K i ddlmZddlmZddlmZddlmZddlm Z ddl m Z m Z ddl mZddlmZmZdd lmZmZdd lmZmZmZmZmZdd lmZdd lmZmZm Z m!Z!dd l"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+ddl,m-Z-ddl.m/Z/ddl0m1Z1m2Z2m3Z3ddl4m5Z5ddl6m7Z7m8Z8m9Z9m:Z:ddl;mZ>ddl?m@Z@ddlAmBZBddlCmDZDddlEmFZFmGZGddlHmIZIddlJmKZKddlLmMZMddlNmOZOmPZPmQZQmRZRddlSmTZTddlUmVZVddlWmXZXddlYmZZZdd l[m\Z\dd!l]m^Z^dd"l_m`Z`dd#lambZbdd$lcmdZdmeZemfZfmgZgdd%lhmiZimjZjmkZkmlZldd&lmmnZndd'lompZpdd(lqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZydd)lzm{Z{m|Z|dd*l}m~Z~mZmZmZmZmZmZmZmZmZmZmZdd+lmZmZmZmZmZdd,lmZdd-lmZmZdd.lmZmZdd/lmZmZmZdd0lmZe:d1\ZZZZZe7d2Zd3Zd4Zd5Zd6Zd7Zd8Zd9Zd:Zd;Zd<Zd=Zd>Zd?Zd@ZdAZdBZdCZdDZdEZdFZdGZdHZdIZdJZdKZdLZdMZdNZdOZdPZdQZdRZdSZdTZdUZdVZdWZdXZdYZdZZd[Zd\Zd]Zd^Zd_Zd`ZdaZdbZdcZddZdeZdfZdgZdhZdiZdjZdkZdlZdmZdnZdoZdpZdqZdrZdsZdtZduZdvZdwZdxZdyZdzZd{Zd|Zd}Zd~ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZ dZ dZ dZ dZ dZdZdZdZy))MatAdd) Quaternion)Q) AccumBounds) Partition)Sum summation)Add)DictTuple)UnevaluatedExprExpr) DerivativeFunctionLambdaSubs WildFunction)Mul)Catalan EulerGamma GoldenRatioTribonacciConstant) EFloatIIntegerRationalnanoopizoo) _exp_is_pow)Pow)EqRelNe)S)DummySymbolWildsymbols) factorial factorial2 subfactorial)Abs)exp)sqrt)cossin) Heaviside)zeta)Integral) EquivalentfalsetrueXor)Matrix) MatrixSymbol)Identity) MatrixSlice) SparseMatrix)factor)Limit)O) Complement FiniteSetIntervalSymmetricDifference) Covariance Expectation ProbabilityVariance) RandomSymbol) import_module)TransferFunctionSeriesParallelFeedbackTransferFunctionMatrix MIMOSeries MIMOParallel MIMOFeedback)secondjoule) PolyrootofRootSumgroebnerringfieldZZQQZZ_IQQ_Ilexgrlex)PointCirclePolygonEllipseTriangle) NDimArray) ArraySymbol ArrayElement)raiseswarns_deprecated_sympy)sstrsstrrepr StrPrinter)Trz x,y,z,w,tdcGddt}t|tdk(sJGddt}t|tdk(sJy)NceZdZdZy)test_printmethod..RcDd|j|jdzS)Nzfoo(%s)r)_printargsselfprinters c/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/printing/tests/test_str.py _sympystrz%test_printmethod..R._sympystr<sw~~diil;; ;N__name__ __module__ __qualname__r|r}r{Rrt;s .R._sympystrAsr}Nr~rr}r{rztest_printmethod..R@s r}r)r/rmx)rs r{test_printmethodr:sJ" #u ,, , s8B?