT   rX   Zvacuumro   rp   rE   rF   rG   rH   r4   r5   r6   r7   r>   r>   r?   Útest_create_f
  s*    ",0"r   c                  C   sÖ  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|  t| ||gd	¡d
ksJ t| t| ||gd	¡d
ksJ t| t| ||gd¡d
ks©J t| t| ||gd	¡t|| ||gd	ksÁJ t	t|dksËJ t
t|dksÕJ tt|dksßJ tt|dkséJ d S )NrK   rL   rn   Tr   r   r   r2   rb   r   ra   zf(p)zAnnihilateFermion(p)zAnnihilateFermion(Symbol('p'))za_{p})r,   r   rZ   r   r[   r\   r+   r]   r   rw   rx   r-   r1   )r;   rR   rS   rT   rX   ro   rp   rE   rF   rG   rH   r4   r5   r6   r7   r>   r>   r?   Útest_annihilate_f&  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 )NrK   r   rL   )
r,   r   rZ   r   r[   r\   r+   r]   r   r)   r^   r>   r>   r?   Útest_create_b?  s   .&r   c                  C   sR   t d\} }}}t| }t|tsJ | | |¡}| t¡|hks#J td}d S )NrK   r   )r,   r   rZ   r   r[   r\   r+   r^   r>   r>   r?   Útest_annihilate_bK  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 )Nr2   Tr   rM   úi j k l©r   rD   rA   ©r   rD   rB   rC   )
r,   r   r   r   r   r   r   r   r$   r#   )r4   r5   r6   r7   rw   ZnstrZfasitr;   rR   ro   rp   rE   rF   rG   rH   r=   r>   r>   r?   Ú
test_wicksT  st   *  ÿþýüÿ$,&"ÿ
ÿ.*$ÿ
ÿ(ÿþý"ü
ÿ(ÿþý"üÿr   c                     s¢  t ddd\} }}}t ddd\}}}}t dtd\ }}	tt t t|t|  tt t tt|t|  ksFJ tt| tt|t|  tt| t| t| ksfJ tddksnJ t| | ksvJ tt|t| t|t|  tt|t| t| tt|t| t|  ksŠJ tt|t|  ¡ t|t| ksŒJ tt|t|   ¡ t|t|  ksÒJ tt t  t t|t|  ¡tt|t tt| t  ksþJ tt t  tt|t|  ¡tt t| tt t|   ks+J tt t  ¡ }
t|
t|
ksBJ tt|t| tt|t|  ksZJ tt|t|  t| t| }d	d
 | ¡ D }|ddgks~J dd
 | 	¡ D }|ddgksJ tt|t|  }|j
dks¢J |jdksªJ t|dks³J t|dksŒJ t|dksÅJ tt fdd d S )Nr   Tr   rA   r   rB   rC   rL   c                 S   ó   g | ]}|qS r>   r>   ©Ú.0Zindr>   r>   r?   Ú
<listcomp>€  ó    ztest_NO.<locals>.<listcomp>r   c                 S   r   r>   r>   r   r>   r>   r?   r   Š  r   ra   rM   rO   z#:CreateFermion(a)*CreateFermion(i):z%NO(CreateFermion(a)*CreateFermion(i))z.\left\{{a^\dagger_{a}} {a^\dagger_{i}}\right\}c                      s   t t t S ©N)r   r   r   r>   ©r4   r5   r>   r?   Ú<lambda>®  s    ztest_NO.<locals>.<lambda>)r,   r#   r   r   r   Z_remove_bracketsr[   r   Ziter_q_creatorsZiter_q_annihilatorsZhas_q_creatorsZhas_q_annihilatorsrw   rx   r1   r0   ÚNotImplementedError)r;   rR   ro   rp   rE   rF   rG   rH   r6   r7   r=   ÚnoÚl1Úl2r>   r   r?   Útest_NO  sN   "&ÿÿ"ÿÿ,,*&ÿ*&
ÿ0$r¢   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 )	NrV   Tr   za,br   zp,qr   rL   )r,   r   r   r   )r;   rR   rE   rF   r4   r5   r>   r>   r?   Útest_sorting±  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 )
Nrn   Tr   r   r   r2   r   c                      s   t t tS r   )r   r   r   r>   ©rE   rF   r>   r?   r   æ  s    z"test_contraction.<locals>.<lambda>)
