K i؉ddlmZddlmZmZddlmZddlmZddl m Z ddl m Z m Z ddlmZddlmZdd lmZmZmZdd lmZmZmZmZmZmZmZmZmZm 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/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;mZ>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKdd lLmMZMmNZNdd lOmPZPdd lQmRZRmSZSe d\ZTZUZVZWdZXdZYdZZdZ[dZ\dZ]dZ^dZ_dZ`dZadZbdZcdZddZedZfdZgdZhd Zid!Zjd"Zkd#Zld$Zmd%Znd&Zod'Zpd(Zqd)Zrd*Zsd+Ztd,Zud-Zvd.Zwd/Zxd0Zyd1Zzd2Z{d3Z|d4Z}d5Z~d6Zd7Zd8Zd9Zd:Zd;Zd<Zd=Zy>)?)dedent)isliceproduct)Basic)Integerordered)Dummysymbols) factorial)Matrix)RGS_enum RGS_unrank Permutation)5 _partition_set_partitionsbinary_partitions braceletscapturecartes common_prefix common_suffixconnected_components dict_mergefilter_symbolsflatten generate_bellgenerate_derangementsgenerate_involutionsgenerate_oriented_forestgrouphas_dupsibiniproductkbinsminlexmultisetmultiset_combinationsmultiset_partitionsmultiset_permutations necklacesnumbered_symbols partitions permutations postfixesprefixesreshape rotate_left rotate_rightrunssiftstrongly_connected_componentssubsetstaketopological_sort unflattenuniq variationsordered_partitions rotationsis_palindromiciterable NotIterablemultiset_derangementssigned_permutationssequence_partitionssequence_partitions_empty)factoring_visitormultiset_partitions_taocp)S)raiseswarns_deprecated_sympyzw,x,y,zc4ddlm}m}t5t |t t gt t gk(sJ dddt5tt t g|t t gk(sJ dddy#1swYDxYw#1swYyxYw)Nrdefault_sort_keyr key)sympy.utilities.iterablesrMr rJlistyxsortedrLs j/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/utilities/tests/test_iterables.pytest_deprecated_iterablesrV!s}C  !/GQFO$A.../  !>q!f"231v===>>//>>s+B'BB BcjtdsJtdsJtdsJtdsJtdrJtdrJtddsJtdd rJtdd d sJtdd d sJtd dsJtd d rJtd d d sJy)NrSxxxyxxyxyzxxxyzzyxxxyzyx)r?rUtest_is_palindromicrf)s "   #   $   %  d## #f%% % )Q '' 'i++ + )Q ++ + )Q ** * (A && &h** * (Au -- -rec|tdddgk(sJtttffttgk(sJddgdggtdk(sJtdgdk(sJtd gd k(sJtd gd k(sJttfd Gd dt}t|tt t g|tt t gk(sJt|tt t g|tt t gk(sJthdthdk(sJy)N)r^r^r^r`r^r_rrrlevels)rirkrlr_)rjr`r^r_rrctdS)Nr`rm)r)lssrUztest_flatten..Dswr"5rec eZdZy)test_flatten..MyOpN__name__ __module__ __qualname__rdrerUMyOprtF rerycls>r^r_ )rrSrI ValueErrorrrRzrQ)ryrqs @rU test_flattenr9s 9 !Q '' ' At9 !Q '' ' V vh 'B 2a B && & 2a $> >> > 2a $8 88 8 2a $8 88 8 :56 u  DAJ? #Q A 66 6 DAJ? -!Q :: : : $z"2 22 2rec ttdgk(sJttggk(sJttgdgdk(sJttddggdgdk(sJttddgddgddggd k(sJtttj d usJtttj tj d usJd ttj vsJd ttj tj vsJdttj tj tj vsJt tttj tj tj d }|D]<\}}}t|tsJt|tsJt|tr!