a
    kº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sXJ || | || |¡|||  ks~J || | || ¡|| ksJ || || || || ||||  || ||  || || || ||  ||||  || ||  }	|| ||||g}
t|	|
|| |||| ||  || || || ksvJ t|| |dksJ t d\}}t|||dks²J 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   úR/var/www/auris/lib/python3.9/site-packages/sympy/physics/tests/test_secondquant.pyÚtest_PermutationOperator   s(    2& ÿþý2ÿ
rD   c                  C   sZ  t d\} }}}t dtd\}}}}ttd\}}	t}
|| |||||| || }t||
| |g|
| ||| ||| ksJ |
| |t|| ||| }|| |||||| || }t||
| |g}|t|ksÚJ || |||||| || }t||
| |g}|t|ksJ || ||||	|| || }t||
| |g}||ksVJ 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   sø  t d\} }}}tddks J tddks0J tdt dt ksHJ ttjt d ttdd d kspJ tt|gt|gksJ ttdt	dks€J tt	dtdksŒJ tt|t	|ksÔJ tt	|t|ksìJ ttdtd t	dt	d ksJ t|| t|t| ks8J tt|t| t	|t	| ksbJ tt|d	 tt|d	 ksJ td
tt
d
ks¢J ttd
t
d
ksŒJ ttdt tdt ksÞJ t| t| ksôJ 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sBJ |jrLJ 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sLJ | | |¡}| t¡|hkslJ td}| t	|g¡t
|d t	|d g ks¢J t|}| t	|g¡|t	|g ksÌJ 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sLJ | | |¡}| t¡|hkslJ td}| t	|g¡t
|t	|d g ksJ t|}| t	|g¡|t	|g ksÈJ 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sFJ | d¡tg d¢ks`J | d¡tg d¢kszJ tdD ]} | | ¡ | ¡|ksJ q| d¡dks²J tdD ]} ||  | ksºJ qºt||g}| d¡t|d |gksúJ | 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rangeZupZdown)r=   rW   rX   rY   r9   rB   rB   rC   Útest_basic_state   s    rn   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stJ d S )NrX   r   rQ   )r-   r   r	   r   r.   r   )rX   ÚerB   rB   rC   Útest_basic_apply   s
    "rp   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sJ d S )Nún,mr   rQ   rT   )r-   r   r   r   r	   r.   r'   )rX   rY   r]   ro   ZanswerrB   rB   rC   Útest_complex_apply   s
     0rr   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]   ro   rB   rB   rC   Útest_number_operator§   s    rs   c                  C   s   t d\} }}}tdg}tdg}t|t|dks:J t||dksLJ t| |g}t||g}t||}|t| |t|| ksJ 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    


ry   c                  C   sZ   t d\} }t| g}t|g}td}t|| | }|t|t| |d  ksVJ d S )Nrq   r   rQ   )r-   r   r	   r   r   r.   r   )rX   rY   rw   rx   r]   ro   rB   rB   rC   Útest_symbolic_matrix_elementsº   s    

rz   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 ]$}||d |f t|d ksbJ qbd S )Nri   r   rh   rQ   )r   r   r   rm   r.   r   )rJ   r]   rY   r=   rB   rB   rC   Útest_matrix_elementsÃ   s    
"
