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    L?h¢¿  ã                	   @   sf  d dl mZ d dlmZ d dlmZ d dlmZmZm	Z	 d dl
mZ d dl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
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EquivalentÚITEÚImpliesÚNandÚNorÚNotÚOrÚPOSformÚSOPformÚXorÚXnorÚ	conjunctsÚ	disjunctsÚdistribute_or_over_andÚdistribute_and_over_orÚeliminate_implicationsÚis_nnfÚis_cnfÚis_dnfÚsimplify_logicÚto_nnfÚto_cnfÚto_dnfÚto_int_reprÚbool_mapÚtrueÚfalseÚBooleanAtomÚ
is_literalÚterm_to_integerÚtruth_tableÚ
as_BooleanÚto_anfÚis_anfÚdistribute_xor_over_andÚ
anf_coeffsÚANFformÚbool_mintermÚbool_maxtermÚbool_monomialÚ_check_pairÚ_convert_to_varsSOPÚ_convert_to_varsPOSÚ	ExclusiveÚgateinputcount)ÚCNF)ÚraisesÚXFAILÚslow)ÚcombinationsÚpermutationsÚproductzA:Dza:e w:zc                   C   s¤   t t@ tt tƒkst‚t tB tt tƒks,t‚t t@ tB ttt tƒtƒksLt‚t t? tt tƒksbt‚t t> ttt ƒksxt‚t  tt ƒksŠt‚t tA tt tƒks t‚dS )z)Test that |, & are overloaded as expectedN)	ÚAÚBr   ÚAssertionErrorr   ÚCr   r   r   © rM   rM   úP/var/www/html/venv/lib/python3.8/site-packages/sympy/logic/tests/test_boolalg.pyÚtest_overloading!   s     rO   c                  C   sÚ  t ƒ tkst‚t tƒtkst‚t dƒtks.t‚t dƒtks>t‚t ddƒtksPt‚t ddƒtksbt‚t ddƒtkstt‚t dtƒtks†t‚t dtƒtks˜t‚t dddƒtks¬t‚t ddtƒtksÀt‚t ddtƒtksÔt‚t dtƒtksæt‚ttdd„ ƒ t tdk tdkƒtkst‚tdk} t | | jƒ| jks0t‚ttkttk ttkttkf\}}}}t ||||ƒt ||ƒksrt‚dd„ t	||||fƒD ƒt ||ƒhksžt‚t t t
tdƒt
tdƒƒt ttdƒt
tdƒƒƒtksÖt‚d S )	NTFé   c                   S   s
   t dtƒS ©Né   )r   rI   rM   rM   rM   rN   Ú<lambda>;   ó    ztest_And.<locals>.<lambda>c                 S   s   h | ]}t |Ž ’qS rM   )r   ©Ú.0ÚirM   rM   rN   Ú	<setcomp>A   s     ztest_And.<locals>.<setcomp>r   )r   r.   rK   rI   r/   rC   Ú	TypeErrorÚ	canonicalrJ   rG   r   ÚaÚbr   Úc©ÚeÚgÚlÚgeÚlerM   rM   rN   Útest_And-   s*    $,rd   c                  C   st  t ƒ tkst‚t tƒtkst‚t dƒtks.t‚t dƒtks>t‚t ddƒtksPt‚t ddƒtksbt‚t ddƒtkstt‚t dtƒtks†t‚t dtƒtks˜t‚t dddƒtks¬t‚t ddtƒtksÀt‚t ddtƒtksÔt‚t dtƒtksæt‚ttdd„ ƒ t tdk tdkƒtkst‚tdk} t | | jƒ| ks.t‚ttkttk ttkttkf\}}}}t ||||ƒt ||ƒkspt‚d S )NTFrP   c                   S   s
   t dtƒS rQ   )r   rI   rM   rM   rM   rN   rS   S   rT   ztest_Or.<locals>.<lambda>)	r   r/   rK   rI   r.   rC   rY   rZ   rJ   r^   rM   rM   rN   Útest_OrE   s&    $re   c                  C   s  t ƒ tkst‚t tƒtkst‚t ttƒtks0t‚t dttƒtksDt‚t tttttƒtks\t‚t dddttƒt ttƒ ks|t‚t dƒtksŒt‚t dƒtksœt‚t ddƒtks®t‚t ddƒtksÀt‚t ddƒtksÒt‚t dtƒt ksæt‚t dtƒtksøt‚t dddƒtkst‚t ddtƒt ks&t‚t ddtƒtks<t‚tt ttƒt ƒsRt‚t ttt ttƒƒt ttttƒksxt‚t ttt ttƒƒt ttƒksšt‚t tdk tdktƒt ddtƒ  krÒt ddtƒksØn t‚tdk} t | | j	ƒt ddƒ  krt ddƒksn t‚d S ©NTFrP   r   )
r   r/   rK   rI   r.   rJ   Ú
isinstancerL   ÚDrZ   )r_   rM   rM   rN   Útest_Xor[   s,     &">ri   c                  C   s.   t tA } |  t¡t tB t  t B @ ks*t‚d S ©N)ÚxÚyÚrewriter   rK   ©ÚexprrM   rM   rN   Útest_rewrite_as_Andt   s    rp   c                  C   s.   t tA } |  t¡t t @ tt  @ B ks*t‚d S rj   )rk   rl   rm   r   rK   rn   rM   rM   rN   Útest_rewrite_as_Ory   s    rq   c                  C   s<   t t@ tt @ B } |  t¡t t@  tt @  @  ks8t‚d S rj   )rl   ÚzÚwrm   r   rK   rn   rM   rM   rN   Útest_rewrite_as_Nand~   s    rt   c                  C   s4   t tt B @ } |  t¡t  tt B  B  ks0t‚d S rj   )rr   rl   rs   rm   r   rK   rn   rM   rM   rN   Útest_rewrite_as_Norƒ   s    ru   c                   C   sb   t tdd„ ƒ tdƒtkst‚tdƒtks.t‚tdƒtks>t‚tdƒtksNt‚tdƒtks^t‚d S )Nc                   S   s
   t ddƒS ©NTF)r   rM   rM   rM   rN   rS   ‰   rT   ztest_Not.<locals>.<lambda>TFr   rP   rR   )rC   rY   r   r/   rK   r.   rM   rM   rM   rN   Útest_Notˆ   s    rw   c                   C   sÞ   t ƒ tkst‚t tƒt ks t‚t dƒtks0t‚t dƒtks@t‚t ddƒtksRt‚t ddƒtksdt‚t ddƒtksvt‚t dtƒt ksŠt‚t dtƒtksœt‚t dddƒtks°t‚t ddtƒt ksÆt‚t ddtƒtksÚt‚d S rv   )r   r/   rK   rI   r.   rM   rM   rM   rN   Ú	test_Nand‘   s    rx   c                   C   sÜ   t ƒ tkst‚t tƒt ks t‚t dƒtks0t‚t dƒtks@t‚t ddƒtksRt‚t ddƒtksdt‚t ddƒtksvt‚t dtƒtksˆt‚t dtƒt ksœt‚t dddƒtks°t‚t ddtƒtksÄt‚t ddtƒtksØt‚d S rv   )r   r.   rK   rI   r/   rM   rM   rM   rN   Útest_Nor    s    ry   c                   C   s"  t ƒ tkst‚t tƒt ks t‚t ttƒtks2t‚t dttƒtksFt‚t tttttƒt ks`t‚t dƒtkspt‚t dƒtks€t‚t ddƒtks’t‚t ddƒtks¤t‚t ddƒtks¶t‚t dtƒtksÈt‚t dtƒt ksÜt‚t dddƒtksðt‚t ddtƒtkst‚t ddtƒt kst‚d S rv   )r   r.   rK   rI   r/   rM   rM   rM   rN   Ú	test_Xnor¯   s    rz   c                   C   sê   t tdd„ ƒ tddƒtks t‚tddƒtks2t‚tddƒtksDt‚tddƒtksVt‚tdtƒtksht‚tddƒtkszt‚tddƒtksŒt‚tt? tt> ks t‚tdk tdk? tdkks¼t‚tdk tj	tk? tksÖt‚tt? tksæt‚d S )Nc                   S   s   t tttƒS rj   )r   rI   rJ   rL   rM   rM   rM   rN   rS   Â   rT   ztest_Implies.<locals>.<lambda>TFr   rP   )