+- .AHQZZQZZ@@@@Arectggk(sJtgdgk(sJtdgdggk(sJtdgddgk(sJtddgddggk(sJtddgddgk(sJtgdgdgk(sJtgdddgk(sJtgddgd gdggk(sJtgddgd k(sJtgd ddggd dgd d ggk(sJtgd dgdk(sJy)NF)multipler^r^r^rkrrr^r_r^r_)rr_r^r)r^r^r_r_r_r^roror_r_r_ro)rkrrror_)r!rdrerU test_groupres6 9?? e $ ** * !:1#   !u %& 11 1 !Q=aVH $$ $ !Q% (VH 44 4   { ** * U +x 77 7  aS1# .. . U +/G GG G ) *1vy1#1v.N NN N )E :?) )) )rec ttgdddgk(sJttgddgdk(sJttgddgdk(sJttgdddgk(sJttd }tt|dd dgk(sJtt|dd gd k(sJtt|dd gd k(sJtt|dd gdk(sJttt|d d dk(sJtt|dddd gk(sJtt|dddd gdk(sJttddgd gdk(sJttddgd gdk(sJttgddgdk(sJttgddd gdk(sJy)Nrrrdr^rr_)rkrrrorT repetitionrrhrr) rlrr^rr_rrorrkrr_r_rroro)rr)rrr_)rrrorrr^r_rr^ro)rr_r_rr_ro)rrororr^r^r_r^r^ror^r_r_r)r^roror)r_r_ro)r_roro)rororo#F)rrrr)rdrhrrrkr)rdrhrrk)rrkrrrr)rQr7rlenls rU test_subsetsrzs   1% &2$ .. .  1% &*< << <  1% &*B BB B  1% &9+ 55 5 U1XA 1. /B4 77 7 1. /3K KK K 1. /4< << < 1. / 4J J J J tGAqT23 4 :: : "1qU3 4 :: : "1qT2 38C CC C A40 10 11 1 A51 2  !! !  1% &  !! !  16 78 99 9rec ttd}tt|dddgk(sJtt|ddgdk(sJtt|ddgd k(sJtt|d dgd k(sJtt|dd dgk(sJtt|dd gdk(sJtt|dd gd k(sJttt|d d dk(sJttt|dd dk(sJtt|ddd dgk(sJtt|ddd d gdk(sJy)NrrFrrdr^rr_) rrrr^rrkrr_rrrrorror^rro)rrrr_r^rrror^)rror_r^rr_)r^rror^r_rr)r^ror)r^ror_r_rr^)r_rror_r^r)r_r^ro)r_ror)r_ror^)rorr^)rorr_)ror^r)ror^r_)ror_rror_r^T)rlrrrrrrkrrrrrrrrr@r)rQrr<rrs rUtest_variationsrs U1XA  1aE2 3t ;; ;  1aE2 37O OO O  1aE2 38X XX X  1aE2 38@ @@ @  1aD1 2rd :: :  1aD1 26N NN N  1aD1 27? ?? ? tJq!56 72 == = tJq!56 73 >> >  1Ra5!6 72 == =  1Ra5!5 6;  rec <ttddggdgdk(sJttdgk(sJttddgk(sJttddd gk(sJttttdd d gk(sJy) Nr^r_rrrda)r)repeat)rrrrh)rQrrrdrerU test_cartesrs 1vy) *8 99 9 >bT !! ! s  (( ( s1% &:, 66 6 tE!H~& 'D$< 77 7rect}t|td}t|dt tdk(sJy)Nzx0 x2 x3rozx1 x4 x5)r,rr r8rQ)sfiltereds rUtest_filter_symbolsrs:Aa!45H ! WZ%8 9 99 9rec tt}tt|tsJttddt dgt dk(sJy)Nr{Cr^C1)startexcludeC2)r,r rnextr )rs rUtest_numbered_symbolsrsNU#A d1gu %% %  A G H   rectttddddggddk(sJtttgdtgtgdk(sJtt j gd d dgik(sJtgd d d ddgddgfk(sJtgd dd dggdfk(sJttdy)Nrcc |dzSNr_rd_s rUrrztest_sift..s !a%rer^ro)rr_rrc,|jtSNhasrSrs rUrrztest_sift..s!%%(re)FTc,|jtSrrrs rUrrztest_sift..s1558reFrr^r_roc |dzSrrdrSs rUrrztest_sift..s AreTbinaryrr_c|dzdk(S)Nror^rdrs rUrrztest_sift..sA rerc$tgdddS)Nrc |dzS)Nrordrs rUrrz-test_sift....s QUreTr)r5rdrerUrrztest_sift..s \?48re) r5rQrrSrRrHOnerIr~rdrerU test_siftrs U1X 0A94M MM M A* +s1#/F FF F + , << <  od ; AA@    24 @ YE   :9:rect}t|dttdk(sJt|dttdk(sJtgddgdk(sJy)Nrczx0:5zx5:10r^r_rorrc)r,r8rQr )Xs rU test_takersZA 1:gfo. .. . 