r{   c                  C   s   t dd} |  d¡}|tdks$J |  |¡dks6J |  d¡| d ksLJ t| dks\J t| dkslJ t| dks|J t| dksJ 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sjJ qjd S )	Nrq   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    

r   c                  C   s:  t ddd\} }ttdtd}|dks.J ttdtd}|dksLJ tt| td}|t| dkspJ ttdtd}|dksJ ttdtd}tt|t| g }|t| gksÈJ ttdtd}tt|t| |g }|dksþJ tt|t	|}|ddt
t	|t|   ks6J tt	|t|}| ¡ ddt
t	|t|   ksrJ t}t dd	d
\}}}|||||dks¢J |||||dksŒJ |||||dksÖJ t ddd\}}	}
}t ddd\}}}}t d\}}}}t}|t	|t|dt
t|t	|  ksBJ |t	|	t
t	|t| jdd||	| t	| ksJ |t	|t| t	|t|	 jdddks¶J tt|t	|}t ||¡dksÞJ tt	|t| t	|t|	 }t|dksJ t|dks$J t|dks6J d S )Nrq   T©Úabove_fermir   rQ   rT   rR   zX,Y,ZF)Zcommutativert   ©Úbelow_fermiúa,b,c,dr4   rS   )r   z8\left[{a^\dagger_{a}} a_{i},{a^\dagger_{b}} a_{j}\right]zWCommutator(CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j))zM[CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j)])r-   r   r   r   r   r0   r   r	   r   r   r   r'   r   Úevalr3   r~   r}   )rX   rY   rK   ro   ÚCÚXÚYÚZr=   rW   ru   rv   rI   rJ   rL   r6   r7   r8   r9   ÚDZc1rB   rB   rC   Útest_commutationë   sJ    &*0@4"r   c                  C   s0  t d\} }}}t| }t|ts&J | | |¡}| t¡|hksFJ td}| t|g¡td|gksnJ | t|g¡t|dg ksJ t|}| tg ¡t|gksŽJ tg dd}|tg ddksÔJ t ddd\} }}}t ddd	\}}	}
}t d
\}}}}t d}t|  t| ||gd¡t||gdksBJ t| t| |	|gd¡t|| |	|gdkstJ t	t
| |¡|t| ksJ tt|dks®J tt|dksÄJ tt|dksÚJ tt|dksðJ tt|| gddksJ tt|| |	|gddks,J d S )NrP   rQ   rh   )Zfermi_levelrt   Tr   r   r   r4   r@   zCreateFermion(p)zCreateFermion(Symbol('p'))z{a^\dagger_{p}}z{a^\dagger_{p_{1}}}z(\left|\left( a, \  i\right)\right\ranglerR   z4\left|\left( a, \  b, \  i, \  j\right)\right\rangle)r-   r   r`   r   ra   rb   r,   rc   r   r   r   r   r~   r/   r3   )r=   rW   rX   rY   r]   Zvacuumru   rv   rI   rJ   rK   rL   r6   r7   r8   r9   r@   rB   rB   rC   Útest_create_f  s2     ".2$r   c                  C   s  t d\} }}}t| }t|ts&J | | |¡}| t¡|hksFJ td}| td|g¡t|gksnJ | t|dg¡t|g ksJ t|}| t|g¡tg ksŽJ 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s`J t| t| ||gd
¡t|| ||gd
ksJ t	t|dksšJ t
t|dksŸJ tt|dksÔJ tt|dksêJ tt|dks J d S )NrP   rQ   rt   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]   ru   rv   rI   rJ   rK   rL   r6   r7   r8   r9   r@   rB   rB   rC   Útest_annihilate_f8  s.     "$$$2r   c                  C   sª   t d\} }}}t| }t|ts&J | | |¡}| t¡|hksFJ td}| t|g¡t	|d t|d g ks|J t|}| t|g¡|t|g ksŠJ 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sFJ 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   sV  t ddd\} }}}t| t| }t|tt| t| t| | ksNJ 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sJ 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sÆJ 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 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sRJ 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   ru   rv   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sJ tt| tt|t|  tt| t| t| ksÌJ tddksÜJ t| | ksìJ tt|t| t|t|  tt|t| t| tt|t| t|  ksNJ tt|t|  ¡ t|t| ks|J tt|t|   ¡ t|t|  ksªJ 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|   ks^J tt t  ¡ }