rC   Ú
ValueErrorr   r.   rK   r/   rI   rJ   r   ÚOnerM   rM   rM   rN   Útest_ImpliesÁ   s    r}   c                   C   s  t ttƒt ttƒ  kr(t tttƒks.n t‚t ƒ tks<t‚t ttƒt tƒ  krZtks`n t‚t ddƒt ddƒ  kr€tks†n t‚t ddƒt ddƒ  kr¦tks¬n t‚t tdƒtks¾t‚t tdƒttƒksÔt‚t ttdƒtt@ ksìt‚t ttdƒt t @ ks
t‚t dtƒtkst‚t dtƒttƒks6t‚t tt ttƒƒt t ttƒtƒks\t‚t tdk tdkƒtksxt‚t tdk tdkdƒtks–t‚t tdk tdkdƒtks´t‚t tdk tj	tkƒt ddƒ  krèt ddƒksîn t‚t t
ttƒt
ttƒƒtkst‚d S rf   )r   rI   rJ   rK   r.   r/   r   rL   r   r|   r   rM   rM   rM   rN   Útest_EquivalentÐ   s"    .$&&&:r~   c                   C   sT   t dddƒtkst‚t dddƒtks(t‚t dddƒtks<t‚t dddƒtksPt‚d S )NFT)r@   r.   rK   r/   rM   rM   rM   rN   Útest_Exclusiveä   s    r   c                   C   sÒ   t tttƒƒ tt tƒt tƒƒ¡dks*t‚tttƒ tt? tt? @ ¡dksNt‚tt B t tB @  t t @ tt@ B ¡dks€t‚tt?  t t ? ¡dksžt‚ttt? ?  ttt? ? ¡dksÀt‚t	t
dd„ ƒ d S )NTFc                   S   s   t t@  t tk¡S rj   )rI   rJ   ÚequalsrM   rM   rM   rN   rS   ñ   rT   ztest_equals.<locals>.<lambda>)r   r   rI   rJ   r€   r   rK   r   rL   rC   ÚNotImplementedErrorrM   rM   rM   rN   Útest_equalsë   s    *$2"r‚   c               	      s@
  dddgdddgdddgdddgg} dddgdddgdddgdddgg}t tttg| ƒttttƒtƒtttƒtƒƒkszt‚tt tttg|ƒƒtttttƒttƒƒtttƒƒƒks´t‚ttttg| | ƒt	ksÐt‚t tttg| | ƒt	ksìt‚t t
ƒ t
ƒ t
ƒ g| | ƒt	kst‚ddddgddddgddddgddddgddddgg‰ ddddgddddgddddgg}t ttttgˆ |ƒttttƒtttƒttƒƒƒks t‚tttttgˆ |ƒttttƒtƒtƒksÎt‚dddddg‰ dddg}t ttttgˆ |ƒttttƒtttƒttƒƒƒkst‚tttttgˆ |ƒttttƒtƒtƒksLt‚dddddgdddddgddddgg‰ dddddgdg}t ttttgˆ |ƒttttƒtttƒttƒƒƒks¼t‚tttttgˆ |ƒttttƒtƒtƒksêt‚dtdtdig‰ dddddgdg}t ttttgˆ |ƒttttƒtttƒttƒƒƒksDt‚tttttgˆ |ƒttttƒtƒtƒksrt‚tdtdidg‰ ddddgg}dddgg‰ tt‡ fd	d
„ƒ tt‡ fdd
„ƒ ttdd
„ ƒ tttttƒƒ}ttttB @ ƒ|ksøt‚ttt@ tt@ B ƒ|kst‚ttttƒƒtttƒtƒks8t‚ttttƒƒttttƒtttƒttƒƒƒksjt‚ttttdƒtƒƒtttdƒtƒks”t‚ttttdƒtƒƒtttdƒtƒks¾t‚tttttƒtƒƒttttƒtƒksèt‚tttttdƒtƒtttdƒtƒƒƒtttdƒtttƒƒks*t‚t t @ t @ t t @ t@ B }tt|ƒ}t|ƒtt @ t @ kstt‚ttdd
„ ƒ ttttktttk tƒƒƒttkks¬t‚ttttktttktƒƒƒttkksÖt‚ttttktttk tƒƒƒttkks t‚tdƒ\	}}}}}}	}
}}||@ |@ |@ |@ |	@ |
@ |@ |@ ||@ |@ |@ |@ |	@ |
@ |@ | @ B }t|ƒ|ksvt‚t||@ |B |B ||@ d||B ks t‚t ttgddggƒ}t ttgddggƒ|ksÒt‚tttgddggƒ|ksðt‚ttdd
„ ƒ t tgdggdggƒt	kst‚t tgdggdggƒt	ks>t‚t tgg g ƒtksVt‚ttdd
„ ƒ ttgdggdggƒt	ks„t‚ttgdggdggƒt	ks¤t‚ttgg g ƒtks¼t‚ttt@ tt@ B ƒtttttƒƒksæt‚tttttƒƒƒdkst‚tttttƒƒƒdkst‚ttttdƒtttƒƒƒtttdƒttdƒƒksTt‚tttd dƒtttƒƒ ¡ tttdƒttdƒƒksŽt‚tttd dƒtttƒƒ ¡ tttdƒtttƒƒksÈt‚tttd dƒtttƒƒ ¡ tttdƒttdƒƒk	st‚tttd dƒtttt ƒttt dƒƒ ¡ tttdƒttdƒttdƒƒk	sTt‚tttd dƒttd dƒƒ ¡ ttdƒk	s†t‚tttd dƒttd dƒƒ ¡ ttdƒk	s¸t‚tttd dƒttd dƒƒ ¡ dk	sät‚tttd dƒttd dƒƒ ¡ tttdƒttdƒƒk
s"t‚tttt ƒƒdk
s<t‚dS )z1
    Test working of simplification methods.
    r   rP   é   é   é   é   rR   é   c                      s   t ttttgˆ ƒS rj   )r   rs   rk   rl   rr   rM   ©ÚmintermsrM   rN   rS   $  rT   z-test_simplification_boolalg.<locals>.<lambda>c                      s   t ttttgˆ ƒS rj   ©r   rs   rk   rl   rr   rM   rˆ   rM   rN   rS   %  rT   c                   S   s   t ttttgdgƒS )NZabcdefgrŠ   rM   rM   rM   rN   rS   '  rT   c                   S   s   t tttB @ ddS )NZblabla)Úform)r(   rI   rJ   rL   rM   rM   rM   rN   rS   8  rT   za b c d e f g h j)Zdontcarec                   S   s   t tgdggdggƒS ©NrP   )r   rk   rM   rM   rM   rN   rS   M  rT   c                   S   s   t tgdggdggƒS rŒ   )r   rk   rM   rM   rM   rN   rS   R  rT   FTéÿÿÿÿN)r   rk   rl   rr   r   r   r   rK   r   r.   r	   rs   rC   r{   rY   rI   rJ   rL   r(   r   r   r   r   r
   r/   r   r   r   )Zset1Zset2Ú	dontcaresZansr\   r_   r[   r]   ÚdÚfr`   ÚhÚjro   rM   rˆ   rN   Útest_simplification_boolalgô   sÊ    $$2 ÿ$(
ÿ"ÿÿ.
ÿÿ.