1:gg./ // /  # 66 6rectidtttidtttik(sJtdtttiidtttik(sJtdtidtttidtdtttik(sJtdtttidtidtdtttik(sJtttddtttidtdtttik(sJtdtttittddtdtttik(sJy)Nr^r_rk)rrSrRrrdrerUtest_dict_mergers b1aA, 'Aq!Q< 77 7 q!QlB 'Aq!Q< 77 7 q!fq!Ql +1aAq/A AA A q!QlQF +1aAq/A AA A !lQ1aL 1aAq!Q5G GG G q!QlaL 1aAq!Q5G GG Grecttggk(sJttdgdggk(sJttddgdgddggk(sJttgddgddggdgdgdgk(sJy)Nr^r_rrr^r_ror)rQr0rdrerU test_prefixesrs   ## # ! 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"sQFm 33 3  /* + q!fi? @@ @recgdgdtfgdk(sJtfdgdk(sJttfdy)N)r_rorc r}) )rr}rr)rcr})ror)ror)r}r_)r}r)r}r)rr)rorcrrr}r_rrc| Srrd)vs rUrrz'test_topological_sort.. s1"rerN)rrcr}rorrrr_c&tdgzfS)N)rr)r9EVsrUrrz'test_topological_sort.. s/A M0BCre)r9rIr~rs@@rUtest_topological_sortrsV"A $A QF #'A AA A QF 5" ## # :CDrectggfgk(sJtgdgfdgdgdggk(sJgd}gd}t||fgdgk(sJgd}gd}t||fdgddgdggk(sJgd}gd }t||fddgddggk(sJy) Nrr^r_rorkrrrrrrkrrrorr)rkrr)rro)r6rrs rU"test_strongly_connected_componentsr s ("b 2b 88 8 ()R 9qcA3_ LL LA0A (!Q 0YK ?? ?A(A (!Q 0aS1a&1#4F FF FA(A (!Q 0aVaV4D DD Drectggfgk(sJtgdgfdgdgdggk(sJgd}gd}t||fgdgk(sJgd}gd}t||fgdgk(sJgd}dd g}t||fddgdd ggk(sJy) Nrr^r_rorrrrkrr)rr s rUtest_connected_componentsr  s R )R // / B 0aS1#sO CC CA0A A 'I; 66 6A(A A 'L> 99 9A A A 'QFQF+; ;; ;recgd}t|dgdk(sJt|dgdk(sJg}t|d}|gk(sJ|jd|gk(sJt|d}|gk(sJ|jd|gk(sJy)Nrr^r_rorr_)r_rorrr^r^)rrr^r_ro)r2r3append)ABs rU test_rotater1sA q!  // / 1  00 0 AQA 7N7HHQK 7N7AqA 7N7HHQK 7N7rec Bgd}tt|ddgdgdgdgdgggk(sJttt|ddk(sJttt|dd k(sJttgd dgd dgggd ddgggd dgggdddggddggdggk(sJttgd dgddggddgddgggddggddgddgggk(sJttgddgddgggddggddgddgggddggddgddggddgddggdggdggk(sJttgddddgdggdgddgggk(sJttdgdgddgdggddgdggdgddggdgdgdgggk(sJttddddgdggddgdggdgddgggk(sJttdgdzddgddgggk(sJttdgdzgd gdgddggdgdgdgggk(sJgd}tt|ttt|k(sJtt|dgk(sJtt|dgdggk(sJtt|dgzdgk(sJtt|dgzdgdggk(sJttddgk(sJttddddgggk(sJttddgggk(sJttddgk(sJttdddggdgdgggk(sJttddddgggk(sJttdddggk(sJttddgdddgggk(sJgd}tdDcgc]}t d|Dc}|k(sJdgddgd dgdd!ggd"gd#gd$g}t ddgDcgc]}t |ddgc}|k(sJycc}wcc}w)%Nrrcrr^r_rorr)r^r^r^r_r_)r^r^r^r_r)r^r^r_r_rrrr)r^r_rr^rorr_rorrrrabbaaa)$)mpsyy)mpsyrR)mpsyy)rrRrR)mpyyr)mpysy)rrrR)mpsyy)r!r rR)r!rr)r!rrRrR)msyyp)msypy)r%r$rR)mspyy)r'r&rR)r'r$r)r'r$rRrR)myyps)r)r$r)mypsy)r+r*rR)r+r&r)r+r$r )r+r$rrR)mpsyy)r-r,rR)r-r*r)r-r*rRrR)r-r(r)r-r&r )r-r&rrR)r-r$r")r-r$r rR)r-r$rr)r-r$rrRrRsympyc3>K|]}dj|ywrXNjoin).0parts rU z+test_multiset_partitions..