t|
t|
ksJ tt|t| tt|t|  ksŒJ tt|t|  t| t| }t| 	¡ }|d	dgksþJ t| 
¡ }|d
dgksJ tt|t|  }|jdks@J |jdksPJ t|dksbJ t|dkstJ 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  ó    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   ru   rv   rI   rJ   rK   rL   r8   r9   r?   ÚnoÚl1Úl2rB   r   rC   Útest_NO  sN    "&ÿÿ"ÿÿ
..*&ÿ
*&ÿ
0$r§   c                  C   sx  t ddd\} }t ddd\}}t d\}}tt|t|gt|t|gdfksXJ tt|t|gt|t|gdfksJ tt|t| gt|t| gdfks°J tt| t|gt|t| gdfksÜJ tt|t| gt|t| gdfks
J tt| t|gt|t| gdfks8J tt|t| gt| t|gdfksfJ tt| t|gt| t|gdfksJ tt|t| gt| t|gdfksÂJ tt| t|gt| t|gdfksðJ tt|t|gt|t|gdfksJ tt|t|gt|t|gdfksLJ tt|t|gt|t|gdfkszJ tt|t|gt|t|gdfksšJ tt|t|gt|t|gdfksÖJ tt|t|gt|t|gdfksJ tt|t|gt|t|gdfks2J tt|t|gt|t|gdfks`J tt| t|gt| t|gdfksJ tt|t| gt| t|gdfksŒJ tt|t| gt|t| gdfksêJ tt| t|gt|t| gdfksJ tt|t| gt| t|gdfksFJ tt| t|gt| t|gdfkstJ d S )	Nr[   Tr   za,br   zp,qr   rQ   )r-   r    r   r   )r=   rW   rI   rJ   r6   r7   rB   rB   rC   Útest_sortingÆ  s6    ,,,,...................rš   c                     s^  t ddd\} }}}t ddd\ }}t d\}}}}	tt| t|t| |ksXJ tt tt ksxJ tt t| dksJ tt t| dks¬J tt| t dksÆJ tt| t dksàJ tt| t|t| |ksJ ttt|t|}
|
js$J ttt|t|}
|
jsFJ tt	 fdd	 d S )
Nrt   Tr   r   r   r4   r   c                      s   t t tS r   )r   r   r   rB   ©rI   rJ   rB   rC   r    û  r¡   z"test_contraction.<locals>.<lambda>)
r-   r   r   r   r   r   Zis_only_below_fermiZis_only_above_fermir2   r$   )r=   rW   ru   rv   rK   rL   r6   r7   r8   r9   ÚrestrrB   r©   rC   Útest_contractionì  s      "r«   c                  C   s,  t d\} }}t| |t|| }t|t| |ks8J t| dt|| }t|t| dt|| kslJ td|t|| }t|td|ksJ t|dt|| }t|td|ksÀJ t| dt| | t|d }t|dksîJ td| td| td| td| }t|dks(J d S )Nzi,j,kr   rQ   rR   )r-   r   r   )r=   rW   ru   r8   rB   rB   rC   Útest_evaluate_deltasþ  s"     ÿÿr¬   c                  C   s  t ddtd\} }}}t ddtd\}}}}t d\}}	}
}t}|d||f| |f|d||f| |f ksnJ |d||f| |f|d||f|| fksJ |d||f| |f|d||f|| f ksÈJ |d||f| |fdksäJ |d||f| | fdksJ |d|||f| |f|d|||f| |f ks6J |d|||f| ||f|d|||f| ||fkslJ |d||f| |f}| |¡sJ | |¡s J | | ¡s°J | |¡sÀJ | ||¡|d||f| |fksæJ d	|  | |¡d	|d||f||f ksJ |jtdks(J t|d