# $ -- -r}c tttzdk(sJttdzdk(sJtttdzzdk(sJttdddd k(sJttddddd k(sJtd tzd k(sJtd tztzttzztdzztdzzdk(sJtdtztdzdz ztdzdz zdk(sJtdtzdtdzzz dzdtzzdk(sJtttz dk(sJtdtz dk(sJttdz dk(sJtttz tz t z dk(sJttttdzztzt zz dk(sJttdtztztzz dk(sJtt tjtdddk(sJtttt tdtt tdddk(sJtttt t dt ddk(sJttttt t dt dt ddk(sJy)Nzx + yrx + 1zx**2 + xrFevaluatez0 + 1z 0 + 0 + 1?1.0*xzx**2 + x*y + x + y**2 + y + 5zx**3/3 + x**2/2 + x + 1z-7*x**2 + 2*x + 3*y + 2zx - yz2 - xzx - 2z-w + x - y - zz-w*y**2*z**2 + xz -x*y**2 + xz^x - x**3/6 + x**5/120 - x**7/5040 + x**9/362880 - x**11/39916800 + x**13/6227020800 + O(x**15)z(-w + x) + (-y + z)z -z + (-x - y)z-t + (-z + (-x - y))) rryr zwr3seriestrr}r{test_AddrLs q1u:  q1u:  q1a4x=J && & s1a%( )W 44 4 s1aU+ , ;; ; s1u:  q1uqy1Q3A%1, -1P PP P q1uq!tAv~1Q& '+D DD D qsQq!tV|a!A#% &*C CC C q1u:  q1u:  q1u:  q1uqy1} !1 11 1 q1QT6!8A:~ "4 44 4 q1Q3q57{ } ,, , s1v}}Q2& ',L LL L s3r1u-sA2qE/JV[\ ]av vv v s3rA2.UC D WW W s3sA2rE2QBG!V[\ ]aw ww wr}c,ttdk(sJy)Nr)rrrr}r{ test_Catalanrbs w<9 $$ $r}c,ttdk(sJy)Nr!)rr!rr}r{test_ComplexInfinityrf s8u  r}cttttdk(sJtttdztddk(sJtttdztz ttddk(sJy)NzDerivative(x, y)rFrzDerivative(x**2, x)zDerivative(x**2/y, x, y))rrrrrr}r{test_Derivativerjss z!Q $6 66 6 z!Q$E2 37L LL L z 1Q1u& '*D EE Er}ctddtzitddtzicxk(rdk(sJJttdzttzddvsJttdzttzddk(sJyNrz {1: x + 1}rrr){1: x**2, 2: x*y}z{2: x*y, 1: x**2}rrrrmrrr}r{ test_dictrqsv 1q5z?dAq1u:. >, >> >> > 1a4AaC !%O OO O AqDQqS! "&9 99 9r}c4ttddtzitddtzicxk(rdk(sJJtttdzttzddvsJtttdzttzddk(sJyr)rr rrmrrr}r{ test_Dictrws tQAJ D!QU$4 D DD DD D t11%& ',2 22 2 A!A#&' (,? ?? ?r}cbttdk(sJtttzdk(sJy)N_dz_d + x)rrqrrr}r{ test_Dummyr~s( q6T>> q1u: !! !r}c,ttdk(sJy)Nr)rrrr}r{test_EulerGammars z?l ** *r}cttdk(sJtd5tttdk(sJ dddy#1swYyxYw)NrTzE**x)rrr"r0rrr}r{test_ExprsE q6S== T %3q6{f$$$%%%s AActdd}ttddk(sJttddk(sJttdd k(sJtt|d k(sJttd |zd k(sJttt|d k(sJttt|dk(sJttt|dk(sJttt|dk(sJtt ddk(sJtt |dk(sJtt d |zdk(sJy)NnTintegerr!r1r5040z factorial(n)rzfactorial(2*n)zfactorial(factorial(n))zfactorial(factorial2(n))zfactorial2(factorial(n))zfactorial2(factorial2(n))r2zsubfactorial(n)zsubfactorial(2*n))r)rr,r-r.)rs r{test_factorialrsFsD!A y}  && & y|  ## # y|  && & y|  .. . y1~ "2 22 2 y1& '+D DD D yA' (,F FF F z)A,' (,F FF F z*Q-( )-H HH H |A 3 && & |A #4 44 4 |AaC !