ÿÿÿ.ÿÿ."ÿ
***$ÿ
"
***"$ÿ*    *6:::,ÿ
22, ÿ
r“   c               
   C   s  ddddgddddgddddgddddgddddgg} t tttƒƒtƒtttifksXt‚t tttttg| ƒt	ttttg| ƒƒt
tttƒtƒtttƒtƒtƒttttttttifks¶t‚t ttttgdddggƒttttgdddggƒƒdksðt‚ttttgdddgdddggƒ}ttttgdddgdddggƒ}t ||ƒ|ttttifksPt‚t tttƒtttƒ ƒdksrt‚t t
ttƒtttƒƒdks’t‚t t
ttƒt
tttƒƒdks´t‚t ttttƒttttƒ ƒdksÚt‚t tttttƒtttttƒ ƒdkst‚dS )z,
    Test working of bool_map function.
    r   rP   FN)r-   r   r[   rK   r   rs   rk   rl   rr   r   r   r   r\   r]   r   )r‰   Z	function1Z	function2rM   rM   rN   Útest_bool_mapi  s0    (
ÿ"ÿ2þÿÿ  ÿ
" "&r”   c                   C   st   t tdƒtkst‚t tddƒtks&t‚t tdƒtks8t‚t tddƒtksLt‚ttdƒtks^t‚ttdƒtkspt‚dS )zBTest that mixing symbols with boolean values
    works as expectedTFN)r   rI   rK   r/   r   r.   rM   rM   rM   rN   Útest_bool_symbol‚  s    r•   c                   C   sÞ   t dtƒdkst‚t ttƒdks$t‚ddks0t‚dtks<t‚dtkdksLt‚ddksXt‚dtksdt‚dtkdkstt‚tjdks‚t‚tt@ jst‚ttB jsžt‚t jsªt‚ttA js¸t‚tjt ttƒksÌt‚t ttƒsÚt‚d S rf   )rg   r   rK   r.   r/   Z
is_BooleanrI   rJ   rM   rM   rM   rN   Útest_is_booleanŽ  s    r–   c                   C   s   t t@  t d¡tkst‚t t@  t d¡tks0t‚t t@  td¡t ksHt‚t t@  td¡tks`t‚t t@  t dtdi¡tks~t‚t tB  t d¡tks–t‚t tB  t d¡tks®t‚t tB  td¡tksÆt‚t tB  td¡t ksÞt‚t tB  t dtdi¡tksüt‚d S rv   )rI   rJ   ÚsubsrK   r/   r.   rM   rM   rM   rN   Ú	test_subs   s    r˜   c                  C   s>   t ttdƒƒ\} }| |@ || @ ks&t‚| |B || B ks:t‚dS )z$Test for commutativity of And and OrzA,BN)Úmapr   r
   rK   )rI   rJ   rM   rM   rN   Útest_commutative³  s    rš   c                   C   s    t t@ t@ t tt@ @ kst‚dS )zTest for associativity of AndN©rI   rJ   rL   rK   rM   rM   rM   rN   Útest_and_associativity»  s    rœ   c                   C   s    t tB tB t ttB B kst‚d S rj   r›   rM   rM   rM   rN   Útest_or_assicativityÁ  s    r   c                  C   s   t ƒ } |   | kst‚d S rj   )r   rK   )r[   rM   rM   rN   Útest_double_negationÅ  s    rž   c                   C   s–   t tttddƒt tB ks t‚t ttttƒ? ? ƒttttƒttƒƒttƒƒksTt‚t ttttt	ƒƒt tB t tB @ t t	B @ t	 tB @ ks’t‚d S )NF©Úevaluate)
r$   r   rI   rJ   rK   rL   r   r   r   rh   rM   rM   rM   rN   Útest_eliminate_implicationsÌ  s     ÿÿ&ÿr¡   c                   C   sx   t tt@ t@ ƒttthkst‚t ttB t@ ƒttB thks>t‚t tƒthksPt‚t dƒdhksbt‚t dƒdhkstt‚d S rv   )r    rI   rJ   rL   rK   rM   rM   rM   rN   Útest_conjunctsÔ  s
     r¢   c                   C   sz   t ttB tB ƒttthkst‚t ttB t@ ƒttB t@ hks@t‚t tƒthksRt‚t dƒdhksdt‚t dƒdhksvt‚d S rv   )r!   rI   rJ   rL   rK   rM   rM   rM   rN   Útest_disjunctsÜ  s
    "r£   c                   C   sŽ   t ttttƒtƒƒttttƒtttƒƒks.t‚ttttttƒƒƒttttƒtttƒƒks\t‚tttt	ttƒƒƒt	tttƒtttƒƒksŠt‚d S rj   )
r#   r   r   rI   rJ   rL   rK   r"   r7   r   rM   rM   rM   rN   Útest_distributeä  s    ..r¤   c               	   C   sˆ  t dƒ\} }}tt| |ƒƒt| |ƒks*t‚tt| |ƒƒt| |t| |ƒƒksNt‚ttt| |ƒt| |ƒ|ƒƒt| d| |@ ddks‚t‚ttt| |ƒt| |ƒt	| |ƒt| |ƒƒƒdks´t‚tt| t
|ƒt| |ƒt| |ƒt||ƒƒƒtdt||ƒt| ||ƒddkst‚tt| |ƒƒt| |ƒks t‚tt
| ƒƒt| dddks@t‚tt| |ƒƒtdt| |ƒddksht‚tt| |ƒƒt| |dt| |ƒddks”t‚tt| |ƒƒt| dt| |ƒddks¾t‚tt| |ƒƒt| |dddksât‚tt| |B | |? ƒddtdtt| |ƒt| |ƒƒddks"t‚tt| |A | |@ ƒddtdtt| |ƒt| |ƒƒddksbt‚t| | |A | A  A ƒdks„t‚d S )Núx,y,zTF©Zremove_true)Údeep)r
   r5   r   rK   r   r   r   r   r   r   r   r   ©rk   rl   rr   rM   rM   rN   Útest_to_anfê  s.    $ÿ2(ÿ
 (,*$ÿ
ÿ
r©   c                   C   s  t tƒtkst‚t tƒtks t‚t tƒtks0t‚t tt B tB ƒtksJt‚t tt @ t@ ƒtksdt‚t tt? ƒt tB ks~t‚t ttttƒƒt tB t tB @ t tB @ ks°t‚t ttA tA ƒttB tB t t B tB @ tt B t B @ t tB t B @ kst‚t ttttƒƒt tB ttB @ ks*t‚t t	ttB tB ƒƒt t @ t @ ksVt‚t t	tt@ t@ ƒƒt t B t B ks‚t‚t t	tt? ƒƒtt @ ks¢t‚t t	ttttƒƒƒt
ttttƒtt t t ƒƒksÜt‚t t	ttA tA ƒƒt tB tB tt B tB @ ttB t B @ t t B t B @ ks2t‚t t	ttttƒƒƒt t B tt B @ ksbt‚t tt? tt? A ƒtt @ t t@ B kst‚t tt? tt? A dƒt t B tB tB tt @ t t@ B @ ksÔt‚ttddƒ  ¡ tksît‚ttddƒ  ¡ t ks
t‚ttdd„ ƒ d S )NFrP   r   c                   S   s   t tdk dgtƒ ¡ S rŒ   )r   rI   rJ   r)   rM   rM   rM   rN   rS     rT   ztest_to_nnf.<locals>.<lambda>)r)   r.   rK   r/   rI   rJ   r   rL   r   r   r   r   rC   rY   rM   rM   rM   rN   Útest_to_nnf  s4    2:ÿ
(,, ::ÿ
0.&ÿ