ks:J t|dksLJ |d||f| |f ||¡|d||f| |fksJ |d|| f||f ||¡|d|| f||fksžJ t d\}}}}td||f||f}t|dksîJ t|dks J d S )Nr   Tr   rE   r   rF   Útr   rR   z{t^{ab}_{ij}}zt((_a, _b),(_i, _j))zalpha1:5Úuz1{u^{\alpha_{1}\alpha_{2}}_{\alpha_{3}\alpha_{4}}}z$u((alpha1, alpha2),(alpha3, alpha4)))	r-   r+   r   Zhasra   Úsymbolr,   r3   r}   )r=   rW   ru   rv   rI   rJ   rK   rL   r6   r7   r8   r9   ÚATZtabijZa1Za2Úa3Za4Zu_alpha1234rB   rB   rC   Útest_Tensors  s6    .,.46&.66r²   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sÖJ 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   ru   rv   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rµ   c                  C   sX   t d\} }tt| |d t| |d ks0J tt| |d t| |d ksTJ d S )Nr[   rR   rQ   )r-   r"   Úatt©r=   rW   rB   rB   rC   Ú'test_substitute_dummies_without_dummiesL  s    $rž   c                  C   s\   t dtd\} }tt| |tt| t|  t|| tt|t|    dksXJ d S ©Núi jrG   r   )r-   r+   r"   r¶   r   r   r   r·   rB   rB   rC   Ú#test_substitute_dummies_NO_operatorR  s    ÿÿr»   c                  C   sT   t dtd\} }tt| |t|  t| t|| t| t|   dksPJ d S r¹   )r-   r+   r"   r¶   r   r   r·   rB   rB   rC   Ú#test_substitute_dummies_SQ_operatorX  s    ÿÿrŒ   c                  C   sh   t ddtd\} }t ddtd\}}t dtd\}}td}t|| |||||| dd	d
ksdJ d S )Nrº   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
    r¿   c                  C   sh   t ddtd\} }}}td}ddlm} || |||gdD ]&}t|| || ||| dks<J q<d S )Nr   Tr   r:   r   ©Ú
variationsrh   )r-   r+   r&   Úsympy.utilities.iterablesrÁ   r"   )r=   rW   ru   rv   r:   rÁ   ÚpermutrB   rB   rC   Ú*test_substitute_dummies_substitution_orderf  s
    rÄ   c                  C   sH  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   r³   r­   rQ   r   ©r-   r+   r&   r!   r"   )ÚiiÚaaru   rv   rK   rL   r³   r­   ÚdumsÚexprsrÃ   rB   rB   rC   Ú*test_dummy_order_inner_outer_lines_VT1T1T1n  s    ****úrÌ   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sVJ t|d t|ks8J q8||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	||  |	|| |	|| |	|| g}|dd  D ]:}|
|d |
|ksrJ t|d t|ksTJ qT||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| ||||||	||  |	|| |	|| |	|| ||||||	|| |	||  |	|| |	|| g}|dd  D ]:}|
|d |
|ksJ t|d t|kspJ qpd S ©Nrº   Tr   rœ   r   rÅ   r   rÆ   r   r³   r­   rQ   r   rÇ   ©rÈ   ÚjjrÉ   Úbbru   rv   rK   rL   r³   r­   rÊ   rË   rÃ   rB   rB   rC   Ú,test_dummy_order_inner_outer_lines_VT1T1T1T1  s>    4444ú
4444ô4444ù	rÑ   c                  C   sÀ   t d\} }}tt| t| t|  d¡tt| t| ksHJ tt| t| t|  d¡tt|t| ksJ tt| t| t|  d¡tt| t| ksŒJ 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    ::rÒ   c                  C   sÎ  t ddtd\} }}}t ddtd\}}}}td}td}	t}
|| ||||	||  |	|| ||| |||	||  |	|| || ||||	||  |	|| g}|dd  D ]4}|
|d	 |
|ksÌJ t|d	 t|ks°J q°|| ||||	||  |	|| ||| |||	||  |	|| g}|dd  D ]:}|