{s.D"''$-.r ra)rr_ro)rar_r_)r_r_r_ro)rQr)rrTtuplerGrF)rransr$ factoringss rUtest_multiset_partitionsr=AsrA #Aq) *aS1#sQC/H.I II I t'1-. /2 55 5 t'1-. /2 55 5 #OQ7 8 si!Q0> >$AQ!Q\+J/1v6 8 a!A ' 8;E FF F  7 8s 3P9Pcgd}ttddDcgc]}dj|c}|k(sJtd}tt|dDcgc]}dj|c}|k(sJt|dDcgc]}dj|c}gk(sJttdgddggddgddgggk(sJt ttddd k(sJt ttdd dk(sJttd ddgd gd ggk(sJt t d ycc}wcc}wcc}w)N)iiiiimiipiisimpimsippipsissmpprmssppspsssss mississippirorXr^r_rrabcrcc2ttddddS)Nror`rr_)rQr(rdrerUrrz,test_multiset_combinations..st$9aB-$KLre)rQr(r3r'rrIr~)r;iMs rUtest_multiset_combinationsrTsc A BB BA &q!, - /1BGGAJ /25 66 6 5a < =1BGGAJ = CC C %sQFmQ7 8qcAq6]O KK K t)#q12 3q 88 8 t)#q12 3q 88 8 %eQ/ 0cUSEC54I II I :LM ; / =sE E EcTgd}tdDcgc]}dj|c}|k(sJttdDcgc]}dj|c}|k(sJttgddddggk(sJttgddddgddgddgddgddgddggk(sJt ttd ddk(sJt ttd d dk(sJgidfD]}tt|ggk(rJttdggk(sJtt|dgk(sJtt|d gk(sJd t fd t dk(sJttdycc}wcc}w)N) abbyabybaybbbabybaybbbaybbyabyabbybayabbybabybbarYrXrr_rrr^rror`cxtddD]+}t|tgd|D] }t|-y)Nr^r)rrr^rr^)rprintr*)rRr$s rUtestz(test_multiset_permutations..tests;q! A !H*?A> a  recSrrd)rdsrUrrz,test_multiset_permutations..s 46rea 1 [0] [1] 2 [0, 0] [0, 1] [1, 0] [1, 1] 3 [0, 0, 0] [0, 0, 1] [0, 1, 0] [0, 1, 1] [1, 0, 0] [1, 0, 1] [1, 1, 0] 4 [0, 0, 0, 1] [0, 0, 1, 0] [0, 0, 1, 1] [0, 1, 0, 0] [0, 1, 0, 1] [0, 1, 1, 0] [1, 0, 0, 0] [1, 0, 0, 1] [1, 0, 1, 0] [1, 1, 0, 0] 5 [0, 0, 0, 1, 1] [0, 0, 1, 0, 1] [0, 0, 1, 1, 0] [0, 1, 0, 0, 1] [0, 1, 0, 1, 0] [0, 1, 1, 0, 0] [1, 0, 0, 0, 1] [1, 0, 0, 1, 0] [1, 0, 1, 0, 0] [1, 1, 0, 0, 0] 6 c0ttdddS)Nror`r)rQr*rdrerUrrz,test_multiset_permutations..st$9aB-$HIre) r*r3r'rQrrrrIr~)r;rRnulrds @rUtest_multiset_permutationsrhs +C 5f = >1BGGAJ ># EE E 5hv6F G H1BGGAJ HC OO O %i3 4!Q @@ @ %i3 4 AAAAAA98 88 8 t)#q12 3q 88 8 t)#q12 3q 88 8B|8)#./B47778 %c1- .2$ 66 6 %c1- ." 44 4 %c2. /2 55 5 > "f'.''' '' P :IJw ? Hs F  F%c  igdifgg}tdD]}ttd|||k(sJttdd|||k(sJttddd|||k(sJttddd|||k7sJttddd|||k7sJttddd|||k(rJttddddidddd ddddigk(sJttddddidddd ddd ddidddd ddddigk(sJttd d d d diddddddddddgcxk(rOtd d d Dcgc]3}td|Dst |j dkr|5c}k(sJJttt ddddidddgk(sJttd dddd ddiddddd igcxk(r0td Dcgc]}td|Ds|c}k(sJJtddD]=}d}t|D]\}}|t||k(sJ|dz }|t|k(r=Jycc}wcc}w)Nrr_)sizer^ra)krorkrrrr)rkr-rrrc3&K|] }|dk yw)rNrdr4rks rUr6z"test_partitions..s1DQ!q&1D)r-c3&K|] }|dk yw)roNrdrms rUr6z"test_partitions..s':1Q':rn) rrQr-allsumvaluesrHrrr)r;rRnr-qs rUtest_partitionsrus* 41b' C 1X;Jqq)*c!f444Jq!!,-Q777Jq!QQ/0CF:::Jq!T23s1v===Jq$23s1v===Jq!QQ/0CF::: ;  1" # AA! !lQF(4 44 4  1" # AA!"aL1a&aA, ! q!f(    1Q' ( AA!"aLaA,-@ !a1*D!c1D!1D.D  Oa  D! !! !! !  