rª   c                	   C   s¨  t ttB  ƒtttƒttƒƒks$t‚t tt@ tB ƒttttƒtttƒƒksNt‚t tt? ƒt tB ksht‚t ttt@ ? ƒt tB t tB @ kst‚t tttB @ t ttB @ B dƒttB ks¼t‚t tt@ ƒtttƒksÖt‚t tttƒƒtttttƒƒttttƒƒƒkst‚t tttt@ ƒƒt tB t tB @ t t B tB @ ksDt‚t ttttB ƒdƒttttƒtƒtttƒtƒtttttƒƒƒksŠt‚t td ƒtd ks¤t‚d S ©NTrP   )	r*   rJ   rL   r   r   rK   rI   r   r   rM   rM   rM   rN   Útest_to_cnf  s    $*(,2"ÿ
*ÿ
r¬   c                     s  t dƒ\} }}}}}}}}}	}
}}}}| |@ |@ |@ |@ |@ |@ |@ |@ | |@ |@ |@ |@ |@ |@ |	@ |@ B | |
@ |@ |@ |@ |@ |@ |@ |@ B ‰ ttˆ ƒƒs¢t‚tt‡ fdd„ƒ tttftt	fƒD ]H\}}|| ||||||||ƒ	‰ tt‡ fdd„ƒ |ˆ dddˆ ksÆt‚qÆd S )Nzx1:16c                      s   t ˆ ddS ©NTr   ©r*   rM   ©ÚeqrM   rN   rS   3  rT   z"test_issue_18904.<locals>.<lambda>c                      s   t ˆ ddS r­   r®   rM   r¯   rM   rN   rS   6  rT   T)r   Úforce)
r
   r&   r*   rK   rC   r{   Úzipr   r   r+   )Úx1Zx2Zx3Zx4Zx5Zx6Zx7Zx8Zx9Úx10Zx11Zx12Zx13Zx14Zx15r   ÚtrM   r¯   rN   Útest_issue_18904-  s    &""ÿ"þr¶   c                   C   s(   t ttdktdktdk @ B ƒƒs$t‚d S )NéûÿÿÿrR   é   )r&   r*   r\   r[   rK   rM   rM   rM   rN   Útest_issue_9949:  s    r¹   c                   C   s  t  t  ttB  ¡¡tttB  ƒks(t‚t  t  tt@ tB ¡¡ttt@ tB ƒksTt‚t  t  tt? ¡¡ttt? ƒksxt‚t  t  ttt@ ? ¡¡tttt@ ? ƒks¤t‚t  t  tttB @ t ttB @ B ¡¡ttttB @ t ttB @ B ƒksìt‚t  t  tt@ ¡¡ttt@ ƒkst‚d S rj   )rB   Z
CNF_to_cnfZto_CNFrJ   rL   r*   rK   rI   rM   rM   rM   rN   Útest_to_CNF>  s    (,$,Hrº   c                   C   s<  t ttB  ƒtttƒttƒƒks$t‚t tttB @ ƒttttƒtttƒƒksNt‚t tt? ƒt tB ksht‚t ttt@ ? ƒt tt@ B ksŠt‚t ttB ƒttB ks¢t‚t tttƒdƒttttƒtttƒttƒƒƒksÔt‚t tttt@ ƒdƒtttttƒtttƒttƒƒtttƒttƒƒƒkst‚t td ƒtd ks8t‚d S r«   )	r+   rJ   rL   r   r   rK   rI   r   r   rM   rM   rM   rN   Útest_to_dnfG  s    $*"ÿ.ÿ
r»   c                     s–   t ttdƒƒ\} }}‡ fdd„‰ ˆ t| |B || B g| ||gƒƒˆ ddgddggƒksXt‚ˆ t| |B ||  B g| ||gƒƒˆ ddgddggƒks’t‚d S )Nr¥   c                    s6   zt ‡ fdd„| D ƒƒW S  tk
r0   |  Y S X d S )Nc                 3   s   | ]}ˆ |ƒV  qd S rj   rM   )rV   rk   ©Úsorted_recursiverM   rN   Ú	<genexpr>Z  s     z=test_to_int_repr.<locals>.sorted_recursive.<locals>.<genexpr>)ÚsortedrY   )Úargr¼   rM   rN   r½   X  s    z*test_to_int_repr.<locals>.sorted_recursiverP   rR   rƒ   r   )r™   r   r
   r,   rK   r¨   rM   r¼   rN   Útest_to_int_reprU  s    ÿ ÿrÁ   c                  C   s¬   t dƒ\} }ttƒdkst‚ttƒdks,t‚t| ƒdks<t‚tt| |ƒƒdksRt‚tt| |t| |ƒƒƒdkspt‚tt| |t| |ƒƒƒdksŽt‚ttt| ƒ|ƒƒdks¨t‚d S )Núx,yTF)	r
   r6   r.   rK   r/   r   r   r   r   ©rk   rl   rM   rM   rN   Útest_is_anfd  s    rÄ   c                   C   s  t tƒdkst‚t tƒdks t‚t t ƒdks2t‚t tt@ ƒdksFt‚t tt@ t t@ B t t@ B t t @ B dƒdks|t‚t ttB t t B @ ƒdksœt‚t ttttƒƒƒdks¶t‚t ttA ƒdksÊt‚t tt@ t t@ B t t@ B t t @ B dƒdkst‚d S rv   )r%   r.   rK   rI   rJ   r   r   rM   rM   rM   rN   Útest_is_nnfo  s    6 rÅ   c                   C   sŽ   t tƒdkst‚t ttB tB ƒdks(t‚t tt@ t@ ƒdks@t‚t ttB t@ ƒdksXt‚t tt@ tB ƒdkspt‚t tt@  tB ƒdksŠt‚d S rv   )r&   rk   rK   rl   rr   rM   rM   rM   rN   Útest_is_cnf{  s    rÆ   c                   C   sŽ   t tƒdkst‚t ttB tB ƒdks(t‚t tt@ t@ ƒdks@t‚t tt@ tB ƒdksXt‚t ttB t@ ƒdkspt‚t ttB  t@ ƒdksŠt‚d S rv   )r'   rk   rK   rl   rr   rM   rM   rM   rN   Útest_is_dnf„  s    rÇ   c                  C   s¢  t dƒ\} }}tdddƒtks"t‚tdddƒtks6t‚tdddƒtksJt‚tdddƒtks^t‚tt| ||ƒtƒstt‚d} t| ||ƒ|ksŒt‚d} t| ||ƒ|ks¤t‚d}tt| |ƒ||ƒ|ksÂt‚tt| dƒt|dƒdƒtksât‚tt| |ƒt	tƒksút‚tt|| ƒtkst‚tdtt
ƒtks&t‚tdtt
ƒt
ks<t‚ttdd„ ƒ ttdd„ ƒ ttd	d„ ƒ ttd
d„ ƒ tdddƒtjksŒt‚ttdddddtƒs¨t‚tttdƒt
tƒttt
tƒksÌt‚tttdƒt
tƒtt t
tƒksòt‚tttdƒt
tƒtt t
tƒkst‚tttdƒt
tƒttt
tƒks<t‚tttjtƒt
tƒttt
tƒksbt‚tttjtƒt
tƒtt t
tƒksŠt‚tttjtƒt
tƒtt t
tƒks²t‚tttjtƒt
tƒttt
tƒksØt‚tttdƒt
tƒtksôt‚tttdƒt
tƒtkst‚tttdƒt
tƒt
ks,t‚tttdƒt
tƒt
ksHt‚tttdƒt
tƒ td¡t
kslt‚tttdƒt
tƒ td¡tkst‚ttdd„ ƒ d S )NzA:CTFrP   r   c                   S   s   t dttƒS rQ   )r   rk   rl   rM   rM   rM   rN   rS      rT   ztest_ITE.<locals>.<lambda>c                   S   s   t dg tƒS rŒ   ©r   rl   rM   rM   rM   rN   rS   ¡  rT   c                   S   s   t ddtƒS )NrP   rM   rÈ   rM   rM   rM   rN   rS   ¢  rT   c                   S   s   t dtg ƒS rŒ   rÈ   rM   rM   rM   rN   rS   £  rT   rŸ   c                   S   s   t tdktttƒS rŒ   )r   rk   rl   rr   rM   rM   rM   rN   rS   ¸  rT   )r