r,   r   r   r   r   r   Zis_only_below_fermiZis_only_above_fermir0   r"   )r;   rR   ro   rp   rG   rH   r4   r5   r6   r7   Zrestrr>   r€   r?   Útest_contraction×  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   rL   rM   )r,   r   r   )r;   rR   ro   r6   r>   r>   r?   Útest_evaluate_deltasé  s"    ÿÿrŠ   c                  C   s¬  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 d S )Nr   Tr   rA   r   rB   Útr   rM   z{t^{ab}_{ij}}zt((_a, _b),(_i, _j)))	r,   r#   r   Zhasr[   Úsymbolr+   r1   rw   )r;   rR   ro   rp   rE   rF   rG   rH   r4   r5   r6   r7   ÚATZtabijr>   r>   r?   Útest_Tensors   s.   .,.24$.6:rª   c                  C   s(  t ddd\} }}}t ddd\}}}}t dtd\}}	}
}td|f|	ftt|t|	  }td	||	f|
|ftt|t|	 t| t|
  d
 }ttt| t| | ddd}|td|f| fkskJ ttt| t| t| t| | ddd}|td	||f| |fksJ d S )Nr   Tr   rA   r   rB   rC   r8   Úvrb   )Zkeep_only_fully_contractedZsimplify_kronecker_deltas)r,   r#   r   r   r   r   r   )r;   rR   ro   rp   rE   rF   rG   rH   r4   r5   r6   r7   ZFockÚVZFaiZVabijr>   r>   r?   Útest_fully_contracted  s*   ÿ"ÿÿþ(þ r­   c                  C   sX   t d\} }tt| |d t| |d ksJ tt| |d t| |d ks*J d S )NrV   rM   rL   )r,   r    Úatt©r;   rR   r>   r>   r?   Ú'test_substitute_dummies_without_dummies1  s   $(r°   c                  C   s\   t dtd\} }tt| |tt| t|  t|| tt|t|    dks,J d S ©Núi jrC   r   )r,   r#   r    r®   r   r   r   r¯   r>   r>   r?   Ú#test_substitute_dummies_NO_operator7  s   ÿÿr³   c                  C   sT   t dtd\} }tt| |t|  t| t|| t| t|   dks(J d S r±   )r,   r#   r    r®   r   r   r¯   r>   r>   r?   Ú#test_substitute_dummies_SQ_operator=  s   ÿÿrŽ   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 )Nr²   Tr   úa br   úp qrC   r8   )Znew_indicesr   )r,   r#   r%   r    )r;   rR   rE   rF   r4   r5   r8   r>   r>   r?   Ú#test_substitute_dummies_new_indicesC  s
   ,r·   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   r8   r   ©Ú
variationsrb   )r,   r#   r%   Úsympy.utilities.iterablesr¹   r    )r;   rR   ro   rp   r8   r¹   Úpermutr>   r>   r?   Ú*test_substitute_dummies_substitution_orderK  s   $ÿrŒ   c                  C   sB  t ddd} t ddd}t ddtd\}}t ddtd	\}}td
}td}t}||||||||  ||| ||| ||||||||  ||| ||| ||||||||  ||| ||| ||||||||  ||| ||| g}	|	dd  D ]}
||	d ||
ksJ t|	d t|
ksJ qd S )Nr;   Tr   rE   r   úk lr   úc dr   r«   r§   rL   r   ©r,   r#   r%   r   r    )ÚiiÚaaro   rp   rG   rH   r«   r§   ÚdumsÚexprsr»   r>   r>   r?   Ú*test_dummy_order_inner_outer_lines_VT1T1T1S  s    ****úþrÄ   c                  C   sª  t ddd\} }t ddd\}}t ddtd\}}t ddtd	\}}td
}td}	t}
||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| g}|dd  D ]}|
|d |
|ksªJ t|d t|ks¶J q||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| g}|dd  D ]}|
|d |
|ks6J t|d t|ksCJ q'||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| g}|dd  D ]}|
|d |