%8 88 8r}ctd}|t}td}t|dk(sJt|dk(sJt|dk(sJy)Nfrzf(x)w_)rrrr)rfxrs r{ test_FunctionrsP A 1BSA q6S== r7f   q6T>>r}c ttdddk(sJtttddddk(sJtttdddddk(sJtt tddtd d tdd d k(sJtt td dtddtddtdd dk(sJtt tddtddtddddk(sJtttddddddk(sJy)Nrz Point2D(0, 0)rzCircle(Point2D(0, 0), 3)rrzEllipse(Point2D(1, 2), 3, 4)rrz6Triangle(Point2D(1, 1), Point2D(7, 8), Point2D(0, -1))rrrzEPolygon(Point2D(5, 6), Point2D(-2, -3), Point2D(0, 0), Point2D(4, 7))Tsympy_integerszGTriangle(Point2D(S(0), S(0)), Point2D(S(1), S(0)), Point2D(S(0), S(1)))z(Ellipse(Point2D(S(1), S(2)), S(3), S(4)))rmrcrdrfrgrerr}r{ test_Geometryrs= a  // / uQ{A& '+E EE E a Q* +/M MM M q!eAqk5B<@ A@ AA A a U2r]E!QKq!M NO PP P q!eAqk5A;?PT UQ RR R a Q*4 @2 33 3r}c,ttdk(sJy)Nr)rrrr}r{test_GoldenRatiors { } ,, ,r}ctttttttjcxk(rdk(sJJtttddk(sJy)Nz Heaviside(x)rzHeaviside(x, 1))rr4rr'Halfrr}r{test_HeavisidersN y| Ia$8 9 K^ KK KK K yA #4 44 4r}c,ttdk(sJy)Nr)rrrr}r{test_TribonacciConstantrs ! "&: :: :r}c,ttdk(sJy)Nr)rrrr}r{test_ImaginaryUnitrs q6S==r}cbttdk(sJtttzdk(sJy)Nroo*I)rrrrr}r{ test_Infinityrs( r7d?? r!t9  r}cttddk(sJttddk(sJttddk(sJttddk(sJttd d k(sJy) Nr-1rrrz-3r025)rrrr}r{ test_Integerrss wr{ t ## # wqz?c !! ! wr{ t ## # wqz?c !! ! wr{ t ## #r}ctttttdk(sJtttttddfdk(sJy)NzIntegral(sin(x), y)rrzIntegral(sin(x), (y, 0, 1)))rr6r3rrrr}r{ test_IntegralrsF xA" #'< << < xAAq * +/L LL Lr}c *tjddtjf}tt |D]Z}t|dzt |D]=}dD]6}dD]/}t ||||||}tt ||k(r/J8?\y)Nrr)TF)r'NegativeInfinityInfinityrangelenrEr)rijlrivals r{ test_Intervalrs  Q1::.A 3q6]0q1uc!f% 0A" 0&0A#AaD!A$15DSY<4///0 0 00r}ctdd}ttd|dk(sJttdddk(sJy)NaTrealrzAccumBounds(0, a)rzAccumBounds(0, 1))r)rr)rs r{test_AccumBoundsrsDsA {1a !%8 88 8 {1a !%8 88 8r}c|ttttdzdk(sJttdddk(sJttdtdk(sJttttfttzdk(sJttttffttzdk(sJy) NrzLambda(_d, _d**2)rrz Lambda((), 1)z Lambda((), x)zLambda((x, y), x + y)zLambda(((x, y),), x + y))rrrqrrrr}r{ test_Lambdars vaA #6 66 6 vb!}  00 0 vb!}  00 0 vq!fac" #'> >> > v1vi1% &*D DD Dr}c0tttttz ttdk(sJttdtz tddk(sJtttttz ttddk(sJy)NzLimit(sin(x)/x, x, y, dir='+')rrzLimit(1/x, x, 0, dir='+')-)dirzLimit(sin(x)/x, x, y, dir='-'))rrAr3rrrr}r{ test_Limitrs{ uSVAXq!$ %)I II I uQqS!Q $? ?? ?  c!fQh1#& (+K LL Lr}cttgttgcxk(rdk(sJJttdzttzdzgttdzttzdzgcxk(rdk(sJJttdzttzggttdzttzggcxk(rdk(sJJy)Nz[x]rrz[x**2, x*y + 1]z[x**2, [x + y]]rrr}r{ test_listrs s8tQCy )E )) )) ) 1acAg 4AqsQw#8 Mz!test_Matrix_str..sr}zMatrix(0, 1, []))r;rrrrmMs r{test_Matrix_strrsB QAJ'(A q63 33 3 7; ;; ;u A q6T!W / // // /AxA q6T!W 3!3 33 33 3A q6T!W 2 2 22 22 2q!