   r   r/   rK   r.   rg   r   r   rk   r   rl   rC   rY   r   r   r   rr   r—   r{   )rI   rJ   rL   rM   rM   rN   Útest_ITE  sL     $&&$&((&$$rÉ   c                   C   sè   t dƒdkst‚t dƒdks t‚t tƒdks0t‚t t ƒdksBt‚t tttƒƒdksXt‚t t t¡ƒdksnt‚t tt t¡ƒƒdksˆt‚t tttƒƒdksžt‚t tt t¡t t¡ƒƒdksÀt‚t t	dk ƒsÐt‚t t	t
 dk ƒrät‚d S )NTFrƒ   )r1   rK   rI   r   rJ   r   Úzeror   r   rk   rl   rM   rM   rM   rN   Útest_is_literal»  s    "rË   c                   C   sò  dt @ t d@   krt ks"n t‚dt @ t d@   kr>dksDn t‚t t@ tt tƒksZt‚dt B t dB   krvdks|n t‚dt B t dB   kr˜t ksžn t‚t tB tt tƒks´t‚t  tt ƒksÆt‚dt ? t d>   krât ksèn t‚dt ? t d>   krdksn t‚t d? dt >   kr.dks4n t‚t d? dt >   krVt  ks\n t‚t t? tt >   kr‚tt tƒksˆn t‚dt A t dA   krªt  ks°n t‚dt A t dA   krÐt ksÖn t‚t tA tt tƒksît‚d S rv   )rI   rK   rJ   r   r   r   r   r   rM   rM   rM   rN   Útest_operatorsÉ  s    """""&&(,(&rÌ   c                  C   s  t tj kst‚ttjkst‚t dk	s(t‚tdk	s4t‚t s<t‚trDt‚t dksPt‚tdks\t‚t dkrht‚tdkrtt‚t tkr€t‚tt ƒtdƒks”t‚ttƒtdƒks¨t‚tt dhƒttdhƒ  krÌdksÒn t‚tt tƒsàt‚tttƒsît‚tt tƒrüt‚tttƒrt‚t	t ƒtkst‚t	dƒtks0t‚t	tƒt ksBt‚t	dƒt ksTt‚t  tksdt‚t t kstt‚t
dt fdtfƒD ]f\} }t| |ƒtks¤t‚t|| ƒtks¸t‚t||ƒtksÌt‚t| | ƒt ksàt‚t| tƒtksôt‚t|tƒtkst‚| dkr|dks@| |@ tks.t‚|| @ tks@t‚|dk	r\||@ tks\t‚| dk	rx| | @ t ksxt‚t| |ƒt ksŒt‚t|| ƒt ks t‚t||ƒtks´t‚t| | ƒt ksÈt‚t| tƒt ksÜt‚t|tƒtksðt‚| dkr|dks(| |B t kst‚|| B t ks(t‚|dk	rD||B tksDt‚| dk	r`| | B t ks`t‚t| |ƒt kstt‚t|| ƒt ksˆt‚t||ƒtksœt‚t| | ƒtks°t‚t| tƒt ksÆt‚t|tƒtksÚt‚| dkrî|dks| |A t ks t‚|| A t kst‚|dk	r.||A tks.t‚| dk	rJ| | A tksJt‚t| |ƒt ks^t‚t|| ƒt ksrt‚t||ƒt ks†t‚t| | ƒtksšt‚t| tƒt ks°t‚t|tƒt ksÄt‚t| |ƒtksØt‚t|| ƒtksìt‚t||ƒt ks t‚t| | ƒtkst‚t| tƒtks(t‚t|tƒt ks>t‚t| |ƒtksRt‚t|| ƒt ksft‚t||ƒt kszt‚t| | ƒt ksŽt‚t| tƒtks¢t‚t|tƒt ks¶t‚tt| ƒt ksÊt‚tt|ƒt ksàt‚| dkrô|dks<| |? tkst‚|| > tkst‚|| ? t ks*t‚| |> t ks<t‚|dk	rj||? t ksXt‚||> t ksjt‚| dk	r˜| | ? t ks†t‚| | > t ks˜t‚t| |ƒtks¬t‚t|| ƒtksÀt‚t||ƒt ksÔt‚t| | ƒt ksèt‚t| tƒtksüt‚t|tƒt kst‚tt| ƒtks&t‚tt|ƒt ks<t‚t| | | ƒt ksRt‚t| | |ƒt ksht‚t| || ƒtks~t‚t| ||ƒtks”t‚t|| | ƒt ksªt‚t|| |ƒtksÀt‚t||| ƒt ksÖt‚t|||ƒtks†t‚q†tdd„ tj tjfD ƒƒst‚d S )NTFrP   c                 s   s   | ]}|  d d¡|kV  qdS )rP   rR   Nr   rU   rM   rM   rN   r¾   _  s     z"test_true_false.<locals>.<genexpr>)r.   r   rK   r/   ÚhashÚlenrg   r0   Úboolr   rH   r   rk   r   r   r   r   r   r   r   Úall)ÚTÚFrM   rM   rN   Útest_true_falseÜ  sà    *







rÓ   c                   C   s°  t tdkdtdkƒ ¡ tdtƒks&t‚ttdktdkƒ ¡ tddƒksJt‚ttdktdkƒ ¡ tt dƒtdtƒ kszt‚t	tdkƒ ¡ tt dƒksšt‚t	ttdktdk ƒƒ ¡ t
tt dƒtdtƒƒksÐt‚t ¡ tjksât‚t ¡ tjksôt‚t ¡ tjkst‚tttdk tdkƒtdk ƒ ¡ t t d¡ks<t‚ttdk ttƒdk ƒ ¡ tdk  ¡ ksht‚ttdd„ ƒ td	tdt ƒd tdt ƒd  ƒ ¡ tjks¬t‚d S )
Nr   FrP   rR   éþÿÿÿrƒ   c                   S   s   t tƒdk  ¡ S rŒ   )r   rk   Úas_setrM   rM   rM   rN   rS   o  rT   z"test_bool_as_set.<locals>.<lambda>r   )r   rl   rÕ   r   r   rK   r   rk   r   r   r   r.   r   ZUniversalSetr/   ZEmptySetÚopenr   rC   r   r   r   rM   rM   rM   rN   Útest_bool_as_setb  s    &$0 ÿ4,r×   c                  C   s„   t dƒ\} }t| dk|dkƒ ¡ tdtƒtdtƒ ks:t‚t| dk|dkƒ ¡ tjtj tt dddƒtt dddƒ  ks€t‚d S )NrÂ   r   T)	r
   r   rÕ   r   r   rK   r   r   ZRealsrÃ   rM   rM   rN   Útest_multivariate_bool_as_sett  s
    .ÿrØ   c                  C   s–   t ddd} | t k| tkf}t|Ž }|jtkrTt|jƒt|ƒ| tj¡ ks`t	‚n|dks`t	‚t
|Ž }|jt
kr†t|jƒdks’t	‚n|dks’t	‚d S )Nrk   T)Zextended_realrR   )r
   r   r   ÚfuncrÎ   ÚargsÚcountr   r.   rK   r   )rk   rÚ   ÚvrM   rM   rN   Útest_all_or_nothing}  s    
$
rÝ   c                   C   s    t jt kst‚tjtkst‚d S rj   )r.   rZ   rK   r/   rM   rM   rM   rN   Útest_canonical_atomsŒ  s    rÞ   c                   C   s    t jtkst‚tjt kst‚d S rj   )r.   Znegatedr/   rK   rM   rM   rM   rN   Útest_negated_atoms‘  s    rß   c                   C   sŠ   t tdkttk ƒ ¡ tdtddks(t‚t tdkttk ƒ ¡ tdtƒksLt‚ttk  ¡ tt tƒksht‚tt k ¡ tt tƒks†t‚d S )NrR   T)Z	left_openrP   )r   rk   r   rÕ   r   rK   rM   rM   rM   rN   Útest_issue_8777–  s    ($rà   c                   C   sJ   t tt tk tdkƒtdtkttk ƒƒ ¡ tt dƒtdtƒ ksFt‚d S )NrÔ   rR   )r   r   r   rk   rÕ   r   rK   rM   rM   rM   rN   Útest_issue_8975  s    *ÿrá   c                   C   s2   t dddddddgƒdkst‚t dƒdks.t‚d S )NrP   r   éR   Z0010101000111001i9*  )r2   rK   rM   rM   rM   rN   Útest_term_to_integer¢  s    rã   c                  C   s  t dƒ\} }}}| |@ |@ | |@ B }| | |@ |¡||@ |B ksDt‚| | |@ |@ |¡| |@ |B ksht‚| |B |B | |B @ }| | |B |¡||B |@ ksœt‚| | |B |B |¡| |B |@ ksÀt‚| |A |A | |A @ }| | |A |¡||A |@ ksôt‚| | |A |A |¡| |A |@ kst‚d S )Nza b c d)r