|ksÄJ t|d t|ksÑJ qµd S ©Nr²   Tr   rµ   r   rœ   r   rŸ   r   r«   r§   rL   r   r¿   ©rÀ   ÚjjrÁ   Úbbro   rp   rG   rH   r«   r§   rÂ   rÃ   r»   r>   r>   r?   Ú,test_dummy_order_inner_outer_lines_VT1T1T1T1l  s@   4444ú4
444ô4444ù	þrÉ   c                  C   sÀ   t d\} }}tt| t| t|  d¡tt| t| ks$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,rrL   r   rM   )r,   r   r   Z	get_subNO)r4   r5   r6   r>   r>   r?   Útest_get_subNO¡  s   ::>rÊ   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   rA   r   r«   r§   rL   r   r¿   ©r;   rR   ro   rp   rE   rF   rG   rH   r«   r§   rÂ   rÃ   r»   r>   r>   r?   Ú$test_equivalent_internal_lines_VT1T1š  sB      ý  þ  þ    üþrÍ   c                  C   s(  t ddtd\} }}}}}t ddtd\}}}}	}
}t ddtd\}}}}t ddtd\}}}}dd	lm} td
}td}t}||||||||| | || ||| }|||||	gd}| t||||gt|¡}|D ]$}t||||g|}| |¡}||||ksJ t	|t	|ksJ qn||||||||||  ||| || }|||||	gd}| t||||gt|¡}|D ]$}t||||g|}| |¡}||||ksÛJ t	|t	|ksåJ qÁ||||||||| | ||| || }|||||	gd}| t||||gt|¡}|D ]'}t||||g|}| |¡}||||ks/J t	|t	|ks:J q||||||||||  || ||| }|||||	gd}| t||||gt|¡}|D ]'}t||||g|}| |¡}||||ksJ t	|t	|ksJ qjd S ©Núi j k l m nTr   úa b c d e fr   úp1 p2 p3 p4úh1 h2 h3 h4r   rž   r«   r§   rb   ©
r,   r#   rº   r¹   r%   r   r[   ÚzipÚnextr    ©r;   rR   ro   rp   rT   rS   rE   rF   rG   rH   ri   r8   Úp1Úp2Úp3Úp4Úh1Úh2Úh3Úh4r¹   r«   r§   rÂ   ÚtemplateÚ
permutatorÚbaser»   Úsubslistr=   r>   r>   r?   Ú(test_equivalent_internal_lines_VT2conjT2Ô  sR   *
*
*
*
ürã   c                  C   sÐ  t ddtd\} }}}}}t ddtd\}}}}	}
}t ddtd\}}}}t ddtd\}}}}dd	lm} td
}td}t}||||||||| | |||| | }|||||	gd}| t||||gt|¡}|D ]$}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 rÎ   rÓ   rÖ   r>   r>   r?   Ú8test_equivalent_internal_lines_VT2conjT2_ambiguous_order  s2   *
*
ürä   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 rË   r¿   rÌ   r>   r>   r?   Ú"test_equivalent_internal_lines_VT2'  s<   òûüþrå   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 rÅ   r¿   rÆ   r>   r>   r?   Útest_internal_external_VT2T2X  s@   ((((ü((((ü((((üþræ   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 )
Nr²   rµ   rœ   rC   rŸ   r«   r§   rL   r   r¿   rÆ   r>   r>   r?   Útest_internal_external_pqrs  s    ((((üþrç   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 )Nrµ   Tr   zk l mr   rŸ   r   r¶   rC   ÚAr   r   )r,   r#   r%   r   )rÁ   rÈ   ro   rp   rT   rG   rH   r4   r5   rè   r   r   rÂ   r>   r>   r?   Útest_dummy_order_well_defined  sP   $$$$0000022288888888,,,,,,,,,,,0ré   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 )Nrµ   Tr   z	i j k l mr   z	a b c d er   r¶   rC   rÑ   zp5 p6 p7 p8rÒ   zh5 h6 h7 h8rè   r   r   rž   rc   )	r,   r#   r%   rº   r¹   r[   rÔ   rÕ   r    )'rÁ   rÈ   r;   rR   ro   rp   rT   rE   rF   rG   rH   ri   r4   r5   r×   rØ   rÙ   rÚ   Zp5Zp6Zp7Zp8rÛ   rÜ   rÝ   rÞ   Zh5Zh6Zh7Zh8rè   r   r¹   rß   rà   rá   r»   râ   r=   r>   r>   r?   Útest_dummy_order_ambiguousÌ  sB   2
2
&