^$A q6T!W 2 2 22 22 2r}ctttz dk(sJtttz dk(sJtttz tz dk(sJttdztdzz dk(sJtdtzdz dk(sJtd tzdz d k(sJtd tzd k(sJtd tzdk(sJtt ddddk(sJtt ddddk(sJtt ddddk(sJtt dddddk(sJtt ddddk(sJtt dt j ddk(sJtt ddt j ddk(sJtt ddddtddk(sJtt ddddk(sJtt ddddk(sJtt dddddttddk(sJtt ddddtzdttddk(sJtt tddtd d!dd"k(sJtt d ttt ttddddd#k(sJtt ttdtz dddd$k(sJddl m }|d5tt ttdtdttdt tdtdd%k(sJ dddGd&d't}Gd(d)t}|}|}ttd|zd*k(sJt|tdzd*k(sJt|td+zd,k(sJt|tdzd-k(sJt|tdz|zd.k(sJt|tdz|zd.k(sJy#1swYxYw)/Nzx/yzy/xzx/(y*z)rrz(x + 1)/(y + 2)rz2*x/3rz-2*x/3z-1.0*xrrrFrz0*1z1*0z1*1z1*1*1z1*2z1*(1/2)z 1*1*(1/2)z 1*1*2*3*xrz1*(-1)z-1*1rz 4*3*2*1*0*y*xz4*3*2*(z + 1)*0*y*xrrz (2/3)*(5/7)z -2*x/(y*y)zx/(1/y)z (-1 - 1*1)/2ceZdZdZy)test_Mul..CustomClass1TNrrris_commutativerr}r{ CustomClass1r,r}rceZdZdZy)test_Mul..CustomClass2TNrrr}r{ CustomClass2r /rr}r z2*CustomClass1()z1.5z1.5*CustomClass1()z2*CustomClass2()z2*CustomClass1()*CustomClass2())rrrrrr'rrr#sympy.core.parametersrrr rr)rrr cc1cc2s r{test_Mulr s qs8u   qs8u   qs1u: "" " AA #4 44 4 qs1u:  r!tAv;( "" " tAv;( "" " s1u:  s1a%( )U 22 2 s1a%( )U 22 2 s1a%( )U 22 2 s1aU+ , 77 7 s1a%( )U 22 2 s1affu- .) ;; ; s1a%0 1[ @@ @ s1aAq51 2k AA A s1b5) *h 66 6 s2q5) *f 44 4 s1aAq!Q7 8O KK K s1aAaCAq59 :>S SS S s8Aq>8Aq>EB C} TT T s2q#c!Au5rEJ9>@ ADP QQ Q s1c!A#rE2UC D QQ Q/ %x3s71:wr{3Sc'RT+W^_`WaFb5cdeiwwwwxtt .C .C x{3 #5 55 5 s8A; #5 55 5 s5< $8 88 8 s8A; #5 55 5 s8A;s" #'H HH H s8A;s" #'H HH Hxxs $A&Q..Q7c,ttdk(sJy)Nr)rrrr}r{test_NaNr;rr}c.tt dk(sJy)Nz-oo)rrrr}r{test_NegativeInfinityr?s s8u  r}ctttdk(sJtttdzdk(sJttttzdk(sJttttdk(sJttttdfdk(sJtttttfdk(sJtttttdk(sJtttttdk(sJtttttfttfdk(sJy) NzO(x)rzO(x**2)z O(x*y, x, y)rz O(x, (x, oo))z O(x, x, y)zO(x, (x, oo), (y, oo)))rrBrrrrr}r{ test_OrderrBs qt9   qAw<9 $$ $ q1v;. (( ( qAw<6 !! ! qQF|  && & qQG}  00 0 qAqz?l ** * qAqz?l ** * qQGaW% &*B BB Br}c Dddlm}m}|df|ddf|dddf|dddd d d d f|d dddd ddffD]\}}t||k(rJ|gdf|gddf|gddf|gd df|gddf|gddf|gdd dffD]\}}t|d|k(rJ|gdf|gddf|gddf|gd df|gddf|gdd f|gdd d!f|gd"d d#ffD]\}}t||k(rJt 5|j }d|_t|gddk(sJ||_dddy#1swYyxYw)$Nr) PermutationCyclez()rz(2)rz(1 2)rrr z(1 2)(6 7)(10)rrz(1 2)(4)zPermutation([]))sizezPermutation([0])zPermutation([0, 1])zPermutation([], size=10))rrrzPermutation([1, 0, 2]))rrrrrrzPermutation([1, 0], size=6)zPermutation([1, 0], size=10)F) perm_cyclicz(0)z(1)z(9)z(2)(0 1)z(5)(0 1)z(9)(0 1))rrrrrrz(9)(2 3))sympy.combinatoricsrrrmrl print_cyclic)rrpsold_print_cyclics r{test_Permutation_Cycler NsS6    q   q!  q!Q1 b !  