   r—   rK   )r[   r\   r]   r   r   rM   rM   rN   Útest_issue_21971§  s     $ $ rä   c                   C   sÌ   t ttttƒttgddƒddddgks,t‚t tttB ttgddƒddddgksVt‚t ttt? ttgddƒddddgks€t‚t ttttƒttgƒƒddgdfddgdfddgdfddgdfgksÈt‚d S )NF)ÚinputTr   rP   )Úlistr3   r   rk   rl   rK   rM   rM   rM   rN   Útest_truth_table¶  s    
ÿ
ÿ
ÿ*ÿrç   c                     s  t jt jfD ]ð‰tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ t jt jtfD ]”‰ tdƒD ]†} tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ tt‡ ‡fd	d„ƒ tt‡ ‡fd
d„ƒ tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ ˆˆ  ‰ ‰qrqfqd S )Nc                      s   ˆ 
 S rj   rM   rM   ©rµ   rM   rN   rS   Ã  rT   z!test_issue_8571.<locals>.<lambda>c                      s   ˆ  S rj   rM   rM   rè   rM   rN   rS   Ä  rT   c                      s   t ˆ ƒS rj   )ÚabsrM   rè   rM   rN   rS   Å  rT   c                      s   t ˆ ƒS rj   )ÚintrM   rè   rM   rN   rS   Ç  rT   rR   c                      s   ˆ ˆ S rj   rM   rM   ©Úorµ   rM   rN   rS   Ë  rT   c                      s   ˆ ˆ S rj   rM   rM   rë   rM   rN   rS   Ì  rT   c                      s   ˆ ˆ S rj   rM   rM   rë   rM   rN   rS   Í  rT   c                      s   ˆ ˆ S rj   rM   rM   rë   rM   rN   rS   Î  rT   c                      s   ˆ ˆ S rj   rM   rM   rë   rM   rN   rS   Ï  rT   c                      s   ˆ ˆ S rj   rM   rM   rë   rM   rN   rS   Ð  rT   )	r   r.   r/   rC   rY   ZZeror|   rk   Úrange)Ú_rM   rë   rN   Útest_issue_8571Á  s    rï   c                  C   s‚   t ddd} t ddd\}}| ||  | d   ||  | d   dk }|tjk	sVt‚| ¡ tjksht‚|dk ¡ tjks~t‚d S )NÚnT)Únegativezp q)ÚpositiverP   r   )r
   r   r/   rK   Úexpandr.   )rð   ÚpÚqÚrrM   rM   rN   Útest_expand_relationalÔ  s    ,r÷   c                   C   s$   t jjdkst‚t jjdks t‚d S )NT)r   r.   Zis_AtomrK   r/   rM   rM   rM   rN   Útest_issue_12717Ý  s    rø   c                     s¦   t ddd} tdd„ dtjd| fD ƒƒs,t‚t ddd}td	d„ d
tjd|fD ƒƒsXt‚tdd„ ttdk fD ƒƒsvt‚dtdƒtd g fD ]‰ tt‡ fdd„ƒ qŠd S )NÚnzT)Znonzeroc                 s   s   | ]}t |ƒtjkV  qd S rj   )r4   r   r.   rU   rM   rM   rN   r¾   ä  s     z"test_as_Boolean.<locals>.<genexpr>rP   rr   )rÊ   c                 s   s   | ]}t |ƒtjkV  qd S rj   )r4   r   r/   rU   rM   rM   rN   r¾   æ  s     Fr   c                 s   s   | ]}t |ƒ|kV  qd S rj   ©r4   rU   rM   rM   rN   r¾   ç  s     rR   c                      s   t ˆ ƒS rj   rú   rM   ©rW   rM   rN   rS   é  rT   z!test_as_Boolean.<locals>.<lambda>)	r
   rÐ   r   r.   rK   r/   rk   rC   rY   )rù   rr   rM   rû   rN   Útest_as_Booleanâ  s      rü   c                  C   sD  t tdk ttƒjtthkst‚ttfD ]F} | tdƒjtƒ ks@t‚| tdƒjthksVt‚| tdƒjthks&t‚q&t	j
jtƒ ks€t‚t	jjtƒ ks’t‚tjthks¢t‚ttttdƒttdƒƒjtthksÈt‚t t¡jtƒ ksÞt‚t td¡jtƒ ksöt‚t t¡jthkst‚t td¡jthks(t‚t t¡jtƒ ks@t‚d S )NrP   TF)r   rk   rl   rr   Zbinary_symbolsrK   r   r   Úsetr   r.   r/   r   r   ÚprimeÚltZis_truer°   )r   rM   rM   rN   Útest_binary_symbolsì  s    &r   c                   C   s,   t ttƒ t¡tdttdƒfdƒks(t‚d S )Nr   F)rP   T)r   rk   rl   Údiffr   r   rK   rM   rM   rM   rN   Útest_BooleanFunction_diffý  s    r  c               	   C   s6  t dƒ\} }}}}}}}||@ |@ | @ ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ |@ | @ B ||@ | @ | @ B ||@ |@ | @ | @ B ||@ |@ | @ | @ B ||@ |  @ | @ | @ B ||@ |  @ | @ | @ B | |@ |@ |@ | @ | @ B }||@ |@ | @ ||@ |@ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ |@ | @ | @ B ||@ |  @ | @ | @ B | |@ |@ |@ | @ | @ B }	||B |B ||B |B @ ||B |B @ ||B |B @ ||B |B @ ||B |B @ ||B | B | B @ | | B | B | B @ || B | B | B | B @ | |B | B | B | B | B @ || B | B | B | B | B @ ||B |B |  B | B | B | B @ }
t|dƒ|	ksPt‚t|dƒ|
ksdt‚ddddgddddgddddgddddgddddgddddgg}ddddgddddgddddgddddgg}tttttg|ƒtt @ tt@ t @ B ks t‚tttttg||ƒtt @ tt@ t @ B ks2t‚d S )NzA B C D E F G HZdnfZcnfr   rP   )r
   r(   rK   r   rs   rk   rl   rr   )rI   rJ   rL   rh   ÚErÒ   ÚGÚHrõ   ZsoldnfZsolcnfr‰   rŽ   rM   rM   rN   Útest_issue_14700  sŽ    8ÿÿÿþþþýýýüüû6ÿÿÿþþþýý.