|d	 |
|ksTJ t|d	 t|ks6J q6|| ||||	||  |	|| || ||||	||  |	|| g}|dd  D ]:}|
|d	 |
|ksàJ t|d	 t|ksÂJ qÂ|| ||||	||  |	|| ||| |||	|| |	||  || ||||	||  |	|| ||| |||	|| |	||  g}|dd  D ]:}|
|d	 |
|ks¬J t|d	 t|ksJ qd S ©
Nr   Tr   rE   r   r³   r­   rQ   r   rÇ   ©r=   rW   ru   rv   rI   rJ   rK   rL   r³   r­   rÊ   rË   rÃ   rB   rB   rC   Ú$test_equivalent_internal_lines_VT1T1Ã  s@       ý  þ  þ    ürÕ   c                  C   s0  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 ]J}t||||g|}| |¡}||||ksJ t	|t	|ksÜJ qÜ||||||||||  ||| || }|||||	gd}| t||||gt|¡}|D ]N}t||||g|}| |¡}||||ksºJ t	|t	|ksJ q||||||||| | ||| || }|||||	gd}| t||||gt|¡}|D ]N}t||||g|}| |¡}||||ksfJ t	|t	|ks0J q0||||||||||  || ||| }|||||	gd}| t||||gt|¡}|D ]N}t||||g|}| |¡}||||ksJ t	|t	|ksÜJ qÜd S ©Núi j k l m nTr   úa b c d e fr   úp1 p2 p3 p4úh1 h2 h3 h4r   rÀ   r³   r­   rh   ©
r-   r+   rÂ   rÁ   r&   r!   ra   ÚzipÚnextr"   ©r=   rW   ru   rv   rY   rX   rI   rJ   rK   rL   ro   r:   r@   rA   Úp3Úp4Úh1Úh2Úh3Úh4rÁ   r³   r­   rÊ   ÚtemplateÚ
permutatorÚbaserÃ   Úsubslistr?   rB   rB   rC   Ú(test_equivalent_internal_lines_VT2conjT2ï  sP    *
*
*
*
ré   c                  C   sØ  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 ]J}t||||g|}| |¡}||||ksJ t	|t	|ksÜJ qÜ||||||||||  |||| | }|||||	gd}| t||||gt|¡}|D ]N}t||||g|}| |¡}||||ksºJ t	|t	|ksJ qd S rÖ   rÛ   rÞ   rB   rB   rC   Ú8test_equivalent_internal_lines_VT2conjT2_ambiguous_order!  s0    *
*
rê   c               	   C   sZ  t ddtd\} }}}t ddtd\}}}}td}td}	t}
|| ||||	||| | ||| |||	||| | || ||||	||| | ||| |||	||| | g}|dd  D ]4}|
|d	 |
|ksÔJ t|d	 t|ksžJ qž|| ||||	||| | || ||||	||| | || ||||	||||  || ||||	||||  g}|dd  D ]:}|
|d	 |
|ksJ t|d	 t|ksfJ qf|| ||||	||| | ||| |||	||||  || ||||	||| | ||| |||	||||  g}|dd  D ]:}|
|d	 |
|ks8J t|d	 t|ksJ qd S rÓ   rÇ   rÔ   rB   rB   rC   Ú"test_equivalent_internal_lines_VT2B  s:    òûürë   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sôJ qô||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| g}|dd  D ]:}|
|d |
|ksþJ t|d t|ksàJ qàd S rÍ   rÇ   rÎ   rB   rB   rC   Útest_internal_external_VT2T2s  s>    ((((ü((((ü((((ürì   c               	   C   s8  t d\} }t d\}}t dtd\}}t dtd\}}td}td}	t}
||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| ||||||	||| | |	|||| g}|dd  D ]6}|
|d	 |
|ksJ t|d	 t|ksüJ qüd S )
Nrº   rœ   rÅ   rG   rÆ   r³   r­   rQ   r   rÇ   rÎ   rB   rB   rC   Útest_internal_external_pqrs  s    ((((ürí   c                  C   sV  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sJ ||	|||
|| ||gksªJ ||	|||
|| ||gksÎJ ||	|||
|| ||gksòJ ||	|||
|| ||| |||gks$J ||	|||
|| ||| |||gksVJ ||	|||
|| ||| |||gksJ ||	|||