q!Q 1a    1Aw!||  R  Ra   Ra   Rb !" $ Y   " ' (% ' 'b 1& (/1 A5)Q...!/& R   Ra    Ra    Rb !   Y   ' (  'b 1  'b 1 1$Aw!||%* !4&33#(  K *+/GGGG#3  444s 3FFc,ttdk(sJy)Nr )rr rr}r{test_Pir"s r7d??r}cTttdtdk(sJttdtdk(sJttttdk(sJttdtzdztdk(sJttdtzdz tdk(sJttd td k(sJttt td k(sJttd tzdztd k(sJttd tzdz tdk(sJtttdz tdk(sJttdtztdzztdk(sJttddtzzdtzdk(sJtttdztzdk(sJttttzdzttzddk(sJtttdz dztdz ddk(sJtttdzdztztdk(sJtttdzdz tztdk(sJtttdzttzztdk(sJtttdzttzz tdk(sJttt tzt zttzzdz ttt dk(sJttt tdzztdzzt zdt zt dzzzdtzt zz dzttt d k(sJtttdzdztd!d"k(sJttdtdzzdtzzd#ztd$!d%k(sJy)&NrzPoly(0, x, domain='ZZ')rzPoly(1, x, domain='ZZ')zPoly(x, x, domain='ZZ')rzPoly(2*x + 1, x, domain='ZZ')zPoly(2*x - 1, x, domain='ZZ')rzPoly(-1, x, domain='ZZ')zPoly(-x, x, domain='ZZ')rzPoly(-2*x + 1, x, domain='ZZ')zPoly(-2*x - 1, x, domain='ZZ')zPoly(x - 1, x, domain='ZZ')rz Poly(x**5 + 2*x, x, domain='ZZ')rz"Poly((3**x)**2, 3**x, domain='ZZ')z)Poly(((x**2)**x), (x**2)**x, domain='ZZ')F)expandz$Poly((x + y)**3, x + y, domain='ZZ')z$Poly((x - 1)**2, x - 1, domain='ZZ')z%Poly(x**2 + y + 1, x, domain='ZZ[y]')z%Poly(x**2 + y - 1, x, domain='ZZ[y]')z"Poly(x**2 + I*x, x, domain='ZZ_I')z"Poly(x**2 - I*x, x, domain='ZZ_I')z,Poly(-x*y*z + x*y - 1, x, y, z, domain='ZZ')rzIPoly(-w*x**21*y**7*z - 2*x*z + (w + 1)*z**3 + 1, x, y, z, domain='ZZ[w]'))moduluszPoly(x**2 + 1, x, modulus=2)rz%Poly(2*x**2 + 3*x + 4, x, modulus=17))rrWrrrrrrr}r{ test_Polyr(s tAqz?7 77 7 tAqz?7 77 7 tAqz?7 77 7 tAaC!GQ $C CC C tAaC!GQ $C CC C tB{ 9 99 9 tQB{ 9 99 9 tBqD1Ha !%E EE E tBqD1Ha !%E EE E tAE1~ "? ?? ? tAaC!Q$J" #'I II I tA!Had# $(L LL L tQTAI #N NN N tQUQJQ6 ; << < tQUQJQ6 ; << <  QTAX\1 "I JJ J  QTAX\1 "I JJ J tAqD1Q3J" #'K KK K tAqD1Q3J" #'K KK K tQBqDFQqSL1$aA. B CC C tQBq"uHQTM!Oq1uadl2QqSU:Q>1aH IS TT T tAqD1Ha+ ,0N NN N tAadFQqSL1$a4 59` `` `r}cttdttddk(sJttdtt ddk(sJttdtdtddk(sJy) Nrrz+Polynomial ring in x over ZZ with lex orderx,yz0Polynomial ring in x, y over QQ with grlex orderx,y,zrz4Polynomial ring in x, y, z over ZZ[t] with lex order)rr[r]rar^rbrr}r{ test_PolyRingr,sl tCS!!