ÿ
ÿÿþþý ý"ü(
 
ÿ,0ÿr  c                  C   s    t ttjƒ} t| ƒ| kst‚d S rj   )r   rk   r   ZIntegersr(   rK   )ZcondrM   rM   rN   Útest_issue_25115  s    r  c                  C   s"  t ddd\} }}}t ddd\}}t||k||k ƒ ¡ tjksDt‚t||k||kƒ ¡ tjksdt‚t||k| | kƒ ¡ tjksˆt‚t||k| | k ƒ ¡ tjks¬t‚t| | k||k ƒ ¡ tjksÐt‚t| | k| | kƒ ¡ tjksøt‚t| | k||kƒ ¡ tjkst‚t| | k| | k ƒ ¡ tjksHt‚t||k||k ƒ ¡ tjksjt‚t||k||kƒ ¡ tjksŒt‚t||k| | kƒ ¡ tjks²t‚t||k| | k ƒ ¡ tjksØt‚t| | k||k ƒ ¡ tjksþt‚t| | k||kƒ ¡ tjks$t‚t| | k| | kƒ ¡ tjksNt‚t| | k| | k ƒ ¡ tjksxt‚t||k ||kƒ ¡ tjksšt‚t||k||kƒ ¡ tjks¼t‚t| | k||kƒ ¡ tjksât‚t| | k ||kƒ ¡ tjkst‚t||k | | kƒ ¡ tjks.t‚t| | k| | kƒ ¡ tjksXt‚t||k| | kƒ ¡ tjks~t‚t| | k | | kƒ ¡ tjks¨t‚t||k ||kƒ ¡ tjksÊt‚t||k||kƒ ¡ tjksìt‚t| | k||kƒ ¡ tjkst‚t| | k ||kƒ ¡ tjks8t‚t||k | | kƒ ¡ tjks^t‚t||k| | kƒ ¡ tjks„t‚t| | k| | kƒ ¡ tjks®t‚t| | k | | kƒ ¡ tjksØt‚t||k| |k ||kƒ ¡ tjks t‚t||k||k ƒ ¡ tjks"t‚t||kt||ƒƒ ¡ ||kksHt‚t||kt||ƒƒ ¡ t||ƒkspt‚tt||ƒ|dkd|k |dk||k ƒ ¡ t||ƒ|dk@ |dk@ ||k@ ksÂt‚tt||ƒ||k| |k ||k ƒ ¡ ||k||kB | |k B kst‚tt||ƒ||k| |k ||k||k ƒ ¡ t||ƒ||k@ | |k @ ksNt‚tt||ƒ|dkd|k |dk||k ƒ ¡ t||ƒ|dk@ |dk@ ||k@ ks t‚t||ƒt||ƒ@ ||k@ ||k@  ¡ t||ƒt||ƒ@ ||k@ ksêt‚tt||ƒt|| ƒƒ ¡ tt|d	ƒt|d	ƒƒks"t‚t	||k||kƒ ¡ t
||ƒksHt‚t|dk|d
k t||ƒƒ ¡ tjksrt‚t||kt|d	ƒƒ ¡ t|d	kt|d	ƒƒks¤t‚tt
|dƒt
|dƒƒ ¡ tjksÊt‚tt|dƒt
d|ƒƒ ¡ t|dƒksôt‚tt|dƒt
d|ƒƒ ¡ t
|dƒkst‚d S )Núw x y zT©Úrealúd eFrP   rR   r‡   r   r   )r
   r   r   r   r.   rK   r   r/   r   r   r   )rs   rk   rl   rr   r   r_   rM   rM   rN   Útest_relational_simplification$  sx      $$$(&*""&&&&**""&&&*&*""&&&&**("&(( ÿ
"ÿ
(ÿ
( ÿ
&ÿ
8&*2&*r  c                  C   s   t ddd} t| dk | dkƒ ¡ tjks,t‚t| dk | dkƒ ¡ tjksLt‚t| dk | dkƒ ¡ tjkslt‚t| dk| dkƒ ¡ tjksŒt‚d S )Nrk   Tr	  rP   r   )r
   r   r   r   r.   rK   r   r/   ©rk   rM   rM   rN   Útest_issue_8373f  s
       r  c                  C   s4   t ddd} tt| dƒt| dƒƒ ¡ tjks0t‚d S )Nrk   Tr	  rP   rR   )r
   r   r   r   r   r/   rK   r  rM   rM   rN   Útest_issue_7950n  s    r  c            	      C   s>  dd„ } t ddd\}}}}t ddd\}}tt||ƒ||k||k ||k||k ƒtt||ƒ|dkd	|k |d
k||k ƒtt||ƒ|dkd	|k |d
k||k ƒt||kt||ƒƒttt||ƒ||k||k t||k||k ƒƒtt||ƒ|dkd	|k |dk||k ƒƒt||ƒt||ƒ@ ||k@ ||k@ f}|D ]}| || ¡ ƒ q$d S )Nc           	      S   s~   | j }t|ƒ}ttttt|d  |ƒƒ| |ƒƒƒ}|D ]@}tt||ƒƒ}|  |¡}| |¡}||ks8t	d 
| ||¡ƒ‚q8d S )NrP   zHOriginal: {}
and simplified: {}
do not evaluate to the same value for {})Zfree_symbolsrÎ   ræ   rý   rF   rí   Údictr²   r—   rK   Úformat)	ÚoriginalÚ
simplifiedÚsymbrð   Ú	valuelistÚvaluesÚsublistÚoriginalvalueÚsimplifiedvaluerM   rM   rN   Ú(test_simplification_numerically_functionu  s    &

  þz\test_relational_simplification_numerically.<locals>.test_simplification_numerically_functionr  Tr	  r  FrP   rR   r‡   r   )r
   r   r   r   r   )	r  rs   rk   rl   rr   r   r_   ZexpressionsÚ
expressionrM   rM   rN   Ú*test_relational_simplification_numericallys  s     $$$*$ÿ"ú	ÿr  c               	   C   s  ddl m}  ddlm}m}m} | dƒ}| dƒ}| dƒ}|||g}t|ƒ gt|ƒ gt|ƒ gg}t	t
tt	tddƒƒd dƒƒƒ}	d	d
„ |	D ƒ}	|D ]r\}
}|D ]d}|
|d jŽ }|d }|	D ]D}tt||ƒƒ}| |¡}| |¡}||ksºtd |d ||¡ƒ‚qºqœqd S )Nr   ©ÚWild)Ú_simplify_patterns_andÚ_simplify_patterns_orÚ_simplify_patterns_xorr[   r\   r]   rÔ   rƒ   c                 S   s*   g | ]"}t d d„ |D ƒƒs"t |ƒs|‘qS )c                 s   s   | ]}|d  V  qdS ©rR   NrM   ©rV   rs   rM   rM   rN   r¾   Ÿ  s     zQtest_relational_simplification_patterns_numerically.<locals>.<listcomp>.<genexpr>©Úany©rV   rÜ   rM   rM   rN   Ú
<listcomp>Ÿ  s       zGtest_relational_simplification_patterns_numerically.<locals>.<listcomp>rP   úGOriginal: {}
and simplified: {}
do not evaluate to the same value for{})Ú
sympy.corer  Úsympy.logic.boolalgr  r   r!  r   r   r   ræ   rý   rF   rí   rÚ   r  r²   ÚxreplacerK   r  )r  r  r   r!  r[   r\   r]   r  Úpatternlistsr  rÙ   ÚpatternlistÚpatternr  r  r  r  r  r  rM   rM   rN   Ú3test_relational_simplification_patterns_numerically’  s2    
þ 

  þr/  c                  C   sT   t dƒ} | dk| dk B | dk| dk @ B  ¡ | dk| dk B | dk| dk @ B ksPt‚d S )Nrð   rƒ   r   )r
   r   rK   )rð   rM   rM   rN   Útest_issue_16803­  s    "ÿr0  c                      sŽ   t ttti‰ tt t dkt t dk ƒ ˆ ¡s0t‚tt t dk t t dk ƒ ˆ ¡rTt‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nr   c                      s    t tt dk tt dk ƒ ˆ ¡S ©Nr   )r   rk   rl   r—   rM   ©rö   rM   rN   rS   ¸  rT   z"test_issue_17530.<locals>.<lambda>c                      s    t tt dktt dk ƒ ˆ ¡S r1  ©r   rk   rl   r—   rM   r2  rM   rN   rS   ¹  rT   c                      s    t tt dktt dk ƒ ˆ ¡S r1  r3  rM   r2  rM   rN   rS   º  rT   )	rk   r   rl   r   r—   rK   r   rC   rY   rM   rM   r2  rN   Útest_issue_17530´  s    $$r4  c                   C   sÜ   t ddgƒddgkst‚t ddddgƒddddgks8t‚t ddddgƒddddgksXt‚t ddddgƒddddgksxt‚t ddddgƒddddgks˜t‚t ddddgƒddddgks¸t‚t ddddgƒddddgksØt‚d S )NrP   r   )r8   rK   rM   rM   rM   rN   Útest_anf_coeffs½  s         r5  c                  C   s   t dƒ\} }t| gddgƒdks$t‚t| gddgƒdks<t‚t| gddgƒt| dddks^t‚t| |gddddgƒtdt| |ƒddksŒt‚d S )NrÂ   rP   Tr   Fr¦   )r