1Q41% & AA! +    1" # ! q!f!lQF(4 <a=8<C':':$:8< << << <1a[  $Q' DAqAq)) )) FA HQK  #D!8.stM!$45re) rrrrr rQrr: array_formnext_trotterjohnsonrIr~)rRrsr$rbis rUtest_bell_permr s05a <1CM!$% & <#AqkA+ ! A+ ++ +  a !&J JJ J 1a[( a ! !  (Bq||,, ,,%%'A ((  :56 =A+s $C*C/c gd}t|D]V\}}tt|dz}t||k(sJt|Dchc]}t |dzc}dk(rVJycc}w)N)r^r_rrLr^r_) enumeraterQrrr)lengthsrsNrRrys rUtest_involutionsrso#G'"81 %a!e, -1v{{q1!KNA%12a77782sA* c tttttddk(sJdj dtdDdk(sJttgdgdgd gd gd gd gd gdgdgdg k(sJttgdgdgdgk(sJttdtdgk(sJt }t|dgk(sJ|dDcgc]}dj |c}dgk(sJ|dDcgc]}dj |c}ddgk(sJ|dDcgc]}dj |c}dgk(sJ|dDcgc]}dj |c}gdk(sJ|dDcgc]}dj |c}gdk(sJ|d Dcgc]}dj |c}gd!k(sJttd"gd#gd#gd$ggd#gd$gd"gd#ggd#gd"gd$gd#gggk(sJycc}wcc}wcc}wcc}wcc}wcc}w)%Nrai rXc3>K|]}dj|ywr1r2r4rRs rUr6z$test_derangements..$sF!2771:Fr7abcdebadecbaecdbcaedbcdeabceadbdaecbdeacbdecabeacdbedacbedcacabedcadebcaebdcdaebcdbeacdeabcdebaceabdcebadcedabcedbadabecdaebcdaecbdcaebdcbeadceabdcebadeabcdeacbdebacdebcaeabcdeadbceadcbecabdecbadecdabecdbaedabcedacbedbacedbcar)r^rror_)r^r_ror)r^rorr_)r_rror^)r_rorr^)r_ror^r)rorr^r_)ror_rr^)ror_r^r)rr^r_r_)r_r_rr^)r_r_r^rbarabbrObcacabaabbbbaaaabbcccc)ccccaabbccccababccccabbaccccbaabccccbabaccccbbaaaabbccc) cccabbacccababcccaabbccacbbaccacbabccacabbcbccbaacbccabacbccaabbcccbaabcccababcccaabbooks) kbsooksboosbkooskboooksbooskbookbsoobksooskoboksobosbokobsokror_r^)rrQrrr3rB)DrRs rUtest_derangementsr"sm t)$uQx.9: ;s BB B 77F'R   !$ (1BGGAJ (TF 22 2 !% )1BGGAJ )eU^ ;; ; !& *1BGGAJ *vh 66 6 !* .1BGGAJ .3  !") -1BGGAJ -2  !"' +1BGGAJ +0# ## # %sQC!qc&:; < qcA3sQC!qc2A4 44 4 ) ) * . . ,s$;H+&H0H5=H:)H?Ic d}g}tddD]/}|j|||dd||dd||ddf1t|tgdgdgd gd gd gd gd gk(sJy)Nc @ttt|||Sr)rrQr+)rsrkfs rUcountztest_necklaces..countDs4 !Q*+,,rer^rr_rro)r^r_r_ro)r_rorora)rorrr)rrara)rcrr')ra \)r)rrr )rr-rRs rUtest_necklacesrCs- A 1a[<  5Aq>5Aq>5Aq>; << !9   recttdd}t|tddgddgddgddgddgddgddgddgddgddgg k(sJttdd}t|tgdgdgdgd gd gd gk(sJy) Nr_rrr^ro)rrrr)rrrr^)rrr^r^)rr^rr^)rr^r^r^)r^r^r^r^)rQrr )bcs rUtest_braceletsrTs i1o B ": A A A A A A A A A A !    i1o B ": !  