|| ||| |||gksºJ ||	|||
|| ||| |||gksìJ ||	|||
|| ||| |||gksJ ||	|||
|| ||| |||gksPJ ||	|||
|| ||| |||gksJ ||	|| ||	||| |	||| |||gksºJ ||	|| ||	||| |	||| |||gksòJ ||	|| ||	||| |	||| |||gks*J ||	|| ||	||| |	||| |||gksbJ ||	|| ||	||| |	||| |||gksJ ||	|| ||	||| |	||| |||gksÒJ ||	|| ||	||| |	||| |||gks
J ||	|| ||	||| |	||| |||gksBJ ||	||||
||| |||gksnJ ||	||||
||| |||gksJ ||	||||
||| |||gksÆJ ||	||||
||| |||gksòJ ||	||||
||| |||gksJ ||	||||
||| |||gksJJ ||
||||	||| |||gksvJ ||
||||	||| |||gks¢J ||
||||	||| |||gksÎJ ||
||||	||| |||gksúJ ||
||||	||| |||gks&J ||
||||	||| |||gksRJ d S )Nrœ   Tr   zk l mr   rÆ   r   rŸ   rG   ÚAr   r   )r-   r+   r&   r!   )rÉ   rÐ   ru   rv   rY   rK   rL   r6   r7   rî   r   r   rÊ   rB   rB   rC   Útest_dummy_order_well_defined¯  sP    $$$$2222222288888888,,,,,,,,,,,rï   c            '      C   sš  t ddd\} }t ddtd\}}}}}t ddtd\}}}	}
}t dtd	\}}t d
dtd\}}}}t ddtd\}}}}t ddtd\}}}}t ddtd\}}}}td}td}ddlm}  |||||| ||| ||| ||| }!| |||	|
|gd}"|! t|||||gt|"¡}#|"D ]:}$t|||||g|$}%|! |%¡}&t|&t|#ks,J q,|||||| ||| ||| ||| }!| |||	|
|gd}"|! t|||||gt|"¡}#|"D ]:}$t|||||g|$}%|! |%¡}&t|&t|#ksÐJ qÐ|||||||||| ||| }!| |||	|
|gd}"|! t|||||gt|"¡}#|"D ]:}$t|||||g|$}%|! |%¡}&t|&t|#kshJ qhd S )Nrœ   Tr   z	i j k l mr   z	a b c d er   rŸ   rG   rÙ   zp5 p6 p7 p8rÚ   zh5 h6 h7 h8rî   r   r   rÀ   ri   )	r-   r+   r&   rÂ   rÁ   ra   rÜ   rÝ   r"   )'rÉ   rÐ   r=   rW   ru   rv   rY   rI   rJ   rK   rL   ro   r6   r7   r@   rA   rß   rà   Zp5Zp6Zp7Zp8rá   râ   rã   rä   Úh5Úh6Zh7Zh8rî   r   rÁ   rå   ræ   rç   rÃ   rè   r?   rB   rB   rC   Útest_dummy_order_ambiguousç  s@    2
2
&
rò   c                  G   s   t d| d d | dd  S )Nr³   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rLtd| d f| d fS d S )Nrh   r­   rR   r   rQ   )rj   r   ró   rB   rB   rC   r¶     s    r¶   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sôJ qôd S )Nr=   Tr   rI   r   rÅ   r   rÆ   r   rQ   r   ©r-   r+   rô   r¶   r"   )rÈ   rÉ   ru   rv   rK   rL   rË   rÃ   rB   rB   rC   Ú-test_dummy_order_inner_outer_lines_VT1T1T1_AT  s    ****úrö   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|| g}|d
d  D ]}	t|d t|	 ksðJ qðt||||t||  t|| t|| t|| t||||t|| t||  t|| t|| g}|d
d  D ] }	t|d t|	ksJ qd S ©Nrº   Tr   rœ   r   rÅ   r   rÆ   r   rQ   r   rõ   ©
rÈ   rÏ   rÉ   rÐ   ru   rv   rK   rL   rË   rÃ   rB   rB   rC   Ú/test_dummy_order_inner_outer_lines_VT1T1T1T1_AT1  s    444ü44ýrù   c            