$ %)V VV V tE2u%a( )-_ __ _ tGRWc*1- .2h hh hr}cttdttddk(sJttdtt ddk(sJttdtdtddk(sJy) Nrrz3Rational function field in x over ZZ with lex orderr*z8Rational function field in x, y over QQ with grlex orderr+rzj jj j AAq 1Q3q5(1, -1P PP P AAq 1Q3q5(1, -1P PP P !Rx!|  9 99 9r}ctdt\}}}td|\}}}}}tdt\}} tdd} t||z dk(sJt|dz dk(sJt|dzdk(sJt|d z d k(sJt||z d k(sJt||z|z d k(sJt|||zz d k(sJt||z||zz dk(sJt|dz |z dk(sJt|dz|z dk(sJt| dz |z dk(sJt|dz||zz dk(sJt| |dzz dk(sJt||z|dzz dk(sJt|dz|z|zdz|dz |zdz z dk(sJt|dz|z|zdz|dz |z||z|zz dz z dk(sJtd| z| z dk(sJtd| z| z| z | z dk(sJy)Nr0zx,y,z,trrrrr1rrzx/3zx/zzx*y/zzx/(z*t)z x*y/(z*t)z (x - 1)/yz (x + 1)/yz (-x - 1)/yz (x + 1)/(y*z)z -y/(x + 1)z y*z/(x + 1)z!((u + 1)*x*y + 1)/((v - 1)*z - 1)z)((u + 1)*x*y + 1)/((v - 1)*z - u*v*t - 1)z (1 + 1*I)/xz((1 + 1*I)*x + (0 + -1*I))/x)r\r]r`r) Fuvr4r5Fxyztrrrrr7r8rs r{test_FracElementr=sfUBHC19c*NE1QqsD!JFB Q A q1u:   q1u:  q1u:  qs8u   qs8u   qs1u:  q!A#w<9 $$ $ qsAaCy>[ (( ( Aqy>[ (( ( Aqy>[ (( ( Qz?l ** * A!}  00 0 r1q5z?l ** * qsAE{ } ,, , Q ! a1q5!)a-0 15X XX X Q ! a1q5!)ac!e"3a"78 9=h hh h !Rx=M )) ) 1b1 b !%C CC Cr}cttdddk(sJttdddk(sJttdddk(sJttdddk(sJttddd k(sJttdd d k(sJttddd k(sJttddd k(sJttdd dk(sJy)Nrrrrrrz-Irz2*Irz-2*Iz1 + Iz-1 - Iz-1 - 2*I)rr_rr}r{test_GaussianIntegerr?s tAqz?c !! ! tB{ t ## # tAqz?c !! ! tAr{ t ## # tAqz?e ## # tAr{ v %% % tAqz?g %% % tB|  (( ( tB|  ** *r}c $ttdddk(sJtttddddk(sJttdtdddk(sJtttddtddd k(sJy) Nrrrrrz2/3z2*I/3rz 1/2 - 2*I/3)rr`r^rr}r{test_GaussianRationalrAs tAqz?c !! ! tBq!Ha !U ** * tAr!Qx !W ,, , tBq!HbQi( )] :: :r}cttdzdk(sJttdzdk(sJttdzdk(sJtttzdzdk(sJtttzdzdk(sJtttzdzd k(sJtttzd tzzd k(sJtttd d zd k(sJtd ttd d zz dk(sJtt t tdk(sJttdzdk(sJtt t ddddk(sJy)Nrz1/xrzx**(-2)rr2z 1/(x + y)z (x + y)**(-2)z (x + y)**2rz(x + y)**(x + 1)rzx**(1/3)z x**(-1/3)zx**(1/4)rz x**(-1.0)Frz 2**(-1.0))rrrrr1r#r'rr}r{test_PowrCsG q"u:   q"u: "" " q!t9   A{ { ** * A{  .. . Az?l ** * AQ $6 66 6 q(1a. !Z // / qHQN"" #{ 22 2 tDG}  ++ + q$w<; && & s1Q4. /; >> >r}ctttdk(sJtttdzdk(sJtdttz dk(sJtdttdzz dk(sJttttz dk(sJttdzd k(sJtdtdzz d k(sJy) Nzsqrt(x)rz sqrt(x**2)rz 1/sqrt(x)z 1/sqrt(x**2)z y/sqrt(x)g?zx**0.5z x**(-0.5))rr1rrrr}r{ test_sqrtrE s