   r9   rK   r   r   rÃ   rM   rM   rN   Útest_ANFformÇ  s    "ÿr6  c                  C   sP   t dƒ\} }td| |gƒt| |ƒks(t‚tddg| |gƒtt|ƒ| ƒksLt‚d S )NrÂ   rƒ   rP   r   )r
   r:   r   rK   r   rÃ   rM   rM   rN   Útest_bool_mintermÐ  s    r7  c                  C   sT   t dƒ\} }td| |gƒtt| ƒ|ƒks,t‚tddg| |gƒtt|ƒ| ƒksPt‚d S )NrÂ   rR   r   rP   )r
   r;   r   r   rK   rÃ   rM   rM   rN   Útest_bool_maxtermÖ  s     r8  c                  C   sF   t dƒ\} }td| |gƒ|ks"t‚tddg| |gƒt| |ƒksBt‚d S )NrÂ   rP   )r
   r<   rK   r   rÃ   rM   rM   rN   Útest_bool_monomialÜ  s    r9  c                   C   s@   t dddgdddgƒdkst‚t dddgdddgƒdks<t‚d S )Nr   rP   rR   r   )r=   rK   rM   rM   rM   rN   Útest_check_pairâ  s    r:  c                  C   s\   t t@ tt @ B t t  @ B } tt @ tt @ B t  t @ B }t| dd}|| |fksXt‚d S r­   )rJ   rL   rI   r+   rK   )ro   Zres1ÚresultrM   rM   rN   Útest_issue_19114ç  s    r<  c                  C   s€   t ttttgddddddddd	d
ddgƒ} tt @ tt@ t@ B tt @ t @ B tt @ t @ B tt @ t @ B }| |ks|t‚d S )NrP   rR   rƒ   r¸   r‡   é   é   é	   r…   é   é   r†   )r   r[   r\   r]   r   rK   )r;  ÚexpectedrM   rM   rN   Útest_issue_20870ï  s    *$ÿÿrC  c                   C   sZ   t dddgtttgƒtttƒtttƒƒks.t‚t dddgtttgƒttttƒƒksVt‚d S ©Nr   rP   rƒ   )r>   rk   rl   rr   r   r   rK   rM   rM   rM   rN   Útest_convert_to_varsSOPö  s    .rE  c                   C   sV   t dddgtttgƒttttƒtƒks*t‚t dddgtttgƒtttƒtƒksRt‚d S rD  )r?   rk   rl   rr   r   r   rK   rM   rM   rM   rN   Útest_convert_to_varsPOSû  s    *rF  c                     sz   t dƒ\‰ ‰} }}ttˆ ˆƒƒdks(t‚tˆ ˆ| @ |@ |ˆ B A B ƒdksLt‚ttˆ dƒƒdksbt‚tt‡ ‡fdd„ƒ d S )Nza:erR   r?  Tr   c                      s   t ˆ ˆ ƒS rj   )rA   rM   ©r[   r\   rM   rN   rS     rT   z%test_gateinputcount.<locals>.<lambda>)r
   rA   r   rK   rC   rY   )r]   r   r_   rM   rG  rN   Útest_gateinputcount   s
    $rH  c                   C   sx  t tdk tdk  ƒrt‚t tdk tdk ƒs.t‚t tdk dtkƒtjksJt‚t tdk tdk ƒtdk ksht‚t tdktdk ƒr€t‚t tdktdkƒs–t‚t tdkdtkƒtjks²t‚t tdktdkƒtdkksÐt‚t tdktdk ƒrèt‚t tdktdkƒsþt‚t tdkdtk ƒtjkst‚t tdktdkƒtdkks<t‚t tdktdk ƒrVt‚t tdktdkƒsnt‚t tdkdtkƒtjksŒt‚t tdktdkƒtdkks¬t‚t ttdƒttdƒ ƒrÊt‚t ttdƒttdƒƒsæt‚t ttdƒtdtƒƒtjkst‚t ttdƒttdƒƒttdƒks.t‚t ttdƒttdƒ ƒrLt‚t ttdƒtdtƒƒtjksnt‚t ttdƒttdƒƒsŠt‚t ttdƒttdƒƒttdƒks°t‚t ttdktdkƒtdkƒtdkksÚt‚t ttdktdkƒtdktdk@ ƒtjks
t‚t t	 
t¡t	 
t¡ƒtjks,t‚t t	 
t¡t	 t¡ƒtjksNt‚t t	 
t¡t	 t¡ƒt	 
t¡kstt‚d S r1  )r   rk   rK   r   r.   rl   r   r   r   r   rò   rñ   r/   r
  rM   rM   rM   rN   Útest_refine  s:      "&"&*0""rI  c               	   C   sð   ddl m}  ddlm} | dƒ}| dƒ}| dƒ}|||g}t|ƒ gg}tttttddƒƒd dƒƒƒ}d	d
„ |D ƒ}|D ]r\}}	|	D ]d}
||
d j	Ž }|
d }|D ]D}t
t||ƒƒ}| |¡}| |¡}||ks¢td |
d ||¡ƒ‚q¢q„qxd S )Nr   r  )Ú_simplify_patterns_and3r[   r\   r]   rÔ   rƒ   c                 S   s*   g | ]"}t d d„ |D ƒƒs"t |ƒs|‘qS )c                 s   s   | ]}|d  V  qdS r"  rM   r#  rM   rM   rN   r¾   7  s     z[test_relational_threeterm_simplification_patterns_numerically.<locals>.<listcomp>.<genexpr>r$  r&  rM   rM   rN   r'  7  s       zQtest_relational_threeterm_simplification_patterns_numerically.<locals>.<listcomp>rP   r(  )r)  r  r*  rJ  r   ræ   rý   rF   rí   rÚ   r  r²   r+  rK   r  )r  rJ  r[   r\   r]   r  r,  r  rÙ   r-  r.  r  r  r  r  r  r  rM   rM   rN   Ú=test_relational_threeterm_simplification_patterns_numerically-  s,    
 

  þrK  c                  C   sJ   t tttƒtttƒƒ} t| t ƒs$t‚t| j	ƒtttƒtttƒhksFt‚d S rj   )
r   r   r[   r]   r   r\   rg   rK   rý   rÚ   r  rM   rM   rN   Útest_issue_25451E  s    rL  N)¶Zsympy.assumptions.askr   Zsympy.assumptions.refiner   Zsympy.core.numbersr   Zsympy.core.relationalr   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr	   r
   Zsympy.functionsr   Z(sympy.functions.elementary.trigonometricr   r   Zsympy.sets.setsr   r   Zsympy.sets.containsr   Zsympy.simplify.simplifyr   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/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   Zsympy.assumptions.cnfrB   Zsympy.testing.pytestrC   rD   rE   Ú	itertoolsrF   rG   rH   rI   rJ   rL   rh   r[   r\   r]   r   r_   rs   rk   rl   rr   rO   rd   re   ri   rp   rq   rt   ru   rw   rx   ry   rz   r}   r~   r   r‚   r“   r”   r•   r–   r˜   rš   rœ   r   rž   r¡   r¢   r£   r¤   r©   rª   r¬   r¶   r¹   rº   r»   rÁ   rÄ   rÅ   rÆ   rÇ   rÉ   rË   rÌ   rÓ   r×   rØ   rÝ   rÞ   rß   rà   rá   rã   rä   rç   rï   r÷   rø   rü   r   r  r  r  r  r  r  r  r/  r0  r4  r5  r6  r7  r8  r9  r:  r<  rC  rE  rF  rH  rI  rK  rL  rM   rM   rM   rN   Ú<module>   sÎ   Ä		u			. 
	
B
	
	%