      C   sT  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 qt| |||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s|J q|t| |||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   ru   rv   rI   rJ   rK   rL   rË   rÃ   rB   rB   rC   Ú'test_equivalent_internal_lines_VT1T1_ATL  s2       ý  þ  þ    ürü   c                  C   sÄ  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 ]4}t||||g|}| |¡}t	|t	|ksÈJ qÈt||||t||||  t|| || }|||||	gd
}| t||||gt|¡}|D ]8}t||||g|}| |¡}t	|t	|ksZJ qZt||||t||| | t|| || }|||||	gd
}| t||||gt|¡}|D ]8}t||||g|}| |¡}t	|t	|ksðJ qðt||||t||||  t| ||| }|||||	gd
}| t||||gt|¡}|D ]8}t||||g|}| |¡}t	|t	|ksJ qd S ©Nr×   Tr   rØ   r   rÙ   rÚ   r   rÀ   rh   ©
r-   r+   rÂ   rÁ   rô   r¶   ra   rÜ   rÝ   r"   ©r=   rW   ru   rv   rY   rX   rI   rJ   rK   rL   ro   r:   r@   rA   rß   rà   rá   râ   rã   rä   rÁ   rå   ræ   rç   rÃ   rè   r?   rB   rB   rC   Ú+test_equivalent_internal_lines_VT2conjT2_ATp  sB    *
*
*
*
r   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 ]4}t||||g|}| |¡}t	|t	|ksÈJ qÈt||||t||||  t||| | }|||||	gd
}| t||||gt|¡}|D ]8}t||||g|}| |¡}t	|t	|ksZJ qZd S rý   rþ   rÿ   rB   rB   rC   Ú;test_equivalent_internal_lines_VT2conjT2_ambiguous_order_AT  s&    *
*
r  c            
   	   C   sÆ  t ddtd\} }}}t ddtd\}}}}t| |||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sJ qt| |||t||| | t|| ||t||||  t| |||t||| | t|| ||t||||  g}|dd  D ] }	t|d t|	ks J q d S rú   rõ   rû   rB   rB   rC   Ú%test_equivalent_internal_lines_VT2_ATµ  s*    üüür  c            
   	   C   sº  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sôJ qôt||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| g}|d
d  D ] }	t|d t|	ksÂJ qÂt||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| t||||t||| | t|||| g}|d
d  D ] }	t|d t|	ksJ qd S r÷   rõ   rø   rB   rB   rC   Útest_internal_external_VT2T2_ATÕ  s2    ((((ü((((ü((((ür  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sèJ qèd S )Nrº   rœ   rÅ   rG   rÆ   rQ   r   rõ   rø   rB   rB   rC   Útest_internal_external_pqrs_ATõ  s    ((((ür  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sZJ d S )Nr³   )rK   rL   Tr   )ru   rv   r   )r-   r+   r   )r³   rK   rL   ru   rv   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$   Zsympy.concrete.summationsr%   Zsympy.core.functionr&   r'   Zsympy.core.numbersr(   r)   Zsympy.core.singletonr*   Zsympy.core.symbolr+   r,   r-   Z(sympy.functions.elementary.miscellaneousr.   Zsympy.printing.reprr/   Zsympy.simplify.simplifyr0   Zsympy.testing.pytestr1   r2   Zsympy.printing.latexr3   rD   rO   rZ   r^   re   rf   rn   rp   rr   rs   ry   rz   r{   r   r   r   r   r   r   r   r   r§   rš   r«   r¬   r²   rµ   rž   r»   rŒ   r¿   rÄ   rÌ   rÑ   rÒ   rÕ   ré   rê   rë   rì   rí   rï   rò   rô   r¶   rö   rù   rü   r   r  r  r  r  r  r  rB   rB   rB   rC   Ú<module>   s   
	
- 	3*&#5,2!1'8+$*  