recttdgdgdgdgdgdgdgdgd gd gd gd gd gdgdgdgdgdgdgdgdgk(sJtttddk(sJy)Nrcr)rr^r_roro)rr^r_ror_)rr^r_ror^)rr^r_ror)rr^r_r_r_)rr^r_r_r^)rr^r_r_r)rr^r_r^r_)rr^r_r^r^)rr^r_r^r)rr^r_rr^)rr^r_rr)rr^r^r^r^)rr^r^r^r)rr^r^rr^)rr^r^rr)rr^rr^r)rr^rrr)rrrrrri2)rQr rrdrerUtest_generate_oriented_forestrmsq (+ ,/?/?/?/?/ 1; ;; ; t,R01 2d :: :rec $ttd}t|tt|ddd|dddk(sJt|dt |ddt |ddgk(sJt t dt t dy)Nrr_r^rcc>tttddS)Nrror:rQrrdrerUrrz test_unflatten..{syeBi!<rec>tttddS)NrrjrrdrerUrrz test_unflatten..|syeBi"=re)rQrr:zipr:rIr~)rs rUtest_unflattenrws U2YA Q<4AccFAaddG 45 55 5 Q?uQrU|U1QR5\: :: : :<= :=>rectgdggk(sJtttdgdk(sJtttdttdgdk(sJtgdgdddgk(sJtgdgddgk(sJtgdggk(sJtttdgdk(sJtttdttdgdk(sJtttdttdgk(sJtgdgd ddgk(sJtgdgd dgk(sJy) Nr^rorrr)r^r_rcr_)r^rorc)rr_ro)rrro)rrQrrrdrerUtest_common_prefix_suffixrs5 aS !R '' ' eAh (I 55 5 eAheAh 8I EE E I .1a& 88 8 I .1# 55 5 aS !R '' ' eAh (I 55 5 eAheAh 8I EE E eAheAh 8B >> > I .1a& 88 8 I .1# 55 5rectgddk(sJtddk(sJtddk(sJtdddk(sJtddk(sJtd t d k(sJy) NrrrrF)directedabaaab)bbrrPrrN)rPrrr)r&rrdrerU test_minlexrsy )  )) ) )  )) ) )  )) ) )e , 99 9 %=E !! ! )s 37N NN Nrec&ttttftdttgttgfvsJttttftdttttftdk(sJttttfttgk(sJgdgdgddgdggdd fg\ttdd dgdggdgdgdgk(sJt t fd y) NF)defaultrrrr_r^ct|Sr)rrs rUrrztest_ordered..s CFrect|Sr)rqrs rUrrztest_ordered..s c!frerwarnc4ttddS)NFTr)rQr keysseqsrUrrztest_ordered..s T5t< =re)rQr rSrRhashrIr~rs@@rU test_orderedrs Ae4 51a&1a&9I II I Ae4 5 WaVT5 12 33 3 A QF ** *Y A3<"$457IC T5u= > qc9i3 44 4 :>?rec>tggk(sJtdgdggk(sJtddgdgdggk(sJtgddgddggk(sJtgdddgdggk(sJtgddgdgdggk(sJddlm}tgd|ddgdggk(sJy)Nr^rr_r)r_r^r^rlt)r4operatorrrs rU test_runsrs 8r>> 9!   A.sw1vt4rec tddgdgS)Nrr^rorrdrerUrrztest_reshape..sw1vs3re)rQrr1r:rIr~)rs rU test_reshapers  uQ{ C 3  |$ %% % 3  |$ %% % 3  |$ %% % 3QC ! QA!QA( )) ) 3s $ 1a& FQF+, -- - 3QC $ aVQ!aVQ( )) ) 5:!a0 1 36  Q/12 33 3 5:Q~ . #q& QCF+, -- - 4b ?QaS,$? @ Q Aq6#6 78 99 9 :45 :34rec ttdtdDddidddddidddddigk(sJttdtdDd dgk(sJttd d gk(sJttd td k(sJttdgddgdggdgddggk(sJttt d dgddfDdgddfddgdfdddgfgk(sJttdddddgdgdgdgdgg ddddgdgdggk(sJdgt t fddggt t fdy)Nc3 K|]}|ywrrdr4r$s rUr6ztest_uniq..s.1Q. rr^rr_rkc3&K|] }|dz yw)r_Nrd)r4rSs rUr6ztest_uniq..s-qQU-rnrcrrababcrOc3 K|]}|ywrrdrs rUr6ztest_uniq..s!9!!9rroc^tDcgc]}j|c}Scc}wrr;removerRrs rUrrztest_uniq..!tAw!?!!((1+!?!?*c^tDcgc]}j|c}Scc}wrrrs rUrrztest_uniq..rr)rQr;r-rr.rI RuntimeError)rs@rU test_uniqrs . 1 .. / QQ11v1|aV< == = -E!H-- .1a& 88 8 S ?se ## # W $u+ -- - qcAq6A3'( )qcAq6] :: : \!9qc1a[!99: ; #q!q1#qkAq1#;/ 00 0 aAq1#sQC!qc:; < Aq1#sQC  !! ! A <?