ýrê   c                  G   s   t d| d d | dd  S )Nr«   rM   )r   ©re   r>   r>   r?   Úatv÷  s   rì   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 )Nrb   r§   rM   r   rL   )rd   r   rë   r>   r>   r?   r®   û  s
   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|| t||||t||  t|| t|| g}|d
d  D ]}t|d t|ksJ qzd S )Nr;   Tr   rE   r   rœ   r   rŸ   r   rL   r   ©r,   r#   rì   r®   r    )rÀ   rÁ   ro   rp   rG   rH   rÃ   r»   r>   r>   r?   Ú-test_dummy_order_inner_outer_lines_VT1T1T1_AT  s   ****úÿrî   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 ©Nr²   Tr   rµ   r   rœ   r   rŸ   r   rL   r   rí   ©
rÀ   rÇ   rÁ   rÈ   ro   rp   rG   rH   rÃ   r»   r>   r>   r?   Ú/test_dummy_order_inner_outer_lines_VT1T1T1T1_AT  s    444ü44ýÿrñ   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   rA   r   rL   r   rí   ©
r;   rR   ro   rp   rE   rF   rG   rH   rÃ   r»   r>   r>   r?   Ú'test_equivalent_internal_lines_VT1T1_AT1  s4      ý  þ  þ    üÿrô   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 ©NrÏ   Tr   rÐ   r   rÑ   rÒ   r   rž   rb   ©
r,   r#   rº   r¹   rì   r®   r[   rÔ   rÕ   r    ©r;   rR   ro   rp   rT   rS   rE   rF   rG   rH   ri   r8   r×   rØ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   r¹   rß   rà   rá   r»   râ   r=   r>   r>   r?   Ú+test_equivalent_internal_lines_VT2conjT2_ATU  sD   *
*
*
*
ýrø   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 rõ   rö   r÷   r>   r>   r?   Ú;test_equivalent_internal_lines_VT2conjT2_ambiguous_order_AT  s(   *
*
ýrù   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 rò   rí   ró   r>   r>   r?   Ú%test_equivalent_internal_lines_VT2_AT  s,   üüüÿrú   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 rï   rí   rð   r>   r>   r?   Útest_internal_external_VT2T2_ATº  s4   ((((ü((((ü((((üÿrû   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 )Nr²   rµ   rœ   rC   rŸ   rL   r   rí   rð   r>   r>   r?   Útest_internal_external_pqrs_ATÚ  s   ((((üÿrü   c                  C   s.   t d} ttt| d t| dksJ d S )NÚ0rM   z(- \left[b_{0},{b^\dagger_{0}}^{2}\right])r+   r1   r   r   r   )rE   r>   r>   r?   Útest_issue_19661ê  s   ÿrþ   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 )Nr«   )rG   rH   Tr   )ro   rp   r   )r,   r#   r   )r«   rG   rH   ro   rp   r>   r>   r?   Ú+test_canonical_ordering_AntiSymmetricTensorð  s   
ÿ
ÿÿrÿ   N)kZ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sympyr#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   Zsympy.testing.pytestr/   r0   Zsympy.printing.latexr1   r@   rJ   rU   rY   r_   r`   rh   rj   rl   rm   rs   rt   ru   ry   r   r   r   r   r   r   r   r¢   r£   r¥   rŠ   rª   r­   r°   r³   rŽ   r·   rŒ   rÄ   rÉ   rÊ   rÍ   rã   rä   rå   ræ   rç   ré   rê   rì   r®   rî   rñ   rô   rø   rù   rú   rû   rü   rþ   rÿ   r>   r>   r>   r?   Ú<module>   sx    8
	
-	3*&5,2!1'8+$*  