tAw<9 $$ $ tAqDz?l ** * qay>[ (( ( qad|  .. . qay>[ (( ( q#v;( "" " qCx=K '' 'r}c tdd}tdd}tdd}tdd}td}td}td}t||zdk(sJt||zdk(sJt|d k(sJt||zd k(sJt||zd k(sJt||zd k(sJt||zd k(sJt||zdk(sJt||zdk(sJt||zdk(sJt||zdk(sJt||zdk(sJt||zdk(sJt||zdk(sJt||zdk(sJt||zdk(sJttddk(sJttddk(sJttddk(sJttddk(sJttddk(sJttdddk(sJttddd k(sJttd!dd"k(sJttd#dd$k(sJttd%dd&k(sJtttddd k(sJtttdd'd(k(sJtd)d*ztdd*zd+k(sJtd)d*zdztdd*zd+k7sJtd)d*zdz tdd*zd+k7sJtd)d*zdz tdd*zd,k7sJtttd-d'dzd.k(sJtdttd-d'dzz d/k(sJttdtdtzk(sJtdtdd0zd1k(sJt tddd23d4k(sJt d5}t |tddzd23d6k(sJt t|tddd23d7k(sJt t||td8dd23d9k(sJy):Nrrrrrrz1/12z1/2z1/8z3/4z7/12z-1/4z1/4z-1/6z-1/2rz1/64z1/2727z-25z1.25z5/4z-2.6e-2z-13/500z25/7z-123/569z0.1[23])rationalz61/495z5.1[666]z31/6z -5.1[666]z-31/6z0.[9]rz-0.[9]r$r{r123122Qz27/8z8/27ld( z2**(1/10000000000)TrzS(2)/3rz x**(S(2)/3)z Eq(x, S(2)/3)rzLimit(x, x, S(7)/2, dir='+')) rrr'r1rrmr)r$rA)n1n2n3n4n5n7n8rs r{ test_RationalrV*s !QB !QB !QB !RB !B !B "B r"u:   r"u:   r7e   r"u:   rBw<5  rBw<6 !! ! rBw<6 !! ! r"u:   rBw<6 !! ! rBw<6 !! ! r"u:   rBw<3   r2v;&  r2v;&  r2v;$   r2v;&  x 5 (( ( x E )) ) x " #y 00 0 qy>V ## # q}  ++ + qQ' (H 44 4 qa( )V 33 3 qq) *g 55 5 q1% &# -- - qA& '4 // / tHQN# $ -- - tHQO$ % .. . RHQO+ , 55 5 R! hq"o- .% 77 7 R! hq"o- .% 77 7 R! hq"o- .% 77 7 tHR$%q( )V 33 3 qhr2&'** +v 55 5 tBx=C!H $$ $ q(1f%% &*> >> > At 4 @@ @s A 8Aq>!$ 7= HH H 1hq!n%d ; NN N aHQN+D A& '' 'r}c"ttdddk(sJttdddk(sJttdddk(sJttjddk(sJttjd d k(sJttjd d k(sJttjd dk(sJttdztdzj dz j ddk(sJt tdddddk(sJt tdddddk(sJt tdddddk(sJt tddddk(sJy)Nz1.23r)dpsz 1.23456789 z1.234567890123456789z3.14rz3.14159265358979AzB3.1415926535897932384626433832795028841971693993751058209749445923rz0.0irrz-0.e+88100Fr) full_precminmaxz1.0e+2z100.0z0.1z0.099)r^r_z9.90000000000000e-2)rrr evalfroundrrmrr}r{ test_Floatrbcs uV' (F 22 2 u\u- ., >> >  $&1 36L MM M rxx 6 )) ) rxx $6 66 6 rxx &J KK K rxx|  %% % C2s7//!,,//2 3y @@ @ e 21 = II I e 21 = HH H e 21 = FF F gBA .2G GG Gr}cttttddk(sJttttztddk(sJttttddk(sJtt tdt tdzd k(sJtt tdt tdzd k(sJy) Nrrrz {1, 2, 3})rrrzfrozenset({1, 2, 3})rrrz{1, x, x**2, x**3, x**4}z#frozenset({1, x, x**2, x**3, x**4}))rmset frozensetrrr}r{test_setrvs ;' !! !   -- - 9    1# #3 33 3  ?k )) )  )$ %)? ?? ?  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