@ A <?@rec tttddddk(sJtttddddk(sJtttddddk(sJtttddd d k(sJtttdddd k(sJd tfd t dk(sJdtfdt dk(sJy)N1123r_r^rr8r}rxrrrcrocldD]/}td|tgdd|D]}td|1y)NNrr^rr} ordered =rr_r )rcr% orderedvalr$s rUtest1ztest_kbins..test1s<. J +z *9a< eQ  recSrrd)rsrUrrztest_kbins.. EGrea# ordered = None [[0], [0, 1]] [[0, 0], [1]] ordered = 0 [[0, 0], [1]] [[0, 1], [0]] ordered = 1 [[0], [0, 1]] [[0], [1, 0]] [[1], [0, 0]] ordered = 10 [[0, 0], [1]] [[1], [0, 0]] [[0, 1], [0]] [[0], [0, 1]] ordered = 11 [[0], [0, 1]] [[0, 0], [1]] [[0], [1, 0]] [[0, 1], [0]] [[1], [0, 0]] [[1, 0], [0]] cdD]?}td|tttdd|D]}td|Ay)Nrrror_rr)rcr%rQrrs rUtest2ztest_kbins..test2sD. J +z *4a>1jA eQ  recSrrd)r srUrrztest_kbins..rrea[ ordered = None [[0], [1, 2]] [[0, 1], [2]] ordered = 0 [[0, 1], [2]] [[0, 2], [1]] [[0], [1, 2]] ordered = 1 [[0], [1, 2]] [[0], [2, 1]] [[1], [0, 2]] [[1], [2, 0]] [[2], [0, 1]] [[2], [1, 0]] ordered = 10 [[0, 1], [2]] [[2], [0, 1]] [[0, 2], [1]] [[1], [0, 2]] [[0], [1, 2]] [[1, 2], [0]] ordered = 11 [[0], [1, 2]] [[0, 1], [2]] [[0], [2, 1]] [[0, 2], [1]] [[1], [0, 2]] [[1, 0], [2]] [[1], [2, 0]] [[1, 2], [0]] [[2], [0, 1]] [[2, 0], [1]] [[2], [1, 0]] [[2, 1], [0]] )rrQr%rr)rr s@@rU test_kbinsr s tE&!Q/0 1R 77 7 tE&!R01 2b 88 8 tE&!R01 2b 88 8 tE&!Q/0 1Q 66 6 tE&!T23 4 99 9 # $0)    0 # $"0") " " " recttdusJtttddusJtgddusJtdgdggdusJtdgdggdusJy)NFrorTr^r_)r"rrQrrdrerU test_has_dupsr 'sz CE?e ## # DqN #u ,, , I $ && & aS1#J 4 '' ' aS1#J 5 (( (rectdgdddgddgdggk(sJtdgddddgddgdggk(sJdgdf}tdg|ddgddgdggk(sJy) Nr)r^rr^r_rrerrPdro)r)outputs rUtest__partitionr/s g / c S#J4' '' ' g 2 c S#J7' '' ' !F g ' 'S#Jc SE+J JJ Jrec hddlm}t}t|ddggk(sJt|ddggk(sJt ddD]g}dgtt d|zD]I}t d|||dDt d|||dDcxk(r|||k(rFJJiy)Nr)nTr^rc3 K|]}dywr^Nrdrs rUr6z*test_ordered_partitions..@*!A*rc3 K|]}dywrrdrs rUr6z*test_ordered_partitions..Arr)%sympy.functions.combinatorial.numbersrr=rQrrq)rrrRrys rUtest_ordered_partitionsr8s8A !Q=RD  !Q=RD  1a[$uQ{++ A*qAqz***qAqz**1a   recttdddgddggk(sJtttdgdgdgdgk(sJtttdd gdgdgdgk(sJy) Nrrrrorrrr`)dir)rQr>rrdrerUtest_rotationsrEsn  $ c3Z#s$< << <  %(# $Iy(I II I  %(+ ,Iy0Q QQ QrecPtdddgk(sJtddgdk(sJtdddk(sJtddddk(sJttdd gd k(sJttdd dgd k(sJttd ttdy)Nror^rT)str11011r_rp)rlrrrrX)000110r ctdS)Ng࿩r#rdrerUrrztest_ibin..Rs tCyrectddS)Nr_r^r&rdrerUrrztest_ibin..Ss tAqzre)r#rQrIr~rdrerU test_ibinr(Ks 7q!f   1: "" " t  $$ $ 1$ 5 (( ( Q #C CC C Q% &*B BB B :() :)*rectddusJtddusJtddusJGddt}t|dusJGddt}t|dusJGd d }t|dusJGd d }t|dusJGd d}t|dusJGdd|}t|dusJy)NrFr^c eZdZy)test_iterable..Test1NrurdrerUTest1r+[rzrer,ceZdZdZy)test_iterable..Test2TNrvrwrx _iterablerdrerUTest2r.` rer1Tc eZdZy)test_iterable..Test3NrurdrerUTest3r4erzrer5ceZdZdZy)test_iterable..Test4TNr/rdrerUTest4r7jr2rer8ceZdZdZy)test_iterable..Test5c3Kdyw)Nr^rd)selfs rU__iter__z%test_iterable..Test5.__iter__ps GsN)rvrwrxr=rdrerUTest5r:os rer>ceZdZdZy)test_iterable..Test6FNr/rdrerUTest6r@us rerA)r@rA)r,r1r5r8r>rAs rU test_iterablerBVs A;%   A;%   D>U "" "   EG  %% %  EG  $$ $   EG  %% % EG  $$ $ EG  $$ $ EG  %% %recpttdgddgggk(sJttddgdddgggk(sJttddgddgdgggk(sJttgddgdggk(sJttgdddgddggddgdgggk(sJttgdddgdgdgggk(sJttgdgk(sJttgdgk(sJttddgdgk(sJttddgdgk(sJy)Nr^r_rror)rQrDrdrerUtest_sequence_partitionsrD{so #QC+ ,1# 77 7 #QFA. /aVH: == = #QFA. /aS1#J< ?? ? #Iq1 2 {m CC C #Iq1 2 #1v!Q! & '' ' #Iq1 2aS1#6G GG G #B* +r 11 1 #B* +r 11 1 #QFA. /2 55 5 #QFA. /2 55 5rec ttgdgggk(sJttgdggggk(sJttgdgggggk(sJttdgddgggk(sJttdgdgdggdggggk(sJttdgdggdgggdgggdgggggk(sJttddgdddgggk(sJttddgdgddggdgdggddggggk(sJttddgdggddgggdgdgggddgggdggdggdgdgggddgggggk(sJttgddgdggk(sJttgddggdgdgddggddgdgggdgggk(sJttgddgggdggdgddgggddgdggggdggdggddggdgdgdggdgddgggddggdggddgdggggdgggg k(sJttgdgk(sJttdgdgk(sJttddgdgk(sJy)Nr^r_rorr)rQrErDrdrerUtest_sequence_partitions_emptyrFsJ )"a0 1rdV ;; ; )"a0 1r2hZ ?? ? )"a0 1r2rl^ CC C )1#q1 2ug == = )1#q1 2QCyA3)6L LL L )1#q1 2 b1#aS" R}5 66 6 )1a&!4 5Aq6( CC C )1a&!4 5 q!faSzQFB<0 11 1 )1a&!4 5 R!Q2sQC.21vr*: b1#!qc2!QR(8:   ))Q7 8i[M II I ))Q7 8 iA3A-1a&1#BH II I ))Q7 8 Rb1#1v. aVaSB 2. b1a&QC!qc? q!fbQFB, Q!bIr2. =   #B* +r 11 1 #QC+ , 22 2 #QFA. /2 55 5recgd}ttd|k(sJttd|k(sJttd|k(sJy)N) r)rr`r^)rr^r`)rr`r`r)r`rr^)r^rr`)r`rr`r)r`r^r)r^r`r)r`r`rrrr)rQrC)r;s rUtest_signed_permutationsrHsV 4C #I. /3 66 6 #I. /3 66 6 #I. /3 66 6reN)textwrapr itertoolsrrsympy.core.basicrsympy.core.numbersrsympy.core.sortingr sympy.core.symbolr r (sympy.functions.combinatorial.factorialsr sympy.matrices.denser sympy.combinatoricsrrrrPrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3r4r5r6r7r8r9r:r;r<r=r>r?r@rArBrCrDrEsympy.utilities.enumerativerFrGsympy.core.singletonrHsympy.testing.pytestrIrJwrSrRrrVrfrrrrrrrrrrrrrrr r rr=rTrhrurzrrrrrrrrrrrrrr r rrrr(rBrDrFrHrdrerUrVs%"&&.>'AA 4 4 4 4 4 4 4 4 4 4 4 4 4 43#? Y  1a> . 3,A,)*%9P08:  :7H@@ EE"<"  ?FD N >KB( V<7"84B"2;? 6O ?050A"K \